We included **HMH Into Math Grade 4 Answer Key PDF** **Module 15 Lesson 1 Add and Subtract Fractions to Solve Problems **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 15 Lesson 1 Answer Key Add and Subtract Fractions to Solve Problems

I Can add and subtract fractions greater than one with like denominators to solve real-world problems.

**Spark Your Learning**

Mrs. Hanson needs 9 servings of almonds. Each serving weighs \(\frac{1}{4}\) pound. She already has \(\frac{3}{4}\) pound of almonds. How many more pounds of almonds does she need?

Draw a fraction model to help you solve the problem.

Answer:

Almonds already has = \(\frac{3}{4}\)

Almonds needed = \(\frac{6}{4}\)

Explanation:

Mrs. Hanson needs 9 servings of almonds.

Each serving weighs \(\frac{1}{4}\) pounds.

Already he has \(\frac{3}{4}\) pounds of almonds.

Total Almonds he needed = \(\frac{9}{4}\) – \(\frac{3}{4}\)

= \(\frac{6}{4}\) pounds.

**Turn and Talk** One classmate represents this problem with an addition equation and another uses a subtraction equation. Who is correct and how do you know?

Answer:

Both are correct.

Explanation:

Addition and subtractions are inverse to each other,

that means we can undo an addition through subtraction,

and we can undo a subtraction through addition.

Addition equation \(\frac{3}{4}\) + \(\frac{6}{4}\) = \(\frac{9}{4}\)

Subtraction equation \(\frac{9}{4}\) – \(\frac{3}{4}\) = \(\frac{6}{4}\)

**Build Understanding**

Question 1.

Brooke and Bailey each bring \(\frac{1}{4}\)-pound bowls of grapes to serve at a class party. This shows the number of bowls each person brings. How many pounds of grapes do they bring?

Show how you could find the total amount.

Answer:

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

A. What does a unit fraction represent in the problem?

Answer:

Unit fraction is \(\frac{1}{4}\)

B. What addition equation models the problem?

Answer:

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

C. How many bowls of grapes do Brooke and Bailey bring?

Answer:

7 bowls

D. What is the weight of the grapes the two students bring?

Answer:

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

Explanation:

Brooke brings 5 bowls of \(\frac{1}{4}\) pounds of grapes = \(\frac{5}{4}\)

Bailey brings 2 bowls of \(\frac{1}{4}\) pounds of grapes = \(\frac{2}{4}\)

Total pounds of grapes = \(\frac{5}{4}\) + \(\frac{2}{4}\)

= \(\frac{7}{4}\) pounds of grapes.

**Step It Out**

Question 2.

Mrs. Hanson makes a snack mix with this bag of raisins and this box of cereal. The students eat \(\frac{14}{12}\) pounds of snack mix at the party. How much snack mix is left?

A. How can you find the weight of the snack mix Mrs. Hanson makes?

Answer:

By adding both the weights of Cereal and Raisins mix.

B. Model this part of the problem with an equation and find how much snack mix Mrs. Hanson makes.

Answer:

\(\frac{8}{12}\) + \(\frac{9}{12}\)

C. How can you find how much is left after the students eat some?

Answer:

By subtracting the eaten portion from the total snack mix.

D. Model this part of the problem with an equation and find how much snack mix is left.

Answer:

\(\frac{17}{12}\) – \(\frac{14}{12}\) = \(\frac{3}{12}\)

Explanation:

Weight of Raisins is \(\frac{8}{12}\)

Weight of Cereals is \(\frac{9}{12}\)

total weight of snack mix = \(\frac{8}{12}\) + \(\frac{9}{12}\)

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

The students eat \(\frac{14}{12}\) pounds of snack mix at the party.

Snack mix is left = \(\frac{17}{12}\) – \(\frac{14}{12}\)pounds

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

**Turn and Talk** In terms of the snack mix, what does it mean for the amount of snack mix Mrs. Hanson makes to be described as a fraction greater than 1?

Answer:

\(\frac{17}{12}\)

Explanation:

When the numerator is greater than denominator than we express the fraction as greater than 1.

**Check Understanding**

Question 1.

Delia has \(\frac{4}{10}\) yard of white ribbon and \(\frac{8}{10}\) yard of red ribbon. How many yards of ribbon does she have?

Answer:

\(\frac{12}{10}\) yards of ribbon.

