Problems on Calculating Speed | Speed Questions and Answers

Solve different types of problems on calculating speed and get acquainted with various models of questions asked in your exams. Be aware of the Formula to Calculate and Relationship between Speed Time and Distance. Practice Speed Problems on a regular basis so that you can be confident while attempting the exams. We even provided solutions for all the Questions provided and explained everything in detail for better understanding. Try to solve the Speed Questions on your own and then cross-check where you are lagging.

We know the Speed of the Object is nothing but the distance traveled by the object in unit time.

Formula to find out Speed is given by Speed = Distance/Time

Word Problems on Calculating Speed

1.  A man walks 25 km in 6 hours. Find the speed of the man?

Solution:
Distance traveled = 25 km
Time taken to travel = 6 hours
Speed of Man = Distance traveled/Time taken
= 25km/6hr
= 4.16 km/hr
Therefore, a man travels at a speed of 4.16 km/hr

2. A car covers a distance of 420 m in 1 minute whereas a train covers 70 km in 30 minutes. Find the ratio of their speeds?

Solution:
Speed of the Car = Distance Traveled/Time Taken
= 420m/60 sec
= 7 m/sec

Speed of the Train = Distance Traveled/Time Taken
= 70 km/1/2 hr
= 140 km/hr

To convert it into m/sec multiply with 5/18
= 140*5/18
= 38.8 m/sec
= 39 m/sec (Approx)
Ratio of Speeds = 7:39

3. A car moves from A to B at a speed of 70 km/hr and comes back from B to A at a speed of 40 km/hr. Find its average speed during the journey?

Solution:
Since the distance traveled is the same the Average Speed= (x+y)/2 where x, y are two different speeds
Substitute the Speeds in the given formula
Average Speed = (70+40)/2
= 110/2
= 55 km/hr
The Average Speed of the Car is 55 km/hr

4. A bus covers a certain distance in 45 minutes if it runs at a speed of 50 km/hr. What must be the speed of the bus in order to reduce the time of journey by 20 minutes?

Solution:
Speed = Distance/Time
50 = x/3/4
50 = 4x/3
4x = 150
x = 150/4
= 37.5 km

Now by applying the same formula we can find the speed

Now, time = 40 mins or 0.66 hr since the journey is reduced by 20 mins

S = Distance/Time
= 37.5/0.66
= 56.81 km/hr

5. Ram traveled 200 km in 3 hours by train and then traveled 140 km in 3 hours by car and 5 km in 1/2 hour by cycle. What is the average speed during the whole journey?

Solution:
Distance traveled by Train is 200 km in 3 hours
Distance Traveled by Car is 140 km in 3 hours
Distance Traveled by Cycle is 5 km in 1/2 hour
Average Speed = Total Distance/Total Time
= (200+140+5)/(3+3+1/2)
= 345/6 1/2
= 345/(13/2)”
= 345*2/13
= 53.07 km/hr

6. A train covers 150 km in 3 hours. Find its speed?

Solution:
Speed = Distance/Time
= 150 km/3 hr
= 50 km/hr
Therefore, Speed of the Train is 50 km/hr.

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Perimeter and Area of Square | How to Calculate the Perimeter and Area of a Square?

The Perimeter and Area of the Square are used to measure the length of the boundary and space occupied by the square. These are two important formulas used in Mensuration. Perimeter and Area of the Square formulas are used in the 2-D geometry.

Square is a regular quadrilateral where are the sides and angles are equal. The concepts of the Perimeter and Area Square formula, Derivation, Properties, are explained here. The solved examples with clear cut explanations are provided in this article. Students can understand how and where to use the formulas of Area and Perimeter of Square.

What is the Area and Perimeter of the Square?

Area of a square: The area of the square is defined as the region covered by the two-dimensional shape. The units of the area of the square are measured in square units i.e., sq. cm or sq. m.

Perimeter of a square: The perimeter of the square is a measure of the length of the boundaries of the square. The units of the perimeter are measured in cm or m.

Area of Square Formula

The area of the square is equal to the product of the side and side.
Area = Side ×  Side sq. units
A = s² sq. units

Perimeter of Square Formula

The perimeter of the square is the sum of the lengths.
P = s + s + s +s
P = 4s units
Where s is the side of the square.

Diagonal of Square Formula

The square has two diagonals with equal lengths. The diagonal of the square is greater than the sides of the square.

  • The relationship between d and s is d = a√2
  • The relationship between d and Area is d = √2A

What is Square?

A square is a regular polygon in which all four sides are equal. The measurement of the angles of the square is also equal.

Properties of Squares

The properties of the square are similar to the properties of the rectangle. Go through the properties of squares from the below section.

  • All sides of the squares are equal.
  • It has 4 sides and 4 vertices.
  • The interior angles of the square are equal to 90º
  • The diagonlas of square bisect at 90º
  • The diagonals of the square are divided into two isosceles triangles.
  • The opposite sides of the squares are parallel to each other.
  • Each half of the square is equal to two rectangles.

Solved Problems on Perimeter and Area of Square

Below we have provided the solved examples of perimeter and area of a square with a brief explanation. Scroll down this page to check out the formulas of Area and Perimeter of Square.

1. What is the Area and Perimeter of the square if one of its sides is 4 meters?

Solution:

Given the side of the square is 4 meters.
Area of the square = s × s
A = 4 m × 4 m
A = 16 sq. meters
The perimeter of the square = 4s
P = 4 × 4 m
P = 16 meters.
Therefore the area and perimeter of the square are 16 sq. meters and 16 meters.

