Add Fractions with Denominators 10 and 100

Students add a fraction with denominator 10 and a fraction with denominator 100 by first converting the tenths fraction to hundredths, then adding the like-denominator fractions. For example, 3/10 + 4/100 = 30/100 + 4/100 = 34/100.

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Grade 4 · Fractions with Denominators 10 and 100 · question 1 of 3

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20 rungs. A star at the top.

+ 13/100 = 23/100

How it is taught

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Tenths and hundredths can be added when the bottoms match.

Matching bottoms means both are hundredths.

Then the tops add and the bottom stays.

Read it: Turn tenths into hundredths

What is 4/10 + 4/100? On the square, 4 columns are shaded and 4 cells more. Each column is 10 cells, so the total is 44/100.

Shade 4/10 as 4 columns of the square.
Shade 4/100 as 4 single cells in the next column.
Count every column as 10 cells: 40 + 4 = 44, so 44/100.

A column is 1/10 of the square, and it holds 10 of the 100 cells, so 1/10 = 10/100.

Tenths and hundredths are different sizes of piece, so the columns must become cells before the two can be added.

Once everything is in cells, adding is just counting: 40 cells and 4 cells make 44 cells.

Rename the tenths as hundredths, then add the hundredths: 4/10 + 4/100 = 40/100 + 4/100 = 44/100.

Adding the tops and the bottoms: 4/10 + 4/100 = 8/110.

8/110 is a sliver, not 4 columns and 4 cells. Rename first: 40/100 + 4/100 = 44/100.

9/10 + 6/100 = ___/100 — 96. 9 columns are 90/100, and 6 cells more makes 96/100.

3/10 + 4/100

Today we'll add a fraction with tenths to a fraction with hundredths.

Our problem is three-tenths plus four-hundredths.

But the denominators are different — ten and one hundred. We can't add them yet.

Let's change three-tenths into hundredths so the denominators match.

Multiply the top AND the bottom by ten.

Three-tenths is the same as thirty-hundredths.

Now both fractions have the same denominator: thirty-hundredths plus four-hundredths.

Add the numerators: thirty plus four equals thirty-four.

Grade 4 · Convert tenths to hundredths, then add

Keep the denominator the same — one hundred.

Three-tenths plus four-hundredths equals thirty-four hundredths. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Standard

CCSS.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

Grade 4

Quoted from the Common Core State Standards.

Where this sits

Comes after

Leads to

Add and Subtract Decimals to Hundredths Using Models and Place Value

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 4

This is one rung of 71 in Grade 4 mathematics, in the order they build on each other.

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