We included **HMH Into Math Grade 4 Answer Key PDF** **Module 15 Lesson 3 Add and Subtract Mixed Numbers to Solve Problems **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 15 Lesson 3 Answer Key Add and Subtract Mixed Numbers to Solve Problems

I Can use visual models and equations to add and subtract mixed numbers with like denominators.

**Spark Your Learning**

A diner serves fresh bread with certain meals. At the end of the night, there are 1\(\frac{3}{4}\) loaves of whole wheat bread left and 1\(\frac{2}{4}\) loaves of white bread left. How many loaves of bread does the diner have at the end of the night?

Draw a visual model to help you solve the problem.

Answer:

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

Visual model

Explanation:

whole wheat bread 1\(\frac{3}{4}\) + white wheat bread 1\(\frac{2}{4}\)

= \(\frac{7}{4}\) + \(\frac{6}{4}\)

= \(\frac{6+7}{4}\)

= \(\frac{13}{4}\)

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

**Turn and Talk** How could you find the solution without using a visual model? Write an equation to model the problem.

Answer:

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

Explanation:

**Build Understanding**

Question 1.

A diner sells pie by the slice. At the end of the night, they have the following slices left. How much pie is left?

Show your work.

Answer:

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

Explanation:

Blueberry + Apple

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

= \(\frac{10}{6}\) + \(\frac{13}{6}\)

= \(\frac{10+13}{6}\)

= \(\frac{23}{6}\)

= 3 \(\frac{5}{6}\)

Total slices of pie = 6 x 5 = 30

= \(\frac{30 – 23}{6}\) = \(\frac{7}{6}\)

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

A. How many wholes do you have? What fraction represents the remaining slices?

Answer:

3 wholes

1\(\frac{1}{6}\) fraction slices

Explanation:

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

= \(\frac{10}{6}\) + \(\frac{13}{6}\)

=\(\frac{10 + 13}{6}\)

=\(\frac{23}{6}\)

=3 \(\frac{5}{6}\) – 30

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

B. Write an equation to model the problem.

Answer:

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

Explanation:

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

= \(\frac{10}{6}\) + \(\frac{13}{6}\)

=\(\frac{23}{6}\)

C. There are __________ pies left.

Answer:

7 pies left

Explanation:

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

= \(\frac{10}{6}\) + \(\frac{13}{6}\)

=\(\frac{23}{6}\) – 30

= \(\frac{7}{6}\) = 1\(\frac{1}{6}\)

**Turn and Talk** How do you know if you need to rename a mixed number in your answer?

Answer:

If the numerator is more than the denominator the fraction is converted into mixed fraction.

Explanation:

By seeing the improper fraction,

for example;

\(\frac{23}{6}\) = 3\(\frac{5}{6}\)

**Step It Out**

Question 2.

At the start of the day, the diner has this bag of potatoes. During breakfast, they serve 8\(\frac{4}{8}\) pounds of potatoes. How many pounds of potatoes remain?

A. Draw a visual model of the number of potatoes they have at the beginning of the day.

Answer:

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

B. Update your drawing to show the potatoes used during the day.

Answer:

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

Explanation:

9 \(\frac{7}{8}\) – 8 \(\frac{4}{8}\)

= \(\frac{79}{8}\) – \(\frac{68}{8}\)

= \(\frac{79 – 68}{8}\)

= \(\frac{11}{8}\)

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

one whole and \(\frac{3}{8}\) fraction

C. Model the problem with an equation and record what is remaining in the drawing as the solution.

There are ___________ pounds of potatoes left after breakfast.

Answer:

1\(\frac{3}{8}\) pounds of potatoes left after breakfast

Explanation:

9 \(\frac{7}{8}\) – 8 \(\frac{4}{8}\)

= \(\frac{79}{8}\) – \(\frac{68}{8}\)

= \(\frac{79 – 68}{8}\)

= \(\frac{11}{8}\)

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

**Turn and Talk** How could you solve this problem without drawing a visual representation?

Answer:

By subtracting the given fractions

9 \(\frac{7}{8}\) – 8 \(\frac{4}{8}\)

Explanation:

9 \(\frac{7}{8}\) – 8 \(\frac{4}{8}\)

= \(\frac{79}{8}\) – \(\frac{68}{8}\)

= \(\frac{79 – 68}{8}\)

= \(\frac{11}{8}\)

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

Question 3.

The diner has 2\(\frac{3}{8}\) pounds of cheddar cheese and 1\(\frac{7}{8}\) pounds of mozzarella cheese. How many pounds of cheese does the diner have?

A. Draw a picture to help you visualize the problem.

Answer:

Explanation:

1 whole is of 8 slices,

2\(\frac{3}{8}\) pounds of cheddar cheese and

1\(\frac{7}{8}\) pounds of mozzarella cheese.