2. Find the area of the square if the side is 10 cm?

Solution:

Given,
s = 10 cm
Area of the square = s × s
A = 10 cm × 10 cm
A = 100 sq. cm
Therefore the area of the square is 100 sq. cm

3. The perimeter of the square is 64 cm. Find the area of the square?

Solution:

Given,
The perimeter of the square is 64 cm
P = 4s
64 cm = 4s
s = 64/4 = 16 cm
Thus the side of the square is 16 cm.
Now the find the area of the square.
Area of the square = s × s
A = 16 cm × 16 cm
A = 256 sq. cm
Therefore the area of the square is 256 sq. cm.

4. If the area of the square is 81 cm², then what is the length of the square?

Solution:

Given,
A = 81 cm²
Area of the square = s × s
81 sq. cm = s²
s² = 81 sq. cm
s = √81 sq. cm
s = 9 cm
Thus the length of the square is 9 cm.

5. The length of the square is 25 cm. What is the area of the square?

Solution:

Given,
The length of the square is 25 cm
Area of the square = s × s
A = 25 × 25
A = 625 sq. cm
Therefore the area of the square is 625 sq. cm.

FAQs on Perimeter and Area of Square

1. How to find the perimeter of the square?

Add all the sides of the square to find the perimeter of the square.

2. What is the formula for the perimeter of a square?

The Perimeter of Square formula is sum of the lengths i.e, side + side + side + side = 4s

3. What is the formula for the area of the square?

The area of the square formula is the product of side and side. A = s × s.

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Examples on Calculating Profit or Loss | Profit and Loss Questions and Answers

Looking for help on finding Profit and Loss Concepts? Then, you have come the right way. Here let us observe some fully solved example problems on calculating profit or loss. You can find step by step solutions to all the Profit and Loss Questions available here. Try Practicing from the Profit and Loss Problems and get acquainted with the concepts better. Learn various methods for Calculating Profit and Loss and solve related problems easily. Assess your preparation standards on the concept and concentrate on the areas you are lagging in accordingly.

Question 1:
If a manufacturer allows 40% commission on the retail price of his product, he earns a profit of 9%. What would be his profit percent if the commission is reduced by 25 percent?

Solution:

We need to find out the profit % when the given commission is reduced by 25 percent.
Given data:
According to the question consider
Cost price (C.P.) of the product = $ 100
Then, a commission of the product = $ 40
Therefore selling price (S.P.) = $ (cost price (C.P.) – commission)
= $ (100 – 40)
= $ 60
Given that profit = 9%
Therefore Cost price (C.P.) = \(\frac { 100 }{ 100+gain%} \)* S.P
So,
C.P. = $ \(\frac { 100 }{ 100+9 } \)* 60
= $ \(\frac { 6000 }{109 } \)
Now new commission = $ 15
Therefore new selling price (S.P.) = $ 100 – 15
= $ 75
Gain = S.P. – C.P.
= $ (75 – \(\frac { 6000 }{109 } \))
= $ \(\frac { 2175 }{109 } \)
Gain% = (\(\frac { Profit }{C.P. } \)*100)%

=(\(\frac { 2175 }{109 } \)*\(\frac { 109 }{6000 } \)*100)%

= 36.25 %
Hence, gain % is 36.25.
Question 2:
After getting two successive discounts, a pant with the least price of $ 200 is available at $ 125. If the second discount is 14%, find the first discount.

Solution:
Let the first discount be ‘P%’
Then, 86% of (100 – P) % of 200 = 125

\(\frac { 86 }{ 100 } \)*\(\frac { (100 – P) }{ 100 } \)*200 = 125

100-P = \(\frac {(125*100*100) }{ 200*86 } \)
100 – P = 72.67
P = 100 – 72.67
P = 27.32%
Therefore, first discount price of pant is 27.32%.
Question 3:
A women sells an article at a profit of 20%. If he had bought it at 15% less and sold it for $ 11.50 less, he would have gained 25%. Find the cost price of the article.

Solution:
Given data:
Consider cost price (C.P.) of article be ‘X’
First selling price of article ‘X’ = 120% of ‘X’

= \(\frac { 120 }{ 100 } \)*X
= \(\frac { 6 }{ 5 } \)*X
Cost price of article for ‘X’ at 75% = 75% of ‘X’
=\(\frac { 75 }{ 100 } \)*X

=\(\frac { 3 }{ 4 } \)*X
Second selling price of article ‘X’ = 125% of 3/4 * X
= \(\frac { 125 }{ 100 } \)*\(\frac { 3x }{ 4 } \)

= \(\frac { 15x }{ 16 } \)

As given the article is sold at $ 11.50 less
Therefore, selling prices are equalized to a reduced price

\(\frac { 6x }{5 } \) –\(\frac { 15x }{ 16 } \) = 11.50
\(\frac { 21x }{80 } \) = 11.50
X = $ 43.8
Almost equal to $ 44
Hence, the cost price of an article is given as $ 44.
Question 4:
A dealer sold three – fourth of his articles at a gain of 25% and the remaining at cost price. Find the profit earned by him in the whole transaction.

Solution:
A dealer sold his ¾ th quantity with a gain of 25% and the remaining ¼ that its cost price.
Given data:
Consider cost price (C.P.) of whole articles be ‘X’
Cost price (C.P.) of \(\frac { 3}{ 4} \)th quantity = $ \(\frac { 3x}{ 4} \)
Cost price (C.P.) of \(\frac { 1}{ 4} \)th quantity = $ \(\frac { x}{ 4} \)
Total selling price (S.P.) = $ ((125% of \(\frac { 3x}{ 4} \)) + \(\frac { x}{ 4} \))
= $ (\(\frac { 15x}{ 16} \) + \(\frac { x}{ 4} \))
= $ (\(\frac { 19x}{ 16} \))
Profit / Gain = S.P. – C.P.
= $ (\(\frac { 19x}{ 16} \) – x)
= $ \(\frac { 3x}{ 16} \).
Gain % = (\(\frac { gain}{ C.P. } \)*100)%

= (\(\frac {3x}{ 16 } \)*\(\frac {1}{ x } \)*100)%

= 18.75%.
Hence, the gain % of the article is 18.75%.
Question 5:
A man sold two flats for $ 775,000 each. On one he gains 18% while on the other he losses 18%. How much does he gain or lose in the whole transaction?

