# Spectrum Math Grade 7 Chapter 1 Lesson 9 Answer Key Problem Solving

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Lesson 1.9 Problem Solving provides detailed answers for the workbook questions.

## Spectrum Math Grade 7 Chapter 1 Lesson 1.9 Problem Solving Answers Key

Solve each problem.

Question 1.
At closing time, the bakery had 2$$\frac{1}{4}$$ apple pies and 1$$\frac{1}{2}$$ cherry pies left. How much more apple pie than cherry pie was left?
There was ___________ more of an apple pie than cherry.
Answer: 0$$\frac{3}{4}$$
Number of apple pies in the bakery at the closing time = 2$$\frac{1}{4}$$
Number of cherry pies in the bakery at the closing time = 1$$\frac{1}{2}$$
Therefore, number of more apple pie than cherry pie = 2$$\frac{1}{4}$$ – 1$$\frac{1}{2}$$
Partition the fractions and whole numbers to subtract them separately.
= (2- 1) + [$$\frac{1}{4}$$ – $$\frac{1}{2}$$]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [$$\frac{1}{4}$$ x $$\frac{2}{2}$$] – [$$\frac{1}{2}$$  x $$\frac{4}{4}$$]
= 1 + $$\frac{2}{8}$$ – $$\frac{4}{8}$$
= 0 + $$\frac{10}{8}$$ – $$\frac{4}{8}$$
= 0 + $$\frac{10 – 4}{8}$$
After simplification,
= 0 + $$\frac{6}{8}$$
= 0 + $$\frac{3}{4}$$
Therefore, the result is given by,
= 0$$\frac{3}{4}$$
There was 0$$\frac{3}{4}$$ more of an apple pie than cherry

Question 2.
The hardware store sold 6$$\frac{3}{8}$$ boxes of large nails and 7$$\frac{2}{5}$$ boxes of small nails. In total, how many boxes of nails did the store sell?
The store sold ____________ boxes of nails.
Answer: 13$$\frac{31}{40}$$
number of boxes of large nails sold by hardware store = 6$$\frac{3}{8}$$
number of boxes of small nails sold by hardware store = 7$$\frac{2}{5}$$
Total number of boxes of nails sold by hardware store =  6$$\frac{3}{8}$$ + 7$$\frac{2}{5}$$
Partition the fractions and whole numbers to add them separately.
= (6 + 7) + $$\frac{3}{8}$$ + $$\frac{2}{5}$$
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 13 + [$$\frac{3}{8}$$ x $$\frac{5}{5}$$] + [$$\frac{2}{5}$$  x $$\frac{8}{8}$$]
= 13 + $$\frac{15}{40}$$ + $$\frac{16}{40}$$
= 13 + $$\frac{15 + 16}{40}$$
After simplification,
= 13 + $$\frac{31}{40}$$
Therefore, the result is given by,
= 13$$\frac{31}{40}$$
The store sold 13$$\frac{31}{40}$$ boxes of nails.

Question 3.
Nita studied 4$$\frac{1}{3}$$ hours on Saturday and 5$$\frac{1}{4}$$ hours on Sunday. How many hours did she spend studying?
She spent ____________ hours studying.
Answer: 9$$\frac{7}{12}$$
Nita studied 4$$\frac{1}{3}$$ hours on Saturday and 5$$\frac{1}{4}$$ hours on Sunday.
Total hours did she spend on studying = 4$$\frac{1}{3}$$ + 5$$\frac{1}{4}$$
Partition the fractions and whole numbers to add them separately.
= (4 + 5) + $$\frac{1}{3}$$ + $$\frac{1}{4}$$
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 9 + [$$\frac{1}{3}$$ x $$\frac{4}{4}$$] + [$$\frac{1}{4}$$  x $$\frac{3}{3}$$]
= 9 + $$\frac{4}{12}$$ + $$\frac{3}{12}$$
= 9 + $$\frac{4 + 3}{12}$$
After simplification,
= 9 + $$\frac{7}{12}$$
Therefore, the result is given by,
= 9$$\frac{7}{12}$$
She spent 9$$\frac{7}{12}$$ hours studying.

