We included **HMH Into Math Grade 4 Answer Key PDF** **Module 15 Lesson 6 Practice Solving Fraction Problems **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 15 Lesson 6 Answer Key Practice Solving Fraction Problems

I Can add and subtract fractions and mixed numbers with like denominators to solve real-world problems.

**Step It Out**

On Monday, Sasha walked to school by way of the library. After school, she walked with Benny to his home to study. How far did Sasha walk on Monday?

A. Write an equation to model the problem. Use d to represent the total distance.

Answer:

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

Explanation:

= 2\(\frac{1}{4}\) + 1\(\frac{1}{4}\) + 1\(\frac{1}{4}\)

= \(\frac{9}{4}\) + \(\frac{5}{4}\) + \(\frac{5}{4}\)

= \(\frac{9 + 5 + 5}{4}\)

= \(\frac{19}{4}\)

= 4\(\frac{3}{4}\)

B. Find the value of d.

Sasha walked _________ miles on Monday.

Answer:

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

Explanation:

d = 2\(\frac{1}{4}\) + 1\(\frac{1}{4}\) + 1\(\frac{1}{4}\)

d = 4\(\frac{3}{4}\)

**Turn and Talk** Describe how you could use a visual representation to help you solve this problem?

Answer:

Explanation:

The visualization helps students to summarize what key information is known and see what the problem is asking them to solve for.

Use of an appropriate visual can also reveal the relationships between the quantities identified in the problem.

Question 2.

Cheyanne and her family ride bikes on trails in the state park. On Saturday, they ride on the Lake Trail and the Wildflower Trail. On Sunday, they ride their bikes on the Forest Trail and the Meadow Trail. On which day do they ride farther? How much farther?

A. How far do Cheyanne and her family ride on Saturday? Show your work.

Answer:

6\(\frac{2}{8}\)miles

Explanation:

On Saturday, they ride on the Lake Trail and the Wildflower Trail.

4\(\frac{3}{8}\) + 1\(\frac{7}{8}\)

= \(\frac{35}{8}\) + \(\frac{15}{8}\)

= \(\frac{35 + 15}{8}\)

= \(\frac{50}{8}\)

= 6\(\frac{2}{8}\)miles

B. How far do Cheyanne and her family ride on Sunday? Show your work.

Answer:

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

Explanation:

On Sunday, they ride their bikes on the Forest Trail and the Meadow Trail

3\(\frac{5}{8}\) + 2\(\frac{1}{8}\)

= \(\frac{29}{8}\) + \(\frac{17}{8}\)

= \(\frac{29 + 17}{8}\)

= \(\frac{46}{8}\)

= 5 \(\frac{6}{8}\)

C. On which day do they ride more? How much more? Show your work.

Answer:

2\(\frac{2}{8}\)

Explanation:

On Sunday, 5 \(\frac{6}{8}\)

On Saturday, 8 miles

Ride on Saturday 8 – 5 \(\frac{6}{8}\)

= 8 – \(\frac{46}{8}\)

= \(\frac{64 – 46}{8}\)

= \(\frac{18}{8}\)

= 2\(\frac{2}{8}\)

**Turn and Talk** If Cheyanne and her family do not want to ride more than 6 miles in one day, on what pairs of trails could they ride?

Answer:

4 miles

Explanation:

Meadow Trail + Wildflower Trail

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

= \(\frac{17}{8}\) + \(\frac{15}{8}\)

= \(\frac{17 + 15}{8}\)

= \(\frac{32}{8}\)

= 4 miles

**Check Understanding**

Question 1.

Jonas has a piece of rope that is 4\(\frac{3}{12}\) feet long. He cuts off 2\(\frac{1}{12}\) feet to give to his brother and 1\(\frac{1}{12}\) feet to give to his sister. How much rope does Jonas have left?

Answer:

1\(\frac{1}{12}\)

Explanation:

Jonas has a piece of rope that is 4\(\frac{3}{12}\) feet long.

He cuts off 2\(\frac{1}{12}\) feet to give to his brother and

1\(\frac{1}{12}\) feet to give to his sister,

= 2\(\frac{1}{12}\) + 1\(\frac{1}{12}\)

= \(\frac{25}{12}\) + \(\frac{13}{12}\)

= \(\frac{25+13}{12}\) = \(\frac{38}{12}\)

= 3\(\frac{2}{12}\)

Total rope left with Jonas = 4\(\frac{3}{12}\) – 3\(\frac{2}{12}\)

= \(\frac{51}{12}\) – \(\frac{38}{12}\)

= \(\frac{13}{12}\) = 1\(\frac{1}{12}\)

Question 2.