Solution:
In this problem he gets an equal amount of profit and loss such cases there is always a loss. Therefore the selling price (S.P.) is immaterial.
Loss % = (\(\frac {common loss and gain %}{ 10 } \))2

= (\(\frac {18 }{ 10 } \))2

= (\(\frac {324 }{ 100 } \))

= 3.24%
The total loss incurred by the person is 3.24%.
Question 6:
Pure petrol costs $ 100 per lit. After adulterating it with kerosene costing $ 50 per lit, a shopkeeper sells the mixture at the rate of $ 96 per lit, thereby making a profit of 20%. In what ratio does he mix the two?

Solution:
Here, we have two different cost prices for different mixtures and one selling price (S.P.).
Given data:
Cost price (C.P.) of petrol = $ 100 per lit
Cost price (C.P.) of kerosene = $ 50 per lit
Selling price (S.P.) of mixture = $ 96 per lit
As we have two cost prices,
Mean cost price = $(\(\frac {100 }{ 120 } \))* 96)

= $ 80 per lit.
Since they asked us to find a ratio it is easy to find out by the allegation rule
Cost price (C.P.) of a unit Cost price (C.P.) of a unit quantity of $ X item quantity of $ Y item
Mean cost
$ M
(M – Y) (X – M)
Similarly using this concept here,
Cost price (C.P.) of a unit Cost price (C.P.) of a unit quantity of $ 100 item quantity of $ 50 item
Mean cost
$ 80
(80 – 50) (100 – 80)
Therefore, required ratio = 30 : 20
= 3 : 2.

Question 7:
Find cost price (C.P.), when
1. Selling price (S.P.) = $ 50, Gain = 18%
2. Selling price (S.P.) = $ 51, Loss = 14%

Solution:
Here, we need to find cost price (C.P.) using below formulae
1. Given data
Selling price (S.P.) = $ 50 & Gain = 18%
C.P. = \(\frac { 100 + Gain%) }{ 100 } \)*S.P.

=$ \(\frac { 100 + 18 }{ 100 } \)*50= $ 59.
2. Given data
Selling price (S.P.) = $ 51, Loss = 14%

C.P. = \(\frac { 100 – Loss% }{ 100 } \)*S.P.

= $ \(\frac { 100 – 14 }{ 100 } \)*51

= $ 43.86.

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Envision Math Common Core Grade 8 Answers | Envision Math Common Core 8th Grade Textbook Answer Key

Envision Math Common Core Grade 8 Answers | Envision Math Common Core 8th Grade Textbook Answer Key

Practice with the help of enVision Math Answer Key regularly and improve your accuracy in solving questions.

Envision Math Common Core Grade 8 Answers | Envision Math Common Core 8th Grade Textbook Answer Key

Envision Math Common Core Grade 8 Volume 1 Answer Key | Envision Math Common Core 8th Grade Volume 1 Answers

Envision Math Common Core 8th Grade Volume 2 Answer Key | Envision Math Common Core Grade 8 Volume 2 Answers

Color by Number | How to Color by Number? | Number by Coloring Examples

Color by Number

On this page, you will learn how to color based on numbers. So many children and students are interested in painting the image, coloring the picture and they are not interested in studying and learning mathematics. Teachers and parents can teach the numbers in the form of image coloring. In the initial stages, parents teach the numbers with respect to color and images and kids can remember them quite easily. Then children can learn the numbers easily and write on their own without taking anyone’s help.

In this article, you will learn color by number, how to color with respect to a given number, and some practice questions on color by number for kids. Parents and teachers can practice and download this with free of cost.

Colors by Number | How to Color based on Number using Pencils?

Colors by Number | How to Color based on Number using Pencils?

Nowadays mathematics is very important in our standard living, so better to learn the numbers from 1 to 100 at preschooler or homeschooling age. Learning numbers from 1 to 100 at the nursery stage is essential and kids can easily identify the numbers without taking anyone’s help. kKds and students can count the group of objects or things fastly. The figure below given is example of color by number,

The above figure is the butterfly, kids can fill the butterfly in given colors. In that given butterfly figure numbers are represented in numeric form. The given numbers are 1, 2, 3, 4, 5, and their respective colors are also given i.e. 1 for blue, 2 for orange, three for yellow, four for green, and five for red.

In the starting stages, kids and students cannot understand the concept of coloring by number early. So the parents and teachers can guide the kids on how to color by number. In Some Images, numbers with colors are given and in some images, colors are not given and we can choose the suitable color and fill the given images or pictures.

The below given figure consists of no colors only a picture is given. Kids and students take your favorite color or suitable image color and fill the images or pictures with colors.

The above given figure consists of cow, flowers, sky, clouds, and ground. Figure consists of only numbers, no colors are given or mentioned. So parents and teachers suggest the suitable color to kids, the kids fill the image with that color.

Practice Questions of Color by Number

Practice Questions of Color by Number

Question 1:

The below given figure is parrot, in that figure only numbers will be given no colors will be given, parents suggest the kids take or choose the suitable color and fill the given picture.

Question 2:

The Picture given as below, the picture is bird in that bird some numbers will be present, the below numbers with respect colors given, colored the image according to given number colors using color pencils.

