We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 9 Lesson 2 Multiply Mixed Numbers** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 9 Lesson 2 Answer Key Multiply Mixed Numbers

I Can solve real world problems involving multiplication of mixed numbers by writing an equation to model the problem.

**Spark Your Learning**

Arun paints on a large rectangular canvas that measures 2\(\frac{1}{4}\) feet by 4\(\frac{1}{3}\) feet. He wants to enter his painting into an art contest. The contest rules say that the area of all canvases must be less than 4\(\frac{1}{3}\) square feet.

Answer:

Arun cannot enter the contest as his painting is too large.

Explanation:

The measurements of Arun’s canva are 8+1+\(\frac{2}{3}\)+\(\frac{1}{12}\) which is 9+\(\frac{8}{12}\)+\(\frac{1}{12}\) = 9\(\frac{9}{12}\) sq ft. So Arun cannot enter the contest as his painting is too large.

**Based on these rules, can Arun enter his painting into the contest? Explain with words or drawings.**

Answer:

**Turn and Talk** How would your answer change if Arun’s canvas measured \(\frac{5}{6}\) foot by 4\(\frac{1}{3}\) feet? Justify your reasoning.

**Build Understanding**

1. Tam draws a logo for her company’s website. The logo is a rectangle that is 1\(\frac{1}{3}\) inches wide and 1\(\frac{3}{4}\) inches long. What is the area of the logo?

A. Each unit square shown represents a square with a side length of 1 inch. Use this area model to represent the area of Tam’s logo.

Answer:

The area is \(\frac{7}{3}\) sq inches.

Explanation:

Given that the logo is a rectangle that is 1\(\frac{1}{3}\) inches wide and 1\(\frac{3}{4}\) inches long. So the area will be 1\(\frac{1}{3}\) × 1\(\frac{3}{4}\) which is \(\frac{4}{3}\) × \(\frac{7}{4}\) = \(\frac{7}{3}\) sq inches.

B. Why does this area model show four unit squares?

Answer:

2\(\frac{4}{12}\) sq in.

Explanation:

The measurements are 1+\(\frac{1}{3}\)+\(\frac{3}{4}\)+\(\frac{3}{12}\) which is 1+\(\frac{4+9+3}{12}\) = 1 + \(\frac{16}{12}\)

= 2\(\frac{4}{12}\) sq in.

C. How did you show the width of 1\(\frac{1}{3}\) inches?

__________________________

Answer:

The width of 1\(\frac{1}{3}\) inches is \(\frac{4}{3}\) inches.

D. How did you show the length of 1\(\frac{3}{4}\) inches?

__________________________

Answer:

The width of 1\(\frac{3}{4}\) inches is \(\frac{7}{3}\) inches.

E. How many equal-sized parts represent the area of the logo?

___________________

___________________

Answer:

The area of each equal-sized part is \(\frac{7}{3}\) sq inches.

F. What is the area of each equal-sized part? How do you know?

___________________

___________________

Answer:

The area of each equal-sized part is \(\frac{7}{3}\) sq inches.

G. What is the area of the logo? Justify your reasoning.

___________________

___________________

Answer:

The area of the logo is \(\frac{7}{3}\) sq inches.

**Step It Out**

2. Tam makes another logo. The area of the logo is represented by the purple shading.

Answer:

The area is \(\frac{27}{10}\) sq in.

Explanation:

The area of the logo is 1\(\frac{4}{5}\) × 1\(\frac{1}{2}\) which is \(\frac{9}{5}\) × \(\frac{3}{2}\) = \(\frac{27}{10}\) sq in.

A. How many equal-sized parts represent the area of the logo?

____________________

Answer:

The equal-sized parts represent the area of the logo is \(\frac{27}{10}\) sq in.

B. Find the area of one equal-sized part.

____________________

C. What is the area of the logo? Explain your reasoning. Write an equation to model the problem.

____________________

Answer:

The area of the logo is \(\frac{27}{10}\) sq in.

Explanation:

The equation to model the problem is 1\(\frac{4}{5}\) × 1\(\frac{1}{2}\) which is \(\frac{9}{5}\) × \(\frac{3}{2}\) = \(\frac{27}{10}\) sq in.

D. Rename 1\(\frac{1}{2}\) and 1\(\frac{4}{5}\) as fractions greater than 1.

____________________

Answer:

\(\frac{27}{10}\) which is greater than 1.

Explanation:

The fraction greater than 1 is \(\frac{9}{5}\) × \(\frac{3}{2}\) = \(\frac{27}{10}\) which is greater than 1.

E. Use your answers from Part D to write an equation to model the area of the logo.

____________________

Answer:

The equation is \(\frac{9}{5}\) × \(\frac{3}{2}\) = \(\frac{27}{10}\).

**Turn and Talk** How are the equations that model the area of the logo in Parts C and E related? How do they connect to the visual model?