Total pounds of cheese does the diner have = 4\(\frac{2}{8}\)

B. Write an equation to model the problem. Use c to represent the total amount of cheese.

Answer:

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

Explanation:

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

= \(\frac{19}{8}\) + \(\frac{15}{8}\)

= \(\frac{19 + 15}{8}\)

= \(\frac{34}{8}\)

= 4\(\frac{2}{8}\)

C. To find the value of c, add the fractional parts of the mixed numbers, and then add the whole number parts.

\(\frac{3}{8}\) + \(\frac{7}{8}\) = ________

2 + 1 = _________

Answer:

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

Explanation:

\(\frac{3}{8}\) + \(\frac{7}{8}\) = \(\frac{10}{8}\) = 1\(\frac{2}{8}\)

2 + 1 =3

D. Write the value of c as a mixed number. Rename if necessary so the fractional part is less than 1. Show your work.

Answer:

\(\frac{2}{8}\) = =\(\frac{1}{4}\) = 0.25

Explanation:

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

= \(\frac{19}{8}\) + \(\frac{15}{8}\)

= \(\frac{19 + 15}{8}\)

=\(\frac{34}{8}\)

= 4\(\frac{2}{8}\)

the fractional part is less than 1

\(\frac{2}{8}\) = \(\frac{1}{4}\) = 0.25

**Check Understanding**

Question 1.

Basketball practice lasts 2\(\frac{6}{12}\) hours on Monday and 1\(\frac{5}{12}\) hours on Wednesday. How many hours does practice last over both days? How much longer is practice on Monday than on Wednesday?

Answer:

Number of practice over both hours = 3\(\frac{11}{12}\)

Number of hours longer on Monday than on Wednesday = 1\(\frac{1}{12}\)

Explanation:

Basket ball practice on Monday and on Wednesday = 2\(\frac{6}{12}\) + 1\(\frac{5}{12}\)

= \(\frac{30}{12}\) + \(\frac{17}{12}\)

= \(\frac{47}{12}\)

= 3\(\frac{11}{12}\)

Monday practice is much longer than on Wednesday

= 2\(\frac{6}{12}\) – 1\(\frac{5}{12}\)

= \(\frac{30}{12}\) – \(\frac{17}{12}\)

= \(\frac{30 – 17}{12}\)

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

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

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

**On Your Own**

Question 2.

**Use Tools** Isabel has 2\(\frac{5}{6}\) hours free to read and play outside. If she spends 1\(\frac{3}{6}\) hours reading, how long does she have to play outside? Represent the situation with a visual fraction model and an equation.

Answer:

1\(\frac{2}{6}\)

Explanation:

Isabel has 2\(\frac{5}{6}\)hours to read

If he spends 1\(\frac{3}{6}\) hours on reading,

Total ours she play out side = 2\(\frac{5}{6}\) – 1\(\frac{3}{6}\)

=\(\frac{17}{6}\) – \(\frac{9}{6}\)

= \(\frac{17 – 9}{6}\)

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

= 1\(\frac{2}{6}\)

Question 3.

**Reason** There are 10\(\frac{5}{8}\) cups of dog food in a bag. Alton feeds his dog \(\frac{3}{8}\) cup of food every day. How many cups of food are left in the bag after 4 days? Show your work.

Answer:

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

Explanation:

There are 10\(\frac{5}{8}\) cups of dog food in a bag.

Alton feeds his dog \(\frac{3}{8}\) cup of food every day,

Total cups of food left in the bag after 4 days,

10\(\frac{5}{8}\) – 4\(\frac{3}{8}\)

= \(\frac{85}{8}\) – \(\frac{35}{8}\)

= \(\frac{50}{8}\) = 6\(\frac{2}{8}\)

Question 4.

Ms. Goldberg rides the train for 1\(\frac{1}{12}\) hours to get to work. Her train ride home from work takes 1\(\frac{3}{12}\) hours because the train makes more stops. How many hours does Ms. Goldberg spend on the train in 1 day? In 3 days?

Answer:

1 day = 2\(\frac{4}{12}\)

3 days = 5\(\frac{4}{12}\)

Explanation:

Ms. Goldberg rides the train for 1\(\frac{1}{12}\) hours to get to work.

Her train ride home from work takes 1\(\frac{3}{12}\) hours.

Total hours Ms. Goldberg spend on the train in 1 day,

= 1\(\frac{1}{12}\) + 1\(\frac{3}{12}\)

= \(\frac{13}{12}\) + 1\(\frac{15}{12}\)

= \(\frac{28}{12}\) = 2\(\frac{4}{12}\)

In 3 days = 3\(\frac{28}{12}\) = \(\frac{64}{12}\)

= 5\(\frac{4}{12}\)

Question 5.

**Attend to Precision** Kyra has 1\(\frac{3}{8}\) pounds of clay. How much clay must she buy to have 2\(\frac{7}{8}\) pounds of clay to make a vase?

Answer:

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

Explanation:

Kyra has 1\(\frac{3}{8}\) pounds of clay.