Question 3:

The below-given are two images are color by number, in that one image which consists of no colors with respect to numbers, you can fill with suitable color and another picture consists of numbers with respect to colors, you must and should fill the colors as per given instruction.

No longer ditch the math workbooks and printables, take the help of our Preschool Math Activities and teach your kid counting, math facts, number sense in an interactive way.

Coloring Sheets

Line of Symmetry – Definition, Facts, Types and Examples

Line Symmetry

Symmetry can be split into two mirror-image halves. Suppose you can fold any picture, in it half you see both sides match, it is called Symmetrical. The word “symmetry” comes from a Greek word that implies measuring together. The two objects are claimed to be symmetrical if they have an identical size and shape with one object having a different orientation from the first. You are already acquainted with the term symmetry which is a balanced and proportionate similarity found in two halves of an object, one – half is the mirror image of the other half.

Line of Symmetry – Introduction

Line of symmetry means, it is the line that passes through the center of the object or any shape and it is considered as the imaginary or axis line of the object. Another name of line symmetry is “Reflection symmetry”, one half is the reflection of the other half. Reflection symmetry sometimes called line symmetry or Mirror symmetry.  The line of symmetry can be in any direction.

For example, if we cut an equilateral triangle into two equal halves, then the two triangles are formed after the intersection is the right-angled triangles. Take one more example, if we cut an orange into two equal halves, then one of the pieces is said to be in symmetry with another. Rectangle, circle, square are also considered examples of line symmetry.

Line of Symmetry

Line of Symmetry – Definition

Line of symmetry is defined as, a line that cuts a shape exactly in half, if you fold the shape or figure along the line, both halves would match exactly that is symmetrical halves. It is also termed as Axis of symmetry.  The line symmetry also called a reflection symmetry or mirror symmetry because it presents two reflections of an image that can coincide.

A line of symmetry may be one or more lines of symmetry. Symmetry has many types such as

  1. Infinite lines of symmetry
  2. One line of symmetry
  3. Two lines of symmetry
  4. Multiple lines of symmetry (more than two lines is called multiple lines)
  5. No line of symmetry means the figure is asymmetrical.

There are many shapes that are irregular and cannot be divided into equal parts. Such shapes are termed asymmetrical shapes. Hence, in such cases, line symmetry is not applicable. Line of symmetry are two types:

  1. Vertical line of symmetry
  2. Horizontal line of symmetry

Also, Read:

Types of Line of Symmetry

Basically, the line of symmetry is of two types. The line or axes may be any combination of Vertical, Horizontal, and Diagonal. Two types of lines of symmetry are

  • Vertical line of symmetry
  • Horizontal line of symmetry

Vertical Line of Symmetry

A vertical line of symmetry refers to one which runs down an image or figure and divides into two identical halves. The mirror image of the other half of the shape can be seen in a vertical or straight standing position. A, H, M, O, U, V, W, T, Y are some of the alphabets that can be divided vertically in symmetry. The trapezoid has only the vertical line of symmetry.

Vertical Line of Symmetry

Example of Vertical Line of Symmetry

Horizontal Line of Symmetry

The Horizontal line of symmetry is a line or axis of a shape which runs across the image, it divides into two identical halves is known as the Horizontal Line of Symmetry. B, C, H, E, are some of the alphabets that can be divided horizontally in symmetry.

Horizontal Line of Symmetry

Horizontal Line of Symmetry ExampleSome other types of lines of symmetries are there. Those are three lines of symmetry, four lines of symmetry, five lines of symmetry, six lines of symmetry, and infinite lines of symmetry.

Three Lines of Symmetry

An Equilateral Triangle has about three lines of symmetry. It is symmetrical along its three medians.

Three Lines of Symmetry
Some other patterns also have three lines of symmetry.

Four Lines of Symmetry

A square has four lines of symmetry. It can be folded in half over either diagonal, the horizontal segment which cuts the square in half, and the vertical segment which cuts the square in half. so, the square has four lines of symmetry.

A square is symmetrical along four lines of symmetry, two along the diagonals and two along with the midpoints of the opposite sides. some other patterns also have four lines of symmetry.

Four Line of Symmetry Five Lines of Symmetry

A regular pentagon has around five lines of symmetry. The lines joining a vertex to the mid-point of the opposite side divide the figure into ten symmetrical halves. Some other patterns also have five lines of symmetry.Five Lines of Symmetry

Six Lines of Symmetry

A regular polygon with N sides has N lines of symmetry. Hexagon is said to have six lines of symmetry, 3 joining the opposite vertices and 3 joining the midpoints of the opposite sides.

Six Lines of Symmetry

Infinite Lines of Symmetry

A circle has its diameter as the line of symmetry, and a circle can have an infinite number of diameters. It is symmetrical along all its diameters.

Examples of Lines of Symmetry

Line of Symmetry has different figures and we have outlined few examples

  1. A Triangle is said to have 3, 1 number lines of symmetry
  2. A quadrilateral has 4 or 2 number lines of symmetry
  3. An Equilateral Triangle has 3- lines of symmetry
  4. A Regular Pentagon has 5lines of symmetry
  5. A Regular Heptagon has 7 lines of symmetry
  6. A circle has an infinite number of lines of symmetry

Real-Life Examples of Lines of Symmetry

Real-Life Examples of Lines of Symmetry

  • Reflection of trees in clear water.
  • Reflection of mountains in a lake.
  • Most butterflies’ wings are identical on the left and right sides.
  • Some human faces are the same on the left and right.
  • People can also have a symmetrical mustache.

FAQ’s on Line of Symmetry

1. How many lines of symmetry does a circle have?

A circle has infinite lines of symmetry.