Gina’s older sister babysits for 1\(\frac{3}{4}\) hours after school on Monday, 2\(\frac{1}{4}\) hours after school on Tuesday, and 1\(\frac{1}{4}\) hours after school on Thursday. How many hours does Gina’s older sister baby sit this week?

Answer:

5\(\frac{1}{4}\) hours

Explanation:

Gina’s older sister babysits for 1\(\frac{3}{4}\) hours after school on Monday,

2\(\frac{1}{4}\) hours after school on Tuesday and

1\(\frac{1}{4}\) hours after school on Thursday.

Total hours Gina’s older sister baby sit this week

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

= \(\frac{7}{4}\) + \(\frac{9}{4}\) + \(\frac{5}{4}\)

= \(\frac{7+9+5}{4}\) = \(\frac{21}{4}\) = 5\(\frac{1}{4}\)

**On Your Own**

Question 3.

**Open-Ended** Mia watches her older sister Amy practice long jumps for the track meet. Amy jumps 3\(\frac{3}{5}\) feet on her first try and 2\(\frac{2}{5}\) feet on her second try. Using the information given, write and solve a word problem involving addition or subtraction. Use an equation to represent the problem.

Answer:

If we apply addition equation , he jumps 6 feet.

If we apply, subtraction equation, he jumps 1\(\frac{1}{5}\) more in first try than in second try.

Explanation:

Amy jumps 3\(\frac{3}{5}\) feet on her first try and

2\(\frac{2}{5}\) feet on her second try.

Difference between first try and second try = 3\(\frac{3}{5}\) – 2\(\frac{2}{5}\)

= \(\frac{18}{5}\) – \(\frac{12}{5}\)

= \(\frac{18-12}{5}\) = \(\frac{6}{5}\)

= 1\(\frac{1}{5}\)

Total jumps in both tries = 3\(\frac{3}{5}\) + 2\(\frac{2}{5}\)

= \(\frac{18}{5}\) + \(\frac{12}{5}\)

= \(\frac{18+12}{5}\) = \(\frac{30}{5}\)

= 6 feet long

Question 4.

**Reason** Jack and his friends go to the movies and each gets a medium-sized bag of popcorn. At the end of the movie, Jack and his friends each have \(\frac{3}{5}\) of their popcorn remaining. If there are 3 full bags of popcorn when the leftovers are combined, how many people went to the movies? Explain your thinking.

Answer:

\(\frac{9}{5}\) people

Explanation:

Jack and his friends each have \(\frac{3}{5}\) of their popcorn remaining.

If there are 3 full bags of popcorn when the leftovers are combined,

Number of people went to the movies = 3 x \(\frac{3}{5}\)

= \(\frac{9}{5}\)

Question 5.

Amir wants to put a fence around a garden and another around a fruit tree. He needs 6\(\frac{3}{8}\) yards to fence in the garden. He needs 1\(\frac{4}{8}\) yards more fencing for the garden than for the fruit tree. How much fencing does he need for the fruit tree? Explain your thinking.

Answer:

7\(\frac{4}{8}\)

Explanation:

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

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

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

= \(\frac{48}{8}\) + \(\frac{12}{8}\)

= \(\frac{48 + 12}{8}\)

= \(\frac{60}{8}\)

=7\(\frac{4}{8}\)

Question 6.

Ms. Aria practices for a holiday concert. She practices for a total of 8\(\frac{6}{8}\) hours on Monday, Wednesday, and Friday. If she practices for 3\(\frac{2}{8}\) hours on Monday and 2\(\frac{7}{8}\) hours on Wednesday, for how many hours does Ms. Aria practice on Friday?

Answer:

3\(\frac{1}{8}\) hours

Explanation:

Aria practices 8\(\frac{6}{8}\) hours on Monday, Wednesday and Friday.

Aria practices for 3\(\frac{2}{8}\) hours on Monday and

2\(\frac{7}{8}\) hours on Wednesday,

Total hours she practice on Friday =

8\(\frac{6}{8}\) – (3\(\frac{2}{8}\) + 2\(\frac{7}{8}\))

= \(\frac{74}{8}\) – (\(\frac{26}{8}\) + \(\frac{23}{8}\)

= \(\frac{74}{8}\) – \(\frac{26+23}{8}\)

= \(\frac{74}{8}\) – \(\frac{49}{8}\)

= \(\frac{74-49}{8}\) = \(\frac{25}{8}\)

= 3\(\frac{1}{8}\) hours

Question 7.

