A cheerful girl jogging on a sunny park path with trees

The Race Day Puzzle

Zoe ran 3/10 of a kilometer, then 4/100 of a kilometer more. How far did she run in all? Let's figure it out!

4th Grade Math

Step 1: Look at the Denominators

3/10 + 4/100 = ?

The denominator is the bottom number of a fraction. Here one is 10 and the other is 100. They do not match!

We can only add fractions when the pieces are the same size. Tenths and hundredths are different sizes, so we make the denominators match first.

Step 2: Change Tenths to Hundredths

This bar shows 3 tenths. Each tenth equals 10 hundredths. So what equivalent fraction matches 3/10?

3/10 = 30/100. Multiply the top and bottom by 10: 3 x 10 = 30 and 10 x 10 = 100. Same amount, smaller pieces!

Step 3: Add the Hundredths

The blue squares show 30 hundredths. The orange squares show 4 more. What is 30/100 + 4/100?

Add the numerators: 30 + 4 = 34. Keep the denominator 100. Zoe ran 34/100 of a kilometer!

Let's Remember

Adding Tenths and Hundredths

          Step 1: Check the denominators. 10 and 100 do not match.

          Step 2: Change tenths to hundredths. Multiply top and bottom by 10.

          Step 3: Add the numerators. Keep the denominator 100.

Example: 3/10 + 4/100 = 30/100 + 4/100 = 34/100

Watch Out!

Coach Rivera says: Many students write 3/10 + 4/100 = 7/100. That is wrong! They added 3 + 4 without changing the tenths first.

A tenth is ten times bigger than a hundredth. Change 3/10 into 30/100 first, then add. The true sum is 34/100, not 7/100.

What Goes in the Blank?

5/10 = ?/100

5/10 = 50/100. Multiply the top and bottom by 10: 5 x 10 = 50 and 10 x 10 = 100.

Solve It!

2/10 + 30/100 = ?

First change 2/10 into 20/100. Then add: 20/100 + 30/100 = 50/100.

Word Problem

Amara's garden got 6/10 cm of rain in the morning. It got 25/100 cm more in the afternoon. How much rain fell in all?

Change 6/10 into 60/100. Then add: 60/100 + 25/100 = 85/100 cm of rain.

Solve It!

40/100 + 4/10 = ?

Change 4/10 into 40/100. Then add: 40/100 + 40/100 = 80/100.

Jump on the Number Line

0

10

20

30

40

50

60

70

80

90

100

This number line counts hundredths, from 0/100 to 100/100.

Start at 70/100. Jump forward 2/10. Where do you land?

A jump of 2/10 equals 20/100. So 70/100 + 20/100 = 90/100.

Challenge!

Mia's bottle holds 1 liter, which is 100/100. She pours in 6/10 of a liter, then 25/100 more. How much more water fills the bottle to the top?

First add: 6/10 = 60/100, and 60/100 + 25/100 = 85/100. Then find the missing part: 100/100 - 85/100 = 15/100 liter.

Money uses hundredths: a penny is 1/100 of a dollar and a dime is 10/100. Where else do you see tenths and hundredths in real life?

Great Work!

0/9

correct

denominator numerator tenths hundredths equivalent fraction