2. What is the figure of reflection symmetry on a vertical mirror?

A rectangle is the figure of reflection symmetry on a vertical mirror.

3. Define Line of Symmetry?

The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry. It is also termed the axis of symmetry. The other names of Line of Symmetry are Reflection Symmetry or Mirror Symmetry.

4. What are the types of Lines of Symmetry?

Lines of Symmetry are of two types, the first one is the Vertical line of symmetry and the second one is the Horizontal line of symmetry.

5. Define Vertical Line of Symmetry?

The axis of the shape or object or figure which divides the shape into two identical halves Vertically is called a Vertical line of symmetry.

6. Define Horizontal Line of Symmetry?

The axis of the shape or figure or object that divides the shape into two identical halves Horizontally is called a horizontal line of symmetry.

Pre School & Kindergarten Math Curriculum, Worksheets, Activities, Problems, Fun Games

Kindergarten Math

The best way to make young kids love math is to make it exciting for them. Preschool Kindergarten Math Topics designed feature images and quirky Characters. You will have the topics from addition to subtraction, sorting and identifying coins, counting, tracing, coloring, etc. Our Kindergarten Math Topics listed here assist young learners with building fundamental math skills.

Some kids will have a strong grasp of numbers and they are ready to dive right into addition and subtraction. Regardless of your child’s early math concepts, our Kindergarten Math Worksheets provided by subject experts are the perfect supplement to your classroom instruction. In fact, our Kindergarten Math Activities are designed in a way that your kids will love practicing math as a fun activity rather than feeling it difficult.

Preschool Kindergarten Math Topics, Textbook Solutions

There are numerous opportunities to engage your kid and help them learn the Kindergarten Math Concepts without even their knowledge. Through our Kindergarten Math Pages, one can sharpen their early math skills. Simply tap on the quick links available and practice the concepts at your convenience. Kindergarten Math Worksheets make it easy for you to test knowledge on related areas in no time and you can download them for free of cost.

Free Printable Kindergarten Math Worksheets

Practice tracing the numbers from 21 to 30

Practice tracing the numbers

Practice tracing the numbers from 31 to 40

Practice tracing the numbers from 41 to 50

Practice tracing the numbers from 51 to 60

Practice tracing the numbers from 61 to 70

Practice tracing the numbers from 71 to 80

Practice tracing the numbers from 81 to 90

Practice tracing the numbers from 91 to 100

Missing Number Worksheets

Missing Number Worksheets

Kindergarten Math Curriculum Goals & Objectives

The goal of the Kindergarten Math Curriculum is to prepare kids for 1st Grade Math.

  • Count Numbers up to 20 and a little beyond.
  • Concept of Equality
  • Count Backwards from 10 to 0.
  • Recognize Numbers and Able to Write Them.
  • Recognize Basic Shapes.
  • To be able to learn the Fundamentals of Basic Directions
  • To be able to understand the Addition and Subtraction with Smaller Numbers
  • Exposes kids to Two-Digit Numbers.

Benefits of referring to Kindergarten Math Concepts

There are several advantages of referring to the Pre School Kindergarten Math Topics and we have outlined some of them here. They are as follows

  • Brain Development in Kids is rapid at a young age, and learning from these Kindergarten Math Topics helps them develop inherent problem-solving skills.
  • You can learn arithmetic operations with ease and can be strong in premath.
  • Kids can explore the outside world around them in their own way.
  • Pre School Math Activities Provided acts as a visual treat for kids and inspires them to learn math skills in a fun and engaging way.
  • All the Kindergarten Games, Assessments, Math Activities provided are as per the latest Kindergarten Curriculum and are prepared by subject experts.

Final Words

We wish the knowledge shared has helped your kids learn math right from an early age. If you have any suggestions or feel any topic is missing do leave us your suggestions so that we can look into them. For more updates on Gradewise Math Worksheets, Practice Problems, Lessons stay tuned to our site.

Common Solid Figures – Definition, Shapes, Formulas, Properties, Examples

Common Solid Figures

Solid shapes or figures are solids having 3 dimensions, namely length, breadth, and height. Solid figures are classified into different categories. The characteristics and properties of solid shapes, the number of faces, edges, and also the number of vertices are explained below. Also, we have given examples for a better understanding of solid shapes. Also, we have given the solid shapes with clear explanations. Check out the complete concept to learn about solid shapes.

Common Solid Figures - Definition, Shapes, Formulas, Properties, Examples

Attributes of Solid Figures

Face: The flat surface present on the solid figure is known as the Face of the solid figure.
Edge: The edge of the solid figure is defined as the line where two faces meet.
Corner: The corner is a point where three or more edges join together is known as a corner.

Different Types of Solid Figures

There are different types of solid figures available in geometry. Check out the detailed explanation of some of the examples of solid figures below.

Cube

The first and important solid figure everyone discusses Cube. A cube is defined as a slid box-shaped that has six identical square faces. One solid figure that called a cube must consist of 6 equal and plane surfaces they appear as a square in shape.

A cube consists of 6 plane surfaces, 8 vertices and, 12 edges. There are two adjoining planes available in a cube which are called surfaces that meet at an edge. Also, it consists of 12 edges that are equal in length. These edges are straight edges. Furthermore, the joining point of two corners called a vertex. In a cube, there are 8 such vertices available.

cube solid figures

Parts of a Cube

Parts of a Cube

(i) Face: The sides of a cube are known as the Face of the cube. A cube consists of six faces. All the faces of a cube are square in shapes. Each face of a cube has four equal sides.
(ii) Edge: When two edges join each other with a line segment, then that corner is called the edge. The cube has 12 edges. All the 12 edges are equal in length as all faces are squares. These edges are straight edges.
(iii) Vertex: A point formed with the joint of the three edges is known as a vertex of a cube. There are 8 vertices in a cube.
(iv) Face Diagonals: Face Diagonals of a cube is the line segment that joins the opposite vertices of a face. There are 12 diagonals in the cube that are formed with 2 diagonals in each face altogether.
(v) Space Diagonals: Space diagonals of a cube are the line segment that joins the opposite vertices of a cube and also cutting through its interior. There are 4 space diagonals in a cube.

