Practice with the help of **Spectrum Math Grade 5 Answer Key Chapter 5 Lesson 5.6 Problem Solving **regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 5 Lesson 5.6 Problem Solving Answers Key

**Solve each problem. Write answers in simplest form. Show your work.**

Question 1.

Caroline needs 3\(\frac{1}{7}\) cups of sugar for her first batch of brownies and 2\(\frac{8}{9}\) cups of sugar for a second batch. How much sugar does she need in all?

Caroline needs ___________ cups of sugar.

Answer:

Given,

Caroline needs 3\(\frac{1}{7}\) cups of sugar for her first batch of brownies and 2\(\frac{8}{9}\) cups of sugar for a second batch.

3\(\frac{1}{7}\) + 2\(\frac{8}{9}\)

3 + 2 + \(\frac{1}{7}\) + \(\frac{8}{9}\)

5 + \(\frac{1}{7}\) + \(\frac{8}{9}\)

5 + 1 \(\frac{2}{63}\) = 6 \(\frac{2}{63}\) cups of sugar

Question 2.

Robert’s gas tank has 5\(\frac{3}{5}\) gallons of gas in it. If he adds 7\(\frac{2}{3}\) gallons, how much gas will be in the tank?

There will be ____________ gallons of gas in the tank.

Answer:

Given,

Robert’s gas tank has 5\(\frac{3}{5}\) gallons of gas in it.

he adds 7\(\frac{2}{3}\) gallons

5\(\frac{3}{5}\) + 7\(\frac{2}{3}\)

5 + 7 + \(\frac{3}{5}\) + \(\frac{2}{3}\)

12 + \(\frac{3}{5}\) + \(\frac{2}{3}\) = 13 \(\frac{4}{15}\)

There will be 13 \(\frac{4}{15}\) gallons of gas in the tank.

Question 3.

A hamburger weighs \(\frac{1}{3}\) pound, and an order of french fries weighs \(\frac{1}{4}\) pound. How many pounds total will a meal of hamburger and french fries weigh?

The meal will weigh _______________ pounds.

Answer:

Given,

A hamburger weighs \(\frac{1}{3}\) pound, and an order of french fries weighs \(\frac{1}{4}\) pound.

\(\frac{1}{3}\) + \(\frac{1}{4}\)

LCM = 12

\(\frac{4}{12}\) + \(\frac{3}{12}\) = \(\frac{7}{12}\)

The meal will weigh \(\frac{7}{12}\) pounds.

Question 4.

Jonn is 5\(\frac{6}{10}\) feet tall ana Jamar is \(\frac{5}{8}\) feet taller than John. How tall ¡s Jamar?

Jamar is _____________ feet tall.

Answer:

Given,

Jonn is 5\(\frac{6}{10}\) feet tall ana Jamar is \(\frac{5}{8}\) feet taller than John.

5\(\frac{6}{10}\) + \(\frac{5}{8}\)

5 + \(\frac{6}{10}\) + \(\frac{5}{8}\) = 6 \(\frac{9}{40}\)

Jamar is 6 \(\frac{9}{40}\) feet tall.

Question 5.

Mrs. Stevenson has used 4\(\frac{2}{3}\) inches of string. She needs 1\(\frac{6}{7}\) inches more. How much string will Mrs. Stevenson have used when she is done?

Mrs. Stevenson will have used ______________ inches of string.

Answer:

Given,

Mrs. Stevenson has used 4\(\frac{2}{3}\) inches of string.

She needs 1\(\frac{6}{7}\) inches more.

4\(\frac{2}{3}\) + 1\(\frac{6}{7}\)

4 + \(\frac{2}{3}\) + 1 + \(\frac{6}{7}\)

4 + 1 + \(\frac{2}{3}\) + \(\frac{6}{7}\)

5 + \(\frac{2}{3}\) + \(\frac{6}{7}\) = 6 \(\frac{11}{21}\)

Mrs. Stevenson will have used 6 \(\frac{11}{21}\) inches of string.

Question 6.

It takes Lacy 8\(\frac{1}{3}\) seconds to climb up the slide and 2\(\frac{1}{4}\) seconds to go down the slide. How many seconds is Lacy’s trip up and down the slide?

Lacy’s trip is _____________ seconds long.