Question 4.
Kwan is 5$$\frac{2}{3}$$ feet tall. Mary is 4$$\frac{11}{12}$$ feet tall. How much taller is Kwan?
Kwan is ___________ foot taller.
Answer: 0$$\frac{3}{4}$$
Kwan is 5$$\frac{2}{3}$$ feet tall. Mary is 4$$\frac{11}{12}$$ feet tall.
Kwan is taller than Mary = 5$$\frac{2}{3}$$ – 4$$\frac{11}{12}$$
Partition the fractions and whole numbers to subtract them separately.
= (5- 4) + [$$\frac{2}{3}$$ – $$\frac{11}{12}$$]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [$$\frac{2}{3}$$ x $$\frac{12}{12}$$] – [$$\frac{11}{12}$$  x $$\frac{3}{3}$$]
= 1 + $$\frac{24}{36}$$ – $$\frac{33}{36}$$
= 0 + $$\frac{60}{36}$$ – $$\frac{33}{36}$$
= 0 + $$\frac{60 – 33}{36}$$
After simplification,
= 0 + $$\frac{27}{36}$$
= 0 + $$\frac{3}{4}$$
Therefore, the result is given by,
= 0$$\frac{3}{4}$$
Kwan is 0$$\frac{3}{4}$$ foot taller.

Question 5.
This week, Jim practiced the piano 1$$\frac{1}{8}$$ hours on Monday and 2$$\frac{3}{7}$$ hours on Tuesday. How many hours did he practice this week? How much longer did Jim practice on Tuesday than on Monday?
Jim practiced _____________ hours this week.
Jim practiced _______ hours longer on Tuesday.
Answer: i)3$$\frac{31}{56}$$
ii) 1$$\frac{17}{56}$$
Jim practiced the piano 1$$\frac{1}{8}$$ hours on Monday and 2$$\frac{3}{7}$$ hours on Tuesday.
Total number of hours practiced by Jim this week = 1$$\frac{1}{8}$$ + 2$$\frac{3}{7}$$
Partition the fractions and whole numbers to add them separately.
= (1+ 2) + $$\frac{1}{8}$$ + $$\frac{3}{7}$$
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [$$\frac{1}{8}$$ x $$\frac{7}{7}$$] + [$$\frac{3}{7}$$  x $$\frac{8}{8}$$]
= 3 + $$\frac{7}{56}$$ + $$\frac{24}{56}$$
= 3 + $$\frac{7 + 24}{56}$$
After simplification,
= 3 + $$\frac{31}{56}$$
Therefore, the result is given by,
= 3$$\frac{31}{56}$$
Jim practiced 3$$\frac{31}{56}$$ hours this week.
Number of hours practiced by Jim on tuesday than monday = 2$$\frac{3}{7}$$ – 1$$\frac{1}{8}$$
Partition the fractions and whole numbers to subtract them separately.
= (2- 1) + [$$\frac{3}{7}$$ – $$\frac{1}{8}$$]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [$$\frac{3}{7}$$ x $$\frac{8}{8}$$] – [$$\frac{1}{8}$$  x $$\frac{7}{7}$$]
= 1 + $$\frac{24}{56}$$ – $$\frac{7}{56}$$
= 1 + $$\frac{24 – 7}{56}$$
After simplification,
= 1 + $$\frac{17}{56}$$
Therefore, the result is given by,
= 1$$\frac{17}{56}$$
Jim practiced 1$$\frac{17}{56}$$ hours longer on Tuesday.

Question 6.
Oscar caught a fish that weighed 4$$\frac{1}{6}$$ pounds and then caught another that weighed 6$$\frac{5}{8}$$ pounds. How much more did the second fish weigh?
The second fish weighed ____ pounds more.
Answer: 2$$\frac{11}{24}$$
Oscar caught a fish that weighed 4$$\frac{1}{6}$$ pounds and then caught another that weighed 6$$\frac{5}{8}$$ pounds.
The second fish weighed more pounds than first fish = 6$$\frac{5}{8}$$ – 4$$\frac{1}{6}$$
Partition the fractions and whole numbers to subtract them separately.
= (6- 4) + [$$\frac{5}{8}$$ – $$\frac{1}{6}$$]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [$$\frac{5}{8}$$ x $$\frac{6}{6}$$] – [$$\frac{1}{6}$$  x $$\frac{8}{8}$$]
= 2 + $$\frac{30}{48}$$ – $$\frac{8}{48}$$
= 2 + $$\frac{30 – 8}{48}$$
After simplification,
= 2 + $$\frac{22}{48}$$
= 2 + $$\frac{11}{24}$$
Therefore, the result is given by,
= 2$$\frac{11}{24}$$
The second fish weighed 2$$\frac{11}{24}$$ pounds more.

