12.3: Identify Equivalent Fractions and Decimals

12.3: Identify Equivalent Fractions and Decimals

Today we are doing equivalent fractions. But first, y'all make me nervous with decimals, so let's do some review. Wanda is scared, too.

So, today, we are going to compare equivalent fractions and decimals.

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

Multiple Select

Spark your learning: Kelly buys 4/10 kilogram of American cheese at the deli counter. Which of these ALSO equals 4/10?

• 40/100

• 0.4

• 4/100

• 0.04

We would write 4/10 as 40/100 and 0.40

• To write the fraction in hundredths, you can use a denominator of 100. When you use a denominator of 100, you are using a whole that is divided into 100 equal parts.

• When you use a denominator of 10, you are using a whole that is divided into 10 equal parts.

• 4 parts out of 10 equal parts is equal to 40 parts out of 100 equal parts.

• This means that 0.4 equals 0.40 and 4/10 equals 40/100

So, what does equivalent mean?

The term “equivalent” in math refers to two values, numbers or quantities which are the same.

Build Understanding Part 1

Joel spends 1 and 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?

Open Ended

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

Possible Answer:

I can multiply the numerator and denominator by 10 to show the fraction in hundredths. I can write 1 and ​3/10 as 1 and ​30/100​. This is the same as 1.30.

Multiple Choice

Which shows how to represent the time (1 and 3/10) spent as a mixed number in hundredths?

• 1 and 3/100

• 1 and 30/100

• 3 and 10/100

We would use 1 and 30/100

When you use a denominator of 10, you are using a whole that is divided into 10 equal parts. When you use a denominator of 100, you are using a whole that is divided into 100 equal parts. 3 parts out of 10 equal parts is equal to 30 parts out of 100 equal parts. The number 1 and 3/10​ can be represented as 1 and 30/100​​ as a mixed number in hundredths.

10 hundredths equals 1 tenth.

You can use a hundredths model and a tenths model. Shade 10 units in a hundredths model. Then find how many tenths is equivalent to 10 hundredths. 10 hundredths is equivalent to 1 tenth.

Multiple Choice

Complete the sentence. How can you use this relationship to rename tenths as an equivalent fraction in hundredths? Since 10 hundredths is the same amount as 1 tenth, _______.

• I can multiply both the numerator and the denominator of the fraction in tenths by 10 to find an equivalent fraction in hundredths.

• I can multiply both the numerator and the denominator of the fraction in tenths by 100 to find an equivalent fraction in hundredths.

• I can multiply both the numerator and the denominator of the fraction in tenths by 1,000 to find an equivalent fraction in hundredths.

To get from 10 to 100, you can multiply 10 by 10.

• To find an equivalent fraction with a denominator of 100 for a fraction that has a 10 as the denominator, multiply the numerator by 10 and multiply the denominator by 10.

Multiple Choice

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

• The digits in the numerator of the fraction in hundredths are the digits that go to the left of the decimal point.

• The digits in the numerator of the fraction in hundredths are the digits that go to the right of the decimal point.

Whole numbers are placed to the left of the decimal point. Fractional parts are placed to the right of the decimal point.

Build Understanding Part 2

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

Multiple Choice

How do we write 0.60 as a fraction?

• 60/10

• 60/100

• 6/100