We included **HMH Into Math Grade 4 Answer Key PDF** **Module 12 Lesson 3 Identify Equivalent Fractions and Decimals **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 12 Lesson 3 Answer Key Identify Equivalent Fractions and Decimals

I Can write a fraction in tenths as a fraction in hundredths and as a decimal in tenths and hundredths.

**Spark Your Learning**

Kelly buys \(\frac{4}{10}\) kilogram of American cheese at the deli counter.

Write the amount of cheese that Kelly buys as a fraction and as a decimal in hundredths. Justify your answer with a visual model.

Answer: 0.4

Explanation:

Kelly buys \(\frac{4}{10}\) kilogram

\(\frac{4}{10}\) = 0.4

**Turn and Talk** How does a numerator of a fraction in tenths relate to the numerator of an equivalent fraction in hundredths? Describe a visual model you could use to support your answer.

Answer:

Both are equivalent to each other.

\(\frac{4}{10}\) = \(\frac{40}{100}\)

Explanation:

If we observe the tenths and hundredths model, each are divided into 10 equal sections.

\(\frac{1}{10}\) = \(\frac{10}{100}\)

\(\frac{4}{10}\) = \(\frac{4×10}{10×10}\)

\(\frac{4}{10}\) = \(\frac{40}{100}\)

**Build Understanding**

Question 1.

Joel spends 1\(\frac{3}{10}\) hours shopping for groceries at the supermarket.

How can you represent the time spent as a mixed number in hundredths and as a decimal in hundredths?

Show your thinking and then write the decimal in the place-value chart.

Answer:1.3

Explanation:

Joel spends 1\(\frac{3}{10}\) hours shopping

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

decimal in hundredths = \(\frac{13×10}{10×10}\) = 1.30

A. What is the relationship between tenths and hundredths?

Answer:

Tenth is the place value that represents the position of digit after decimal place equal to 1/10th

and hundredth represents the position of digit in a number after decimal place equal to 1/100th.

Explanation:

For example, nine tenths is equal to 4/10 = 0.4

and 5 hundredth is equal to \(\frac{5}{100}\) = 0.05

decimal pace changes between tenths and hundredths

Connect to Vocabulary

Equivalent decimals are two or more decimals that name the same number.

B. How can you use that relationship to rename tenths as an equivalent fraction in hundredths?

Answer:

Decimal in tenths and decimal in hundredths also divided evenly and both are equivalent.

\(\frac{1}{10}\) ÷ \(\frac{1}{100}\)= 10

C. How can you write the fraction in hundredths as a decimal in hundredths?

Answer:

hundredth is equal to \(\frac{5}{100}\)

= 0.05

Explanation:

To write fraction in hundredths as a decimal in hundredths,

divide the numerator with denominator.

**Step It Out**

Question 2.

Pam walks with her mother from the market to her home. Write the distance in fraction form and decimal form in tenths.

A. Write the distance as a fraction in hundredths.

Answer:

\(\frac{60}{100}\)

Explanation:

Pam walks with her mother from the market to her home = 0.6 miles

Distance fraction form in hundredths = \(\frac{60}{100}\)

B. Use division to rename the fraction in hundredths as a fraction in tenths. Show your work.

Answer:

By dividing both the denominator by 10.

and when we go from hundredths to tenths and you would also divide the numerator by.

10 going from hundredths to tenths

C. Write the fraction in tenths as a decimal in tenths.

Answer:

\(\frac{6}{10}\) = 0.6

Explanation:

Pam walks with her mother from the market to her home = 0.6 miles

Distance fraction form = \(\frac{6}{10}\)

Distance in decimal tenths = 0.6

**Turn and Talk** How can you rename a decimal in tenths as a decimal in hundredths without multiplying?

Answer:

Decimal in tenths and decimal in hundredths also divided evenly

\(\frac{1}{10}\) ÷ \(\frac{1}{100}\)= 10

Explanation:

one tenth = one hundredth

0.1 = 0.01

100 ÷ 10 = 10

**Check Understanding**

Question 1.