**Check Understanding Math Board**

Question 1.

Jonah’s new poster has a width of 1\(\frac{1}{4}\) yards and a length of 1\(\frac{1}{3}\) yards. Use this area model to represent the area of the poster. What is the area of the poster? Write an equation using fractions greater than 1 to model the problem.

Answer:

The area is 1\(\frac{2}{3}\) sq yards.

Explanation:

Given that Jonah’s new poster has a width of 1\(\frac{1}{4}\) yards and a length of 1\(\frac{1}{3}\) yards. So the area is 1\(\frac{1}{4}\) × 1\(\frac{1}{3}\) which is \(\frac{5}{4}\) × \(\frac{4}{3}\) = \(\frac{5}{3}\) sq yards.

**On Your Own**

Question 2.

**Use Structure** The flagpole at a park is 3\(\frac{1}{3}\) yards tall. The flagpole at a museum is 1\(\frac{1}{2}\) times as tall as the height of the flagpole at the park.

- Explain how to write an equation to model the height of the museum’s flagpole.
- What is the height of the museum’s flagpole?

Answer:

The equation is 3\(\frac{1}{3}\) × 1\(\frac{1}{2}\) = 5 sq yards.

Explanation:

Given that the flagpole at a park is 3\(\frac{1}{3}\) yards tall and the flagpole at a museum is 1\(\frac{1}{2}\) times as tall as the height of the flagpole at the park. So the equation will be 3\(\frac{1}{3}\) × 1\(\frac{1}{2}\) which is \(\frac{10}{3}\) × \(\frac{3}{2}\) = 5 sq yards.

Question 3.

**Model with Mathematics** Debbie measures the length and the width of a cell phone. The length is 5\(\frac{3}{5}\) inches, and the width is 2\(\frac{4}{5}\) inches. What is the area of the front of the cell phone? Write an equation using fractions greater than 1 to model the problem.

Answer:

5\(\frac{3}{5}\) × 2\(\frac{4}{5}\) = 15\(\frac{17}{25}\) sq in.

Explanation:

Given that the length is 5\(\frac{3}{5}\) inches, and the width is 2\(\frac{4}{5}\) inches. So the equation is 5\(\frac{3}{5}\) × 2\(\frac{4}{5}\) which is \(\frac{28}{5}\) × \(\frac{14}{5}\) = \(\frac{392}{25}\) sq in.

**Multiply.**

Question 4.

2\(\frac{1}{5}\) × 3\(\frac{1}{2}\) = ___________________

Answer:

2\(\frac{1}{5}\) × 3\(\frac{1}{2}\) = 7\(\frac{7}{10}\).

Explanation:

The product of 2\(\frac{1}{5}\) × 3\(\frac{1}{2}\) which is \(\frac{11}{5}\) × \(\frac{7}{2}\) = \(\frac{77}{10}\)

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

Question 5.

____ = 5\(\frac{1}{2}\) × 1\(\frac{1}{3}\)

Answer:

5\(\frac{1}{2}\) × 1\(\frac{1}{3}\) = 7\(\frac{1}{3}\).

Explanation:

The product of 5\(\frac{1}{2}\) × 1\(\frac{1}{3}\) which is \(\frac{11}{2}\) × \(\frac{4}{3}\) = \(\frac{44}{6}\)

= 7\(\frac{1}{3}\).

Question 6.

2\(\frac{1}{4}\) × 1\(\frac{2}{3}\) = ___________________

Answer:

2\(\frac{1}{4}\) × 1\(\frac{2}{3}\) = 3\(\frac{3}{4}\).

Explanation:

The product of 2\(\frac{1}{4}\) × 1\(\frac{2}{3}\) which is \(\frac{9}{4}\) × \(\frac{5}{3}\) = \(\frac{45}{12}\)

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

Question 7.

**STEM** An early computer connection called USB 1.0 transfers about 1\(\frac{1}{2}\) megabytes of data each second. A later connection called USB 2.0 transfers data 40\(\frac{1}{2}\) times as fast as the speed of the USB 1.0. How many megabytes can a USB 2.0 connection transfer each second? _______

Answer:

The megabytes can a USB 2.0 connection transfer each second will be 60\(\frac{3}{4}\) mb.

Explanation:

Given that about 1\(\frac{1}{2}\) megabytes of data each second and later connection called USB 2.0 transfers data 40\(\frac{1}{2}\) times as fast as the speed of the USB 1.0. So the megabytes can a USB 2.0 connection transfer each second will be 1\(\frac{1}{2}\) × 40\(\frac{1}{2}\) which is \(\frac{3}{2}\) × \(\frac{81}{2}\) = \(\frac{243}{4}\) = 60\(\frac{3}{4}\) mb.

**I’m in a Learning Mindset!**

How did I use feedback my teacher gave me?

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