Properties of a Cube

Volume: The volume of a cube is shown by s³ where s is the length of one edge.
Surface Area: The surface area of a cube is 6s², where s is the length of one edge.

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Cuboid

The cuboid consists of 6 rectangular faces which form a convex polyhedron. The opposite rectangular plane surfaces are equal. It has 8 vertices and 12 edges.

A cuboid consists of 6 rectangular plane surfaces. There are 8 vertices and 12 edges. All the faces of a cuboid are equal and square. Therefore, a cube has all the six faces equal, whereas a cuboid has the opposite faces equal.

cuboid solid figures

Properties of a Cuboid

Properties of a Cuboid

Volume: The volume of a cuboid is lwh, where l is the length, h is the height, and w is the width.
Lateral Surface Area: The lateral surface area of a cuboid is 2lh + 2wh, where l is the length, w is the width, and h is the height.
Surface Area: The surface area of a cuboid is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.

Cylinder

The cylinder is one of the basic 3d shapes that stands on a circular plane surface consisting of circular plane surfaces on its top and bottom. A cylinder has two circular plane surfaces. One surface presents at its base and the other one presents at its top. Also, it has a curved surface in the middle. Two edges at which the two plane surfaces meet with the curved surface present on a cylinder. The edges are curved in a shape.

A cylinder has 2 plane surfaces and 1 curved surface. There are 2 edges and no vertices. Furthermore, the top and bottom of the cylinder are of the same shape as well as in size. They both are equal.

cylinder solid figures

Cone

A cone is a distinctive three-dimensional geometric figure that has one plane circular surface. It consists of a base and only one curved surface. There are 1 edge and 1 vertex present in the cone. The edge of the cone is a curved edge. It is formed by the circular plane surface meeting with the curved surface.

Cone solid figures

Sphere

A sphere is a geometrical figure that has a ball-like shape. There is only one curve surface present in the sphere and no edge and no vertex present in it.

sphere solid figures

Greater than Less than and Equal to Symbols | How to Remember Greater, Less than, Equal to Signs?

Greater than Less than and Equal to

In the Comparison of Numbers, we use symbols like Greater than, Less than, or Equal to. Greater than, Less than Symbols helps us to determine how one number is different from the other. These symbols denote if a number is greater than the other, or less than the other or else equal. Symbols for greater than is >, for less than, is <, and for equal to is = sign. Go through the further modules and fill in the blanks with relevant signs in the problems stated.

Once you get grip on the concepts of Comparison of Numbers start practicing using the Greater or Less than and Equal to Worksheets available. Take a Printout of these Greater, Less than, Equal to Activity Worksheets for free and access them offline too.

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Greater, Less than, and Equal to Signs

Greater, Less than, and Equal to Signs

Important Signs used for the Identification of Bigger, Smaller, and Equal to Numbers are as follows

= If two values are equal
then we use the sign equals to
Example: 3+3 = 6
If two values are not equal
we use the not equal to sign
Example: 4+3 ≠ 9
< If one value is smaller than the other
we use the less-than sign
Example: 2 < 6
> If one value is bigger than the other
we use the “greater than” symbol
Example: 8 > 4

Applications of Greater than, Less than or Equal to Signs

There are numerous applications of the greater than, less than, or equal to signs in mathematics. During the Comparison of Numbers, we will not always end up with an equality sign. At times, there arise scenarios of inequality and we end up using symbols greater than, less than. The statement can be expressed as a mathematical expression.

While dealing with the inequalities pay attention to the inequalities direction. Few tricks that don’t affect the inequalities direction in a problem is as follows

  • Multiplying or Dividing the Inequalities on both sides with the same positive number.
  • Adding or Subtracting with the same number on both sides of an inequality expression.

Examples of Greater than, Less than, or Equal to

Examples of Greater than, Less than, or Equal to

Example 1.
Write the Correct Comparison Symbol >, <, = in the blanks
1. 140 …….. 142
2. 155 ……. 152
3. 16 …….19
4. 18 ………18
5. 34 …….38
6. 71 …….74
7. 89…….88
8. 98……95
Solution:
1. 140 …<….. 142, 140 is less than 142
2. 155 …>…. 152, 155 is greater than 152
3. 16 ..<…..19, 16 is less than 19
4. 18 …..=….18, 18 is equal to 18
5. 34 …<….38, 34 is less than 38
6. 71 …<….74, 71 is less than 74
7. 89…<….88, 89 is greater than 88
8. 98…>….95,98 is greater than 95

Example 2.
Compare the numbers given and Place a sign in the below set.
Practice Worksheet on Comparison of NumbersExample 3:
Fill in the Boxes using>, <, or = sign. Take a Printout of the handy Worksheet on Greater than Less than or Equal to for free and begin your practice.
Greater than Less than Equal to Worksheets

Names of the Numbers – Definition, Facts, Examples | Number Names for 1 to 50(Spellings of Numbers)

Names of the Numbers

In mathematics, Numbers are usually used for counting, measuring, and checking quantities. Just like everything in the world numbers also have their respective words. Here, on this page, you will find the complete information about the Names of the Numbers. Students will already know some number names like from 1 – 20 but, here you can learn from 1 to n-digit number names. In preschool children are taught by number names which are fundamentals of maths.

