Spectrum Math Grade 6 Chapter 3 Lesson 1 Answer Key Understanding Ratios

Go through the Spectrum Math Grade 6 Answer Key Chapter 3 Lesson 3.1 Understanding Ratios and get the proper assistance needed during your homework.

Spectrum Math Grade 6 Chapter 3 Lesson 3.1 Understanding Ratios Answers Key

A ratio compares 2 numbers. When written out, several phrases can show how the ratio should be written.
4 to 2 4:2 \(\frac{4}{2}\) or \(\frac{2}{1}\)
6 out of 8 6:8 \(\frac{6}{8}\) or \(\frac{3}{4}\)

Express each ratio as a fraction in simplest form.

Question 1.
a. 15 feet out of 36 feet ___________
Answer:
Fraction in simplest form of 15 feet out of 36 feet is \(\frac{5}{12}\).

Explanation:
15 feet out of 36 feet
= 15 ÷ 36
= \(\frac{5}{12}\).

b. 5 pounds to 35 pounds ______
Answer:
Fraction in simplest form of 5 pounds to 35 pounds is \(\frac{1}{7}\).

Explanation:
5 pounds to 35 pounds
= 5 ÷ 35
= \(\frac{1}{7}\).

Question 2.
a. 8 rainy days out of 60 days ___________

a. 8 rainy days out of 60 days
Answer:
Fraction in simplest form of 8 rainy days out of 60 days is \(\frac{2}{15}\).

Explanation:
8 rainy days out of 60 days
= 8 ÷ 60
= 4 ÷ 30
= 2 ÷ 15 or \(\frac{2}{15}\).

b. 28 snow days out of 49 days ______
Answer:
Fraction in simplest form of 28 snow days out of 49 days is \(\frac{4}{7}\).

Explanation:
28 snow days out of 49 days
= 28 ÷ 49
= 4 ÷ 7 or \(\frac{4}{7}\).

Question 3.
a. 10 pints to 20 pints __________
Answer:
Fraction in simplest form of 10 pints to 20 pints is

Explanation:
10 pints to 20 pints
= 10 ÷ 20
= 1 ÷ 2 or \(\frac{1}{2}\).

b. 40 cups to 55 cups ____
Answer:
Fraction in simplest form of 40 cups to 55 cups is \(\frac{8}{11}\).

Explanation:
40 cups to 55 cups
= 40 ÷ 55
= 8 ÷ 11 or \(\frac{8}{11}\).

Question 4.
a. 10 miles out of 12 miles ____________
Answer:
Fraction in simplest form of 10 miles out of 12 miles is \(\frac{5}{6}\).

Explanation:
10 miles out of 12 miles
= 10 ÷ 12
= 5 ÷ 6 or \(\frac{5}{6}\).

b. 28 red bikes out of 40 bikes ____

28 red bikes out of 40 bikes
Answer:
Fraction in simplest form of 28 red bikes out of 40 bikes is \(\frac{7}{10}\).

Explanation:
28 red bikes out of 40 bikes
= 28 ÷ 40
= 14 ÷ 20
= 7 ÷ 10 or \(\frac{7}{10}\).

Question 5.
a. 18 beetles out of 72 insects ___________
Answer:
Fraction in simplest form of 18 beetles out of 72 insects is \(\frac{1}{4}\).

Explanation:
18 beetles out of 72 insects
= 18 ÷ 72
= 9 ÷ 36
= 1 ÷ 4 or \(\frac{1}{4}\).

b. 63 gallons to 8tf gallons ______
Answer:
Fraction in simplest form of 63 gallons to 8tf gallons is

Explanation:
63 gallons to 8tf gallons
Conversion:

Question 6.
a. 49 dimes out of 77 coins ___________
Answer:
Fraction in simplest form of 49 dimes out of 77 coins is 490 dimes.

Explanation:
49 dimes out of 77 coins
Conversion:
1 dollar = 100 coins/cents.
= 49 dollars × 100 coins
= 4900 coins.
1 dime = 10 coins.
=> 4900 coins÷ 10
=> 490 dimes.

b. 12 cakes out of 36 cakes ______
Answer:
Fraction in simplest form of 12 cakes out of 36 cakes is \(\frac{1}{3}\).

Explanation:
12 cakes out of 36 cakes
= 12 ÷ 36
= 1 ÷ 3 or \(\frac{1}{3}\).

