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5.13 Adding fractions with tenths and hundredths

Lesson

Are you ready?

Let's review the relationship between tenths and hundredths.

Complete the following to make an equivalent fraction:

  1. $\frac{3}{10}$310$=$=$\frac{\editable{}}{100}$100

Learn

Remember that the numerator of a fraction represents a number of parts, and the denominator represents the size of those parts. To add fractions together, we want to add parts that are the same size - that is, we want to add together fractions with the same denominator.

For example, the sum $\frac{3}{100}+\frac{12}{100}$3100+12100 represents "$3$3 hundredths plus another $12$12 hundredths", which is $15$15 hundredths in total. That is,

$\frac{3}{100}+\frac{12}{100}$3100+12100 $=$= $\frac{15}{100}$15100

 

We can use the relationship between tenths and hundredths to add together these types of fractions as well.

For example, the sum $\frac{2}{10}+\frac{7}{100}$210+7100 represents "$2$2 tenths plus $7$7 hundredths". Since we know that $2$2 tenths can also be written as $20$20 hundredths, this means we have "$20$20 hundredths plus another $7$7 hundredths", for a total of $27$27 hundredths. That is, 

$\frac{2}{10}+\frac{7}{100}$210+7100 $=$= $\frac{20}{100}+\frac{7}{100}$20100+7100
  $=$= $\frac{27}{100}$27100

Apply

Question 1

Find the value of $\frac{4}{10}+\frac{50}{100}$410+50100.

Remember!
  • To add fractions, we want them to have the same denominator.
  • We can use the fact that $1$1 tenth is the same as $10$10 hundredths to add fractions involving tenths and hundredths together.

Outcomes

4.NF.C.5

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

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