Solve each problem.

Question 1.
One cake recipe calls for $$\frac{2}{3}$$ cup of sugar. Another recipe calls for 1$$\frac{1}{4}$$ cups of sugar. How many cups of sugar are needed to make both cakes?
_____ cups of sugar are needed.
Answer: 1$$\frac{11}{12}$$
One cake recipe calls for $$\frac{2}{3}$$ cup of sugar. Another recipe calls for 1$$\frac{1}{4}$$ cups of sugar.
total cups of sugar that are needed to make both cakes = $$\frac{2}{3}$$ + 1$$\frac{1}{4}$$
Partition the fractions and whole numbers to add them separately.
= (0+ 1) + $$\frac{2}{3}$$ + $$\frac{1}{4}$$
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [$$\frac{2}{3}$$ x $$\frac{4}{4}$$] + [$$\frac{1}{4}$$  x $$\frac{3}{3}$$]
= 1 + $$\frac{8}{12}$$ + $$\frac{3}{12}$$
= 1 + $$\frac{8 + 3}{12}$$
After simplification,
= 1 + $$\frac{11}{12}$$
Therefore, the result is given by,
= 1$$\frac{11}{12}$$
1$$\frac{11}{12}$$ cups of sugar are needed.

Question 2.
Nicole and Daniel are splitting a pizza. Nicole eats $$\frac{1}{4}$$ of a pizza and Daniel eats $$\frac{2}{3}$$ of it. How much pizza is left?
____ of the pizza is left.
Answer: $$\frac{1}{12}$$
Nicole and Daniel are splitting a pizza. Nicole eats $$\frac{1}{4}$$ of a pizza and Daniel eats $$\frac{2}{3}$$ of it.
Piece of pizza ate by Nicole and Daniel = $$\frac{1}{4}$$ + $$\frac{2}{3}$$
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [$$\frac{1}{4}$$ x $$\frac{3}{3}$$] + [$$\frac{2}{3}$$  x $$\frac{4}{4}$$]
= $$\frac{3}{12}$$ + $$\frac{8}{12}$$
= $$\frac{3 + 8}{12}$$
After simplification, the result is given by,
= $$\frac{11}{12}$$
The piece of pizza left = 1 – $$\frac{11}{12}$$ (consider whole pizza as 1 part, so subtract the completed piece of pizza from 1)
= $$\frac{12-11}{12}$$
= $$\frac{1}{12}$$
$$\frac{1}{12}$$ of the pizza is left.

Question 3.
The Juarez family is making a cross-country trip. On Saturday, they traveled 450.8 miles. On Sunday, they traveled 604.6 miles. How many miles have they traveled so far?
They have travelled ____ miles.
On Saturday, they traveled 450.8 miles. On Sunday, they traveled 604.6 miles.
total miles they have traveled so far = 450.8 + 604.6 = 1055.4
They have travelled 1055.4 miles.

Question 4.
Kathy’s science book is 1$$\frac{1}{6}$$ inches thick. Her reading book is 1$$\frac{3}{8}$$ inches thick. How much thicker is her reading book than her science book?
It is ____ inches thicker.
Answer: 0$$\frac{5}{24}$$
Kathy’s science book is 1$$\frac{1}{6}$$ inches thick. Her reading book is 1$$\frac{3}{8}$$ inches thick
Kathy’s reading book is thicker than her science book by = 1$$\frac{3}{8}$$ – 1$$\frac{1}{6}$$
Partition the fractions and whole numbers to subtract them separately.
= (1- 1) + [$$\frac{3}{8}$$ – $$\frac{1}{6}$$]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 0 + [$$\frac{3}{8}$$ x $$\frac{6}{6}$$] – [$$\frac{1}{6}$$  x $$\frac{8}{8}$$]
= 0 + $$\frac{18}{48}$$ – $$\frac{8}{48}$$
= 0 + $$\frac{18 – 8}{48}$$
After simplification,
= 0 + $$\frac{10}{48}$$
= 0 + $$\frac{5}{24}$$
Therefore, the result is given by,
= 0$$\frac{5}{24}$$
It is 0$$\frac{5}{24}$$ inches thicker.

Question 5.
A large watermelon weighs 10.4 pounds. A smaller watermelon weighs 3.6 pounds. How much less does the smaller watermelon weigh?
It weighs ____ pounds less.