Explanation:

Delia has \(\frac{4}{10}\) yard of white ribbon,

\(\frac{8}{10}\) yard of red ribbon.

Total yards of ribbon she have = \(\frac{4}{10}\) + \(\frac{8}{10}\)

= \(\frac{12}{10}\) yards ribbon.

Question 2.

Frankie has \(\frac{3}{8}\) pound of sunflower seeds and \(\frac{7}{8}\) pound of cracked corn that he mixes together for bird feed. He puts \(\frac{9}{8}\) pounds in a bird feeder. How many pounds does he have now?

Answer:

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

Explanation:

Frankie has \(\frac{3}{8}\) pound of sunflower seeds,

\(\frac{7}{8}\) pound of cracked corn that he mixes together for bird feed.

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

He puts \(\frac{9}{8}\) pounds in a bird feeder.

Total pounds he have now = \(\frac{10}{8}\) – \(\frac{9}{8}\)

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

**On Your Own**

Question 3.

**Reason** Brad has some water in a bucket. He pours \(\frac{3}{10}\) liter of water on some house plants. Now there is \(\frac{4}{10}\) liter of water in the bucket. How many liters of water did Brad have in the bucket before watering the plants? Show your work.

Answer:

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

Explanation:

Brad pours \(\frac{3}{10}\) liter of water on some house plants.

Now there is \(\frac{4}{10}\) liter of water in the bucket.

Total liters of water Brad have in the bucket before watering the plants

= \(\frac{3}{10}\) + \(\frac{4}{10}\)

= \(\frac{3+4}{10}\) = \(\frac{7}{10}\)

Question 4.

**Use Tools** Lily spends \(\frac{3}{5}\) hour reading, \(\frac{2}{5}\) hour helping her mother, and \(\frac{1}{5}\) hour playing with her little brother. How many hours does Lily spend on these tasks? Make a visual fraction model to represent the problem.

Answer:

Lily spends \(\frac{6}{5}\) hours.

Explanation:

Lily spends \(\frac{3}{5}\) hour reading,

\(\frac{2}{5}\) hour helping her mother,

and \(\frac{1}{5}\) hour playing with her little brother.

Total hours Lily spend on these tasks

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

= \(\frac{3+2+1}{5}\) = \(\frac{6}{5}\)

Question 5.

A state park has 4 trails that are less than 1 mile in length. Spencer wants to walk more than \(\frac{15}{10}\) miles, but less than \(\frac{19}{10}\) miles. Which trails could he walk? Justify your response.

Answer:

Trail C \(\frac{4}{10}\) miles.

Explanation:

A state park has 4 trails that are less than 1 mile in length.

Spencer wants to walk more than \(\frac{15}{10}\) miles,

but less than \(\frac{19}{10}\) miles.

Preferable trails he could walk = \(\frac{19}{10}\) – \(\frac{15}{10}\)

= \(\frac{4}{10}\) miles on trail C.

**Find the sum or difference.**

Question 6.

\(\frac{3}{6}\) + \(\frac{7}{6}\) = ___________

Answer:

\(\frac{10}{6}\) = \(\frac{5}{3}\)

Explanation:

\(\frac{3}{6}\) + \(\frac{7}{6}\) = \(\frac{3+7}{6}\)

= \(\frac{10}{6}\) = \(\frac{5}{3}\)

Question 7.

\(\frac{11}{10}\) – \(\frac{3}{10}\) = __________

Answer:

\(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation:

\(\frac{11}{10}\) – \(\frac{3}{10}\) = \(\frac{11- 3}{10}\)

= \(\frac{8}{10}\) = \(\frac{4}{5}\)

Question 8.

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

Answer:

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

Explanation:

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

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

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

Question 9.

\(\frac{8}{12}\) + \(\frac{6}{12}\) + \(\frac{5}{12}\) = ___________

Answer:

\(\frac{19}{12}\)

Explanation:

\(\frac{8}{12}\) + \(\frac{6}{12}\) + \(\frac{5}{12}\)

= \(\frac{8+6+5}{12}\) = \(\frac{19}{12}\)

**I’m in a Learning Mindset!**

What strategy worked best for me when solving these problems?

Answer:

Combined operations of addition and subtractions.

Explanation:

Combined operations refers to problems where you need to do more than one operation,

like addition and subtraction.