Question 7.
a. 15 students out of 30 students ____________
Answer:
Fraction in simplest form of 15 students out of 30 students is \(\frac{1}{2}\).

Explanation:
15 students out of 30 students
= 15 ÷ 30
= 1 ÷ 2 or \(\frac{1}{2}\).

b. 3 floors out of 18 floors ____
Answer:
Fraction in simplest form of 3 floors out of 18 floors is \(\frac{1}{6}\).

Explanation:
3 floors out of 18 floors
= 3 ÷ 18
= 1 ÷ 6 or \(\frac{1}{6}\).

Question 8.
a. 36 meters out of 100 meters ______
Answer:
Fraction in simplest form of 36 meters out of 100 meters is \(\frac{18}{25}\).

Explanation:
36 meters out of 100 meters
= 36 ÷ 100
= 18 ÷ 25 or \(\frac{18}{25}\).

b. 14 hats out of 20 accessories ____
Answer:
Fraction in simplest form of 14 hats out of 20 accessories is \(\frac{7}{10}\).

Explanation:
14 hats out of 20 accessories
= 14 ÷ 20
= 7 ÷ 10 or \(\frac{7}{10}\).

Question 9.
a. 80 scores out of 90 scores ____________
Answer:
Fraction in simplest form of 80 scores out of 90 scores is \(\frac{8}{9}\).

Explanation:
80 scores out of 90 scores
= 80 ÷ 90
= 8 ÷ 9 or \(\frac{8}{9}\).

b. 2 sports out of 9 sports ______
Answer:
Fraction in simplest form of 2 sports out of 9 sports is \(\frac{2}{9}\).

Explanation:
2 sports out of 9 sports
= 2 ÷ 9 or \(\frac{2}{9}\).

Question 10.
a. 42 cars out of 124 cars ___________

42 cars out of 124 cars
Answer:
Fraction in simplest form of 42 cars out of 124 cars is \(\frac{21}{62}\).

Explanation:
42 cars out of 124 cars
= 42 ÷ 124
= 21 ÷ 62 or \(\frac{21}{62}\).

b. 7 messages out of 84 messages __________
Answer:
Fraction in simplest form of 7 messages out of 84 messages is \(\frac{1}{12}\).

Explanation:
7 messages out of 84 messages
= 7 ÷ 84
= 1 ÷ 12 or \(\frac{1}{12}\).

Ratios can be written based on the number of objects in a set.
There are 2 bottles of soda and 5 bottles of water in the refrigerator. Write the ratio of sodas to waters.
Answer:
The ratio of sodas to waters = \(\frac{2}{5}\).

Explanation:
Number of bottles of Soda = 2.
Number of bottles of water = 5.
Ratio of sodas to waters = Number of bottles of Soda ÷ Number of bottles of water
= 2 ÷ 5 or \(\frac{2}{5}\).

Express each ratio as a fraction in simplest form.

Question 1.
a. There are 2 cubes and 15 spheres in a geometry box. Write the ratio of spheres to cubes.
_____________
Answer:
Ratio of spheres to cubes = \(\frac{15}{2}\).

Explanation:
Number of cubes in a geometry box = 2.
Number of spheres in a geometry box = 15.
Ratio of spheres to cubes = Number of spheres in a geometry box ÷ Number of cubes in a geometry box
= 15 ÷ 2 or \(\frac{15}{2}\).

b. There are 5 cars and 4 vans in a parking lot. Write the ratio of vans to cars.
_____________
Answer:
Ratio of vans to cars = \(\frac{4}{5}\).

Explanation:
Number of cars in a parking lot = 5.
Number of vans in a parking lot = 4.
Ratio of vans to cars = Number of vans in a parking lot ÷ Number of cars in a parking lot
= 4 ÷ 5 or \(\frac{4}{5}\).

Question 2.
a. There are 5 horses and 15 elephants in a circus. Write the ratio of elephants to horses.
_____________
Answer:
Ratio of elephants to horses = 3.

Explanation:
Number of horses in a circus = 5.
Number of elephants in a circus = 15.
Ratio of elephants to horses = Number of elephants in a circus ÷ Number of horses in a circus
= 15 ÷ 5
= 3 ÷ 1
= 3.

b. There are 16 horses and 14 elephants in a circus. Write the ratio of horses to elephants.
_____________

There are 16 horses and 14 elephants in a circus
Answer:
Ratio of horses to elephants = \(\frac{8}{7}\).