Cara drinks \(\frac{2}{10}\) liter of apple juice. Write the amount of juice as a fraction and a decimal in hundredths.

fraction: ________

decimal: _________

Answer:

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

decimal : 0.2

Explanation:

Cara drinks \(\frac{2}{10}\) liter of apple juice.

Amount of juice as a fraction and a decimal in hundredths = \(\frac{1}{5}\) = 0.2

Question 2.

A store clerk unpacks 2\(\frac{4}{10}\) cases of milk cartons. Rename the number of cases as a mixed number and a decimal in hundredths.

Answer:

2.4 cartons

Explanation:

2\(\frac{4}{10}\) cases of milk cartons

Rename mixed number into fraction = \(\frac{20 + 4}{10}\)

decimal in hundredths = \(\frac{24}{10}\) = 2.4

Question 3.

Jennifer buys \(\frac{70}{100}\) kilogram of mixed nuts. Rename the number of kilograms as a fraction and a decimal in tenths.

Answer:

0.7 kilograms

Explanation:

Jennifer buys \(\frac{70}{100}\) kilogram of mixed nuts

To convert decimal in tenths divided both numerator and denominator with 10.

\(\frac{70÷10 }{100÷10}\) = \(\frac{7}{10}\) = 0.7

**On Your Own**

Question 4.

Janelle saves \(\frac{1}{10}\) of her paycheck each week. Shade the hundredths model to show that amount.

What is \(\frac{1}{10}\) written as a decimal in hundredths?

Answer:

\(\frac{10}{100}\) = 0.1

Explanation:

Janelle saves \(\frac{1}{10}\) of her pay check each week.

To write decimal in hundredths multiply both numerator and denominator with 10.

\(\frac{1×10}{10×10}\) = \(\frac{10}{100}\)= 0.1

Question 5.

**Use Structure** Mr. Vidal serves 0.40 liter of turkey gravy. Explain how you can rename 0.40 in tenths in fraction form and in decimal form.

Answer:

\(\frac{40}{100}\) = 0.4 liter

Explanation:

Mr. Vidal serves 0.40 liter of turkey gravy.

Rename 0.40 in tenths in fraction form is \(\frac{40}{10}\)

Question 6.

A roll of foil has 3\(\frac{9}{10}\) meters left on the roll. Rename the length of foil as a mixed number and as a decimal in hundredths.

Answer:

3.90 meters

Explanation:

A roll of foil has 3\(\frac{9}{10}\) meters left on the roll.

3\(\frac{9}{10}\) = \(\frac{39}{10}\)

To write decimal in hundredths multiply numerator and denominator with 10

= \(\frac{39×10}{10×100}\) = \(\frac{390}{100}\) = 3.90

Question 7.

Mason waits for 4\(\frac{50}{100}\) minutes. Rename the amount of time as a mixed number and as a decimal in tenths.

Answer:

4.5

Explanation:

Mason waits 4\(\frac{50}{100}\)

= \(\frac{450}{100}\)

To write decimal in tenths divided the numerator and denominator with 10

= \(\frac{450÷10 }{100÷10}\) = \(\frac{45 }{10}\)

= 4.50

Question 8.

**Critique Reasoning** Chloe says that 0.90 is equivalent to \(\frac{9}{100}\). Is Chloe correct? Explain.

Answer:

No, Chloe is wrong.

Explanation:

0.90 is equivalent to \(\frac{9}{100}\)

\(\frac{9}{100}\) = 0.09

\(\frac{90}{100}\) = 0.90

**I’m in a Learning Mindset!**

What strategies for writing a fraction and an equivalent decimal did I share with a partner?

Answer:

To find the equivalent fractions for any given fraction,

we should multiply the numerator and the denominator by the same number.

For example, to find an equivalent fraction of 2/3,

multiply the numerator and the denominator by 2 as below

\(\frac{2×2}{3×2}\) = \(\frac{4}{6}\)