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

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.

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?

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.
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?

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?
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.
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.
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?
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.
9 $$\frac{7}{8}$$

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

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.
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 = _________
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.
$$\frac{2}{8}$$ = =$$\frac{1}{4}$$ = 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?
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$$\frac{1}{12}$$

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.
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.
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?
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?

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$$\frac{4}{8}$$

Question 6.
1$$\frac{9}{10}$$ + 1$$\frac{8}{10}$$ = ____________
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$$\frac{2}{4}$$ = ____________
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.
$$\frac{5}{6}$$ + $$\frac{5}{6}$$ + $$\frac{5}{6}$$ = ___________
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$$\frac{7}{8}$$ = ____________
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.

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?
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.
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$$\frac{4}{10}$$ = ____________
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$$\frac{1}{8}$$ = __________
$$\frac{6}{8}$$ = $$\frac{3}{4}$$
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$$\frac{1}{6}$$ = ___________
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$$\frac{8}{12}$$ = ___________
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!

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