These Names of the Numbers are helpful to students not only in primary but also in high school too. Many of the problems are related to these Number Names. Teaching the Names of the Numerics will help the students to write them correctly. All students should be known by Number Names of counting numbers. Names of Numbers are represented in alphabetical form. Each Number Name refers to a specific word. Furthermore, check the below sections to know in detail about the Names of the Numbers like Objectives of teaching Number names, etc.

Also, Read: Formation of Numbers

What are Number Names? | Numbers in Words

A number is a series of symbols that have a special significance in themselves. In maths, a Number name is a process of describing numbers in words.

How to Write Number Names in Words?

How to Write Number Names in Words?

To write Number Names in words you should know the place value of a digit. Based on the position of numbers we expand the numbers first and write their names of the number and combine those Number Names.

This is the easiest way to write down the Name of the Numbers. With the help of given examples, you can remind them how to expand and spell the words promptly. Let’s dive into the below sections for more details like importance, number names 1-50, etc.

Importance of Number Names in Words

  • Numbers play a main role in mathematics similarly, Number Names are fundamental for students to know.
  • These Names help the students when they are ready to solve any problem in classes.
  • Also, It is the basic rule in maths.
  • In our real-life situations, we can relate numbers to quantities.

Number Names 1 – 50

Now, let us practice the numbers from 1 – 20 with their Number Names and memorize them easily. Number Name is the method of representing the numbers in words. Have a glance at the below table:

Number Names 1 to 20

1-20 number names

Now, learn the Number Names for 30, 40, 50, 60, 70, 80, 90, and 100.

30 – Thirty 70 – Seventy
40 – Forty 80 – Eighty
50 – Fifty 90 – Ninety
60 – Sixty 100 – One Hundred

Number Names 21 to 30

21 22 23 24 25 26 27 28 29 30
Twenty-one Twenty-Two Twenty Three Twenty Four Twenty Five Twenty Six Twenty Seven Twenty Eight Twenty Nine Thirty
31 32 33 34 35 36 37 38 39 40
Thirty-One Thirty-Two Thirty-Three Thirty-Four Thirty-Five Thirty-Six Thirty-Seven Thirty-Eight Thirty-Nine Forty
41 42 43 44 45 46 47 48 49 50
Forty-One Forty-Two Forty-Three Forty-Four Forty-Five Forty-Six Forty-Seven Forty-Eight Forty-Nine Fifty

Examples of Names of Numbers

Example 1:

Write 75 in words?

Solution:

Now, write the place values i.e., 7 = seventy and, 5 = five. Let us expand the numbers
75 = 70 + 5 = seventy-five.

Example 2:

Write 479 in words.

Write 479 in words.

Solution:

Expand the numbers, 479 = 400 + 70 + 9. The Number Name is Four hundred seventy-nine.

Example 3:
Write 862 in words.

Solution:

First, write the given number in expanded form and write the Number Names and then merge that name.
862 = 800 + 60 + 2 i.e., eight hundred + sixty + two.
Now, we’ll merge the Number names. The Name of the Number is Eight Hundred Sixty-Two.

Example 4:

Write 7569 in words?

Solution:
Given number is 7569
First expand the given number into place value
Ie., 7569 = 7000 + 500 + 60 + 9
Now, write in words for each place value
Ie., Seventy thousand + five hundred + sixty + nine

Hence, The Number Name for 7569 is Seventy Thousand Five Hundred Sixty-Nine.

FAQs on Number Names

1. Why is it important to know Number Names for Numbers?

It helps the children how numbers are connected to each other. They understand the Number words and use them in different circumstances.

2. What do Names of the Numbers mean?

What do Names of the Numbers mean

Numbers with words are the alphabetical form of numbers in mathematics. With the help of number words, we could make the higher value of the number in words easily.

3. How do you get the Number Name of the highest number?

You should expand the given highest number with the place values and write the names for the respective place values then combine those expanded Number Names. For instance, if the number is 2336. Now, expand the number i.e., 2000 + 300 + 30 + 6 (in words two thousand + three hundred + thirty + six), then merge the number words i.e., 2336 = two thousand three hundred thirty-six.

Types of Symmetry – Line, Translation, Rotational, Reflection, Glide | Different Types of Symmetry with Examples

Types of Symmetry

Symmetry is one of the important concepts of geometry. If one part of the object looks like the same as another part of the object when we turn, flip, or slide, then it is called symmetry. If an object is not looking like another part of the object then it is called asymmetric.

To find out a given object is symmetric, we need to follow some steps. Firstly, draw a line on the middle of the image or object, and observe the image or object whether the left side of the object is the same as the right side or not. If the image is symmetrical, then the left side of the image is looking like a mirror image of the right side of the image or not. We can define different types of symmetries as below.

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Example Images of Symmetry

Types of Symmetry. Example for Symmetry. Image 1. jpg

Line of Symmetry

An object is divided into two parts with the help of a line and the two parts are mirror images of an object, then it is called a line of symmetry. The line of symmetry is also called as ‘axis of symmetry’. The line may be either vertical or horizontal or diagonal.

Vertical Line of Symmetry

The above figure shows the hexagonal image divided into two parts with the help of a vertical line. Here, the vertical line divides the above image into two parts and these two parts are mirror images for each other. That means, both the parts of an image are the same. This type of symmetry is called as Vertical line of Symmetry.

Types of Symmetry. vertical line of Symmetry. Image 2

Horizontal Line of Symmetry

The above diagram shows that the image is split into two parts with the help of a horizontal line. Here, the horizontal line dividing the above image into two parts, and these two parts are equal halves of the image. This type of symmetry is called a horizontal line of symmetry.

