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.

Answer: 1055.4

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.

Answer: 6.8

A large watermelon weighs 10.4 pounds. A smaller watermelon weighs 3.6 pounds.

The smaller watermelon weighs less than the larger watermelon by = 10.4 – 3.6 = 6.8

It weighs 6.8 pounds less.

Question 6.

Terrance picked 115.2 pounds of apples on Monday. He picked 97.6 pounds of apples on Tuesday. How many pounds of apples did Terrance pick altogether?

Terrance picked ____ pounds of apples.

Answer: 212.8

Terrance picked 115.2 pounds of apples on Monday. He picked 97.6 pounds of apples on Tuesday.

total number of pounds of apples did Terrance pick altogether = 115.2 + 97.6 = 212.8

Terrance picked 212.8 pounds of apples.