We included **HMH Into Math Grade 6 Answer Key PDF** **Module 15 Measures of Center **to make students experts in learning maths.

## HMH Into Math Grade 6 Module 15 Answer Key Measures of Center

**DOT PLOT LOGIC**

The dot plot shows the lengths of eight hiking trails in a park.

- Use the dot plot and the clues to complete the table.

- Wolf Trait is longest, and tree Trail is shortest
- Pine Trait is \(\frac{3}{8}\) mile longer than Creek Trail.
- Deer Trait is longer than Pine Trail.
- North Trait is \(\frac{1}{4}\)-mile shorter than Pine Trail.
- Ridge Trail and Summit Trail are the same length.

Answer:

wolf trail is the longest = 3 and creek trail = 2

Pine Trait is \(\frac{3}{8}\) + 2

Pine Trait = \(\frac{19}{8}\) = 2 \(\frac{3}{8}\)

Deer Trait > pine trail

Deer Trait = 2 \(\frac{7}{8}\)

North Trait = \(\frac{19}{8}\) – \(\frac{1}{4}\)

North Trait = \(\frac{17}{8}\) = 2\(\frac{1}{8}\)

Ridge Trail = Summit Trail

Ridge Trail = 2\(\frac{5}{8}\) + 2\(\frac{1}{4}\) = 2.625 + 2.25 = 4.875

Summit trail = 2.125 + 2.75 = 4.875 = 2 1/8 + 2 3/4

Eagle = 2 1/2

Explanation:

**Turn and Talk**

Question 1.

Explain how you determined the length of the Deer Trail.

Answer:

Deer Trait is larger than pine trail

The pine trail is 2 \(\frac{3}{8}\). So we need to select larger than the given number. Hence by comparing all other Trails we can determine the length of the Deer Trail is 2 \(\frac{7}{8}\).

Question 2.

Explain how you determined the lengths of Ridge Trail and Summit Trail.

Answer:

Ridge Trail and Summit Trail are the same lengths.

From the given figure we need to select Trail lengths.

Hence we can select 2\(\frac{5}{8}\) + 2\(\frac{1}{4}\) to calculate Ridge Trail. The answer is 4 \(\frac{7}{8}\).

Next, we can select 2\(\frac{1}{8}\) + 2\(\frac{3}{4}\) to calculate Summit trail. The answer is 4 \(\frac{7}{8}\).

Therefore both the trails have the same lengths.

**Are You Ready?**

Complete these problems to review prior concepts and skills you will need for this module.

**Make and Interpret Line Plots**

For Problems 1-4, use the following information.

An art teacher has a bag of ribbon pieces. The ribbon pieces are measured to the nearest \(\frac{1}{8}\) foot. The length of each piece is shown in the line plot.

Question 1.

How many pieces of ribbon measure less than \(\frac{1}{2}\) foot?

Answer:

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

Explanation:

\(\frac{1}{8}\) + \(\frac{2}{8}\) + \(\frac{3}{8}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\).

Hence there are \(\frac{3}{4}\) pieces of ribbon measure less than \(\frac{1}{2}\) foot.

Question 2.

How many pieces of ribbon measure greater than \(\frac{1}{2}\) foot?

Answer:

\(\frac{9}{4}\).

Explanation:

There are \(\frac{9}{4}\) pieces of ribbon measure greater than \(\frac{1}{2}\) foot.

Question 3.

What is the difference in length between the longest and the shortest piece of ribbon?

Answer:

1 – \(\frac{1}{8}\) foot = \(\frac{7}{8}\).

Explanation:

The difference in length between the longest and the shortest piece of ribbon is \(\frac{7}{8}\).

Question 4.

How many pieces of ribbon measure at least \(\frac{3}{4}\) foot?

Answer:

\(\frac{1}{8}\) + \(\frac{2}{8}\) + \(\frac{3}{8}\) + \(\frac{4}{8}\) + \(\frac{5}{8}\) = \(\frac{3}{4}\)

**Division Involving Decimals**

**Divide.**

Question 5.

Answer:

$2.06

Explanation:

Question 6.

Answer:

2.23

Explanation:

Question 7.

Answer:

$5.7

Explanation:

**Write the fraction as a decimal.**

Question 8.

\(\frac{40}{16}\) __________

Answer:

2.5

Explanation:

The fraction as a decimal is 2.5

\(\frac{40}{16}\) = \(\frac{5}{2}\) = 2.5

Question 9.

\(\frac{108}{16}\) ____________

Answer:

6.75

Explanation:

The fraction as a decimal is 6.75.

\(\frac{108}{16}\) = \(\frac{27}{4}\)

Question 10.

\(\frac{115}{8}\) ____________

Answer:

14.375

Explanation:

The fraction as a decimal is 14.375.

**Write the mixed number as a decimal.**

Question 11.

80\(\frac{2}{5}\) ____________

Answer:

80.4

Explanation:

Let us solve the given number

80\(\frac{2}{5}\) = \(\frac{402}{5}\)

80.4

Question 12.

20\(\frac{4}{16}\) ____________

Answer:

20.25

Explanation:

Let us solve the given number

20\(\frac{4}{16}\) = \(\frac{324}{16}\)

20.25

Question 13.

110\(\frac{9}{12}\) ____________

Answer:

110.75

Explanation:

Let us solve the given number

110\(\frac{9}{12}\) = \(\frac{1329}{12}\)

110.75