Types of Symmetry. Horizontal line of Symmetry. Image 3. jpg

Diagonal Line of Symmetry

From the above diagram, an image is divided into two equal halves by the diagonal line. These two equal halves are mirror images of each other. This type of line of symmetry is called as Diagonal Line of Symmetry.

Again we have a number of types in line of symmetry. Yes, we can divide the image into a number of parts with the help of one line, two-line,s or more lines. Every part must be the mirror image of another.

Types of Symmetry. Diagonal line of Symmetry.image 4

One Line of Symmetry

By using the vertical or horizontal or diagonal line, we need to divide the image into equal halves and it is called one line of symmetry. Above mentioned, vertical, horizontal, and diagonal lines of symmetry are examples of one line of symmetry.

Two Lines of Symmetry

Same like one line of symmetry, in two lines of symmetry also we can use the vertical or horizontal or diagonal lines but we need to use only two lines to divide the image equally. This type of line of symmetry is called Two lines of Symmetry.

Types of Symmetry. Two lines of Symmetry.image 5

Infinite Lines of Symmetry

An image or object is divided into a number of parts with the help of a number of lines and these equal halves of the image. It is called Infinite Lines of Symmetry. These lines are either vertical or horizontal or diagonal lines.

Types of Symmetry. Infinite lines of Symmetry.image 6

Some Other Types of Symmetry

We have different types of symmetries considered depending on the various cases. They are

  1. Translational Symmetry
  2. Rotational Symmetry
  3. Reflexive Symmetry
  4. Glide Symmetry

1.Translational Symmetry

An object or image is moving forward or backward or changing the position from one place to another, but there is no change in the image or object. This type of Symmetry is called Translational Symmetry.

Types of Symmetry. Translational Symmetry.image 7

2.Rotational Symmetry

An object or image is rotated in a particular direction but the position of an object or image is identical to the origin of an image or object, then it is called rotational symmetry. It is also called radial symmetry.

Types of Symmetry. Rotational Symmetry.image 8

From the above figure, we can observe the rotational symmetry. If you rotate the hexagonal object or image in a 60° clockwise direction with respect to the origin, there is no change in the shape of an image. More Examples for Rotational Symmetry are Circle, Hexagonal, Square, Rectangle, and etc…

3.Reflexive Symmetry

Reflexive Symmetry is the same as a line of symmetry. Yes, in this type of symmetry one part of the image or object represents the mirror image of another part of the image. Reflexive Symmetry is also called a line of symmetry or mirror symmetry. The below figure is a better example of Reflexive symmetry.

Types of Symmetry. Reflexive Symmetry.image 9

The above object is divide into two parts and the left side part is the mirror image of the right side of the image.

4.Glide Symmetry

It is the combination of both translation symmetry and reflection symmetry.

Point Symmetry

When an object is in opposite direction, every part of the object must be matched with the original object. It is called Point Symmetry. It is the same as Rotational Symmetry, so we can call it Rotational Symmetry order 2.

Types of Symmetry. Translational Symmetry.image 7

Solved Examples on Types of Symmetry

1. Name and draw the shape which possesses linear symmetry, point symmetry, and rotational symmetry?

Solution:
(i) Line Segment

Types of Symmetry. Line segment.image 11

  • Linear symmetry is a line of symmetry. here, it indicates ‘AB’.
  • Point symmetry, the mid-point of the line of origin of the image that is ‘O’.
  • Rotational Symmetry, If we move the above image in any direction with respect to the origin, there is no change in the image. Here, the origin of the image is ‘O’

(ii) Square

Types of Symmetry. Square.image 12

  • Linear symmetry, two lines of symmetry.
  • Point symmetry, the intersection of two lines that is ‘O’.
  • Rotational Symmetry order of 2.

2. If the following figure shows a line of symmetry, then complete the figure?

Types of Symmetry. line of symmetry.image 13

Solution:
The line of symmetry, vertical or horizontal line divides the image into two equal halves and two parts are look as same. So, the remaining part of the image also the same as the above figure. That is,
Types of Symmetry. line of symmetry.image 14

3. Identify which of the following figure is the example for symmetry?

Types of Symmetry. symmetry.image 15

Solution:
In the symmetry method, an image or object is divided into equal halves either it may be vertical lines or horizontal lines. Each part must be a mirror image of the other part of the image. That particular image, we can consider as the example for symmetry. In the above diagrams, figure ‘c’ is showing as an example of symmetry. In that one only, the image is divided into two equal halves and the remaining A and B are not divided into equal halves.

4. How many lines of symmetry does a rectangle have?

Types of Symmetry. symmetry.image 16

Solution:
Four lines of symmetry. One horizontal line, one vertical line, and two diagonal lines.

5. Identify which of the following image indicates the rotational symmetry?

Types of Symmetry. Rotational symmetry.image 17

Solution:
By moving in a forward or backward direction, an object or image will be in the same as the original image, which is called rotational symmetry. From the above, Figure (A) is the best example for Rotational symmetry.

FAQs on Types of Symmetry

1. What is Symmetry?

In symmetry, an object is divided into equal parts and each part of an object is a mirror image of another part of the object. 

2. What are the Types of Symmetry?

There are four types of symmetry. They are

  1. Translational Symmetry
  2. Rotational Symmetry
  3. Reflexive Symmetry
  4. Glide Symmetry

3. What is a Line of Symmetry?

An object or image is divided into equal halves with horizontal or vertical or diagonal lines. But the left side of the image is the same as the right side of the image that is called a line of symmetry.

4. What is Point Symmetry?

If we place the image or object in the opposite direction, then every part of the image must be matched with the equal distance that is called point symmetry.

5. What is Asymmetric?

An object is divided into equal parts but the left side of the image is not the same as the right side of the image and it is called an asymmetric method.