Explanation:
Number of horses in a circus = 16.
Number of elephants in a circus = 14.
Ratio of horses to elephants = Number of horses in a circus ÷ Number of elephants in a circus
= 16 ÷ 14
= 8 ÷ 7 or \(\frac{8}{7}\).

Question 3.
a. There are 11 blue marbles and 7 red marbles in a box. Write the ratio of red marbles to blue marbles.
_____________
Answer:
Ratio of red marbles to blue marbles = \(\frac{7}{11}\).

Explanation:
Number of blue marbles in a box = 11.
Number of red marbles in a box = 7.
Ratio of red marbles to blue marbles = Number of red marbles in a box ÷ Number of blue marbles in a box
= 7 ÷ 11 or \(\frac{7}{11}\).

b. There are 12 apples and 15 oranges in a fruit basket. Write the ratio of apples to oranges.
_____________
Answer:
Ratio of apples to oranges = \(\frac{4}{5}\).

Explanation:
Number of apples in a fruit basket = 12.
Number of oranges in a fruit basket = 15.
Ratio of apples to oranges = Number of apples in a fruit basket ÷ Number of oranges in a fruit basket
= 12 ÷ 15
= 4 ÷ 5 or \(\frac{4}{5}\).

Question 4.
a. There are 5 blue marbles and 16 red marbles in a box. Write the ratio of blue marbles to red marbles.
_____________
Answer:
Ratio of blue marbles to red marbles = \(\frac{5}{16}\).

Explanation:
Number of blue marbles in a box = 5.
Number of red marbles in a box = 16.
Ratio of blue marbles to red marbles = Number of blue marbles in a box ÷ Number of red marbles in a box
= 5 ÷ 16 or \(\frac{5}{16}\).

b. There are 12 dogs and 7 cats in a park. Write the ratio of cats to dogs.
_____________
Answer:
Ratio of cats to dogs = \(\frac{7}{12}\).

Explanation:
Number of dogs in a park = 12.
Number of cats in a park = 7.
Ratio of cats to dogs = Number of cats in a park ÷ Number of dogs in a park
= 7 ÷ 12 or \(\frac{7}{12}\).

Question 5.
a. There are 14 cars and 7 vans in a parking lot. Write the ratio of cars to vans.
_____________
Answer:
Ratio of cars to vans = 2.

Explanation:
Number of cars in a parking lot = 14.
Number of vans in a parking lot = 7.
Ratio of cars to vans = Number of cars in a parking lot ÷ Number of vans in a parking lot
= 14 ÷ 7
= 2 ÷ 1
= 2.

b. There are 7 blue marbles and 8 red marbles in a bag. Write the ratio of red marbles to blue marbles.

There are 7 blue marbles and 8 red marbles in a bag
_____________
Answer:
Ratio of red marbles to blue marbles = \(\frac{8}{7}\) or 1\(\frac{1}{7}\).

Explanation:
Number of blue marbles in a bag = 7.
Number of red marbles in a bag = 8.
Ratio of red marbles to blue marbles = Number of red marbles in a bag ÷ Number of blue marbles in a bag
= 8 ÷ 7
= \(\frac{8}{7}\) or 1\(\frac{1}{7}\).

Question 6.
a. There are 6 pennies and 10 dimes in a jar. Write the ratio of pennies to dimes.
_____________
Answer:
Ratio of pennies to dimes = \(\frac{3}{5}\).

Explanation:
Number of pennies in a jar = 6.
Number of dimes in a jar = 10.
Ratio of pennies to dimes = Number of pennies in a jar ÷ Number of dimes in a jar
= 6 ÷ 10
= 3 ÷ 5 or \(\frac{3}{5}\).

b. There are 24 butterflies and 16 snails on the ground. Write the ratio of butterflies to snails.
_____________
Answer:
Ratio of butterflies to snails = \(\frac{3}{2}\) or 1\(\frac{1}{2}\).

Explanation:
Number of butteries on the ground = 24.
Number of snails on the ground = 16.
Ratio of butterflies to snails = Number of butteries on the ground ÷ Number of snails on the ground
= 24 ÷ 16
= 12 ÷ 8
= 3 ÷ 2
= \(\frac{3}{2}\) or 1\(\frac{1}{2}\).

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