Total clay she must buy to have 2\(\frac{7}{8}\) pounds of clay to make a vase,

= 2\(\frac{7}{8}\) – 1\(\frac{3}{8}\)

= \(\frac{23}{8}\) – \(\frac{11}{8}\)

= \(\frac{12}{8}\) = 1\(\frac{4}{8}\)

**Find the sum. Write your answer as a mixed number.**

Question 6.

1\(\frac{9}{10}\) + 1\(\frac{8}{10}\) = ____________

Answer:

3\(\frac{7}{10}\)

Explanation:

1\(\frac{9}{10}\) + 1\(\frac{8}{10}\)

= \(\frac{19}{10}\) + \(\frac{18}{10}\)

= \(\frac{37}{10}\) = 3\(\frac{7}{10}\)

Question 7.

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

Answer:

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

Explanation:

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

= \(\frac{13}{4}\) + \(\frac{6}{4}\)

= \(\frac{19}{4}\) = 4\(\frac{3}{4}\)

Question 8.

\(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) = ___________

Answer:

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

Explanation:

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

= \(\frac{15}{6}\) = 2\(\frac{3}{6}\)

Question 9.

2\(\frac{5}{8}\) + 1\(\frac{7}{8}\) = ____________

Answer:

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

Explanation:

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

= \(\frac{21}{8}\) + \(\frac{15}{8}\)

= \(\frac{36}{8}\) = 4\(\frac{4}{8}\)

Question 10.

**Open-ended** Write and solve a subtraction word problem to match this visual fraction model. Write an equation to represent your problem.

Answer:

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

Cat use to drink 2\(\frac{3}{5}\) cups of milk daily but on that day it drank 1\(\frac{2}{5}\) milk only.

How much milk is left?

Explanation:

2\(\frac{3}{5}\) – 1\(\frac{2}{5}\)

=\(\frac{13}{5}\) – \(\frac{7}{5}\)

=\(\frac{13 – 7}{5}\)

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

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

Question 11.

**Reason** Jana has 3 bags of dried fruit. Each bag has 1\(\frac{4}{8}\) cups in it. How many cups of dried fruit does Jana have?

Answer:

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

Explanation:

Jana has 3 bags of dried fruit.

Each bag has 1\(\frac{4}{8}\) cups in it.

Convert mixed number to improper fraction = \(\frac{12}{8}\)

Total cups of dried fruit Jana have = 3\(\frac{12}{8}\)

= \(\frac{36}{8}\) = 4\(\frac{4}{8}\)

Question 12.

**Critique Reasoning** Kevin writes 1\(\frac{3}{6}\) + 2\(\frac{4}{6}\) = \(\frac{13}{6}\) + \(\frac{24}{6}\) = \(\frac{37}{6}\) = 6\(\frac{1}{6}\) . What does Kevin do wrong? Find the correct sum by changing the mixed numbers to fractions.

Answer:

Kevin add the whole number with numerator, instead of multiplying with the denominator.

Explanation:

Correct solution follows as shown below,

1\(\frac{3}{6}\) + 2\(\frac{4}{6}\) = \(\frac{9}{6}\) + \(\frac{16}{6}\) = \(\frac{25}{6}\) = 4\(\frac{1}{6}\)

**Find the difference. If possible, write your answer as a mixed number.**

Question 13.

2\(\frac{6}{10}\) – 1\(\frac{4}{10}\) = ____________

Answer:

1\(\frac{2}{10}\)

Explanation:

2\(\frac{6}{10}\) – 1\(\frac{4}{10}\)

convert into improper fraction

\(\frac{26}{10}\) – \(\frac{14}{10}\)

\(\frac{12}{10}\) = 1\(\frac{2}{10}\)

Question 14.

5\(\frac{7}{8}\) – 5\(\frac{1}{8}\) = __________

Answer:

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

Explanation:

5\(\frac{7}{8}\) – 5\(\frac{1}{8}\)

convert into improper fraction

\(\frac{47}{8}\) – \(\frac{41}{8}\)

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

Question 15.

2\(\frac{5}{6}\) – 1\(\frac{1}{6}\) = ___________

Answer:

1\(\frac{4}{6}\)

Explanation:

2\(\frac{5}{6}\) – 1\(\frac{1}{6}\)

convert into improper fraction

\(\frac{17}{6}\) – \(\frac{7}{6}\)

\(\frac{10}{6}\) = 1\(\frac{4}{6}\)

Question 16.

3\(\frac{9}{12}\) – 2\(\frac{8}{12}\) = ___________

Answer:

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

Explanation:

3\(\frac{9}{12}\) – 2\(\frac{8}{12}\)

convert into improper fraction

\(\frac{45}{12}\) – \(\frac{32}{12}\)

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

**I’m in a Learning Mindset!**

How do I choose effective strategies to add and subtract mixed numbers?

Answer:

By observing the denominators, whether they are like fractions or unlike fractions.

Explanation:

The most effective strategy to add and subtract mixed numbers is to first convert into like fraction,

by taking LCD or LCM of the denominators.