Answer:

Given,

It takes Lacy 8\(\frac{1}{3}\) seconds to climb up the slide and 2\(\frac{1}{4}\) seconds to go down the slide.

8\(\frac{1}{3}\) + 2\(\frac{1}{4}\)

8 + \(\frac{1}{3}\) + 2 + \(\frac{1}{4}\)

10 + \(\frac{7}{12}\) = 10\(\frac{7}{12}\)

Lacy’s trip is 10\(\frac{7}{12}\) seconds long.

**Solve each problem. Write answers in simplest form. Show your work.**

Question 1.

Eric needs \(\frac{1}{2}\) deck of playing cards for a magic trick. He only has \(\frac{2}{7}\) of a deck. What fraction of a deck does Eric still need?

Eric still needs _______________ of a deck.

Answer:

Given,

Eric needs \(\frac{1}{2}\) deck of playing cards for a magic trick.

He only has \(\frac{2}{7}\) of a deck

\(\frac{1}{2}\) – \(\frac{2}{7}\) = \(\frac{3}{14}\)

Eric still needs \(\frac{3}{14}\) of a deck.

Question 2.

Randy ran 1\(\frac{3}{4}\) miles. Natasha ran \(\frac{9}{10}\) miles. How many more miles did Randy run than Natasha?

Randy ran ______________ miles more than Natasha.

Answer:

Given,

Randy ran 1\(\frac{3}{4}\) miles. Natasha ran \(\frac{9}{10}\) miles.

1\(\frac{3}{4}\) – \(\frac{9}{10}\) = \(\frac{17}{20}\)

Randy ran \(\frac{17}{20}\) miles more than Natasha.

Question 3.

A soccer ball weighs 6 ounces when fully inflated. Raymundo has inflated the ball to 4\(\frac{2}{3}\) ounces. How many more ounces must be added before the ball is fully inflated?

The ball needs _____________ more ounces to be fully inflated.

Answer:

Given,

A soccer ball weighs 6 ounces when fully inflated.

Raymundo has inflated the ball to 4\(\frac{2}{3}\) ounces.

6 – 4\(\frac{2}{3}\)

5 \(\frac{3}{3}\)– 4\(\frac{2}{3}\) = 1\(\frac{1}{3}\)

The ball needs 1\(\frac{1}{3}\) more ounces to be fully inflated.

Question 4.

In January, employees at Home Real Estate Company worked 6\(\frac{3}{4}\) hours a day. In February, employees worked 7\(\frac{1}{8}\) hours a day. How many more hours did employees work daily during February than during January?

Employees worked _____________ hours more during February.

Answer:

Given,

In January, employees at Home Real Estate Company worked 6\(\frac{3}{4}\) hours a day. In February, employees worked 7\(\frac{1}{8}\) hours a day.

7\(\frac{1}{8}\) – 6\(\frac{3}{4}\) = \(\frac{3}{8}\)

Employees worked \(\frac{3}{8}\) hours more during February.

Question 5.

Peter’s hat size is 7\(\frac{3}{8}\) units. Cal’s hat size is 6\(\frac{7}{12}\) units. How many units larger is Peter’s hat size than Cals?

Peter’s hat size is ____________ units larger than Cal’s.

Answer:

Given,

Peter’s hat size is 7\(\frac{3}{8}\) units.

Cal’s hat size is 6\(\frac{7}{12}\) units.

7\(\frac{3}{8}\) – 6\(\frac{7}{12}\) = \(\frac{19}{24}\)

Peter’s hat size is \(\frac{19}{24}\) units larger than Cal’s.

Question 6.

Mrs. Anderson uses 3\(\frac{1}{5}\) cups of apples for her pies. Mrs. Woods uses 4\(\frac{2}{3}\) cups of apples for her pies. How many more cups of apples does Mrs. Woods use than Mrs. Anderson?

Mrs. Woods uses _______________ more cups of apples.

Answer:

Given,

Mrs. Anderson uses 3\(\frac{1}{5}\) cups of apples for her pies.

Mrs. Woods uses 4\(\frac{2}{3}\) cups of apples for her pies.

4\(\frac{2}{3}\) – 3\(\frac{1}{5}\) = 1 \(\frac{7}{15}\)

Mrs. Woods uses 1 \(\frac{7}{15}\) more cups of apples.