Express Tenths as Equivalent Hundredths

Students convert fractions with denominator 10 to equivalent fractions with denominator 100 by multiplying numerator and denominator by 10. They use visual models (10×10 grids) to see why this equivalence holds.

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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.

50/100 = 10

How it is taught

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Tenths and hundredths can name the same amount.

Ten hundredths make one tenth.

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.

3/10 = ___/100 — 30. 3 columns are 3/10, and every column is 10 cells: 30/100.

3/10 = 30/100

Today we'll see how tenths can be written as hundredths. Let's start with three-tenths.

Here is three-tenths — three out of ten equal parts shaded.

Now look at a hundredths grid: ten rows of ten — that's one hundred tiny squares in all.

Let's shade the SAME amount. Three full