**STEM** Humans can have a large impact on the environment. Suppose a person generates 4\(\frac{3}{5}\) pounds of trash per day. If that person recycles 1\(\frac{4}{5}\) pounds of that trash, how much will be left to go to the landfill?

Answer:

2\(\frac{4}{5}\) pounds

Explanation:

A person generates 4\(\frac{3}{5}\) pounds of trash per day.

If that person recycles 1\(\frac{4}{5}\) pounds of that trash,

Total trash left to go to the landfill = 4\(\frac{3}{5}\) – 1\(\frac{4}{5}\)

= \(\frac{23}{5}\) – \(\frac{9}{5}\)

= \(\frac{23-9}{5}\) = \(\frac{14}{5}\)

= 2\(\frac{4}{5}\)

Question 8.

Zach and his brother go fishing at the lake. Zach catches a fish that is 4\(\frac{5}{12}\) pounds and his brother catches a fish that is 6\(\frac{2}{12}\) pounds heavier than Zach’s fish is. What is the total weight of the fish that they catch at the lake?

Answer:

15 pounds

Explanation:

Zach catches a fish that is 4\(\frac{5}{12}\) pounds and

his brother catches a fish that is 6\(\frac{2}{12}\) pounds heavier than Zach’s fish is,

= 4\(\frac{5}{12}\) + 6\(\frac{2}{12}\)

= \(\frac{53}{12}\) + \(\frac{74}{12}\)

= \(\frac{53+74}{12}\) = \(\frac{127}{12}\)

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

The total weight of the fish that they catch at the lake = 4\(\frac{5}{12}\) + 10\(\frac{7}{12}\)

= \(\frac{53}{12}\) + \(\frac{127}{12}\) = \(\frac{53+127}{12}\)

= \(\frac{180}{12}\) = 15 pounds

Question 9.

**Reason** Adrienne is 12\(\frac{4}{6}\) years old. Her dad is 28\(\frac{5}{6}\) years older than Adrienne is, and her mom is \(\frac{8}{6}\) years younger than her dad is. How old are Adrienne’s mom and dad?

Answer:

Adrienne’s mom and dad ages are

mom age

40\(\frac{1}{6}\)

dad age:

41\(\frac{3}{6}\)

Explanation:

Father age:

12\(\frac{4}{6}\) + 28\(\frac{5}{6}\)

= 12\(\frac{4}{6}\) + 28\(\frac{5}{6}\)

=\(\frac{76}{6}\) + \(\frac{173}{6}\)

=\(\frac{249}{6}\)

=41\(\frac{3}{6}\)

Mother age:

41\(\frac{3}{6}\) – \(\frac{8}{6}\)

= \(\frac{249}{6}\) – \(\frac{8}{6}\)

=\(\frac{249 – 8}{6}\)

=\(\frac{241}{6}\)

=40\(\frac{1}{6}\)

Question 10.

Mr. Tate wants to paint a house. He has some paint and buys another 5\(\frac{3}{6}\) gallons. He now has 14\(\frac{1}{6}\) gallons of paint. How much paint does Mr. Tate start with?

Answer:

8\(\frac{4}{6}\) gallons

Explanation:

Tate buys another 5\(\frac{3}{6}\) gallons.

He now has 14\(\frac{1}{6}\) gallons of paint.

With how much paint does Mr. Tate start = 14\(\frac{1}{6}\) – 5\(\frac{3}{6}\)

= \(\frac{85}{6}\) – \(\frac{33}{6}\)

= \(\frac{85-33}{6}\) = \(\frac{52}{6}\)

= 8\(\frac{4}{6}\)

Question 11.

**Attend to Precision** Jasmine buys a piece of fabric that is 3 yards long. She wants to cut the fabric into pieces that are \(\frac{5}{6}\) yards long. How many pieces can she cut? Will she have any left over? If so, how much? Explain your thinking.

Answer:

3 pieces and \(\frac{3}{6}\) she have any left over fabric

Explanation:

a piece of fabric that is 3 yards long & cut the fabric into pieces that are \(\frac{5}{6}\) yards long

3 – \(\frac{15}{6}\)

= \(\frac{18 – 15}{6}\)

= \(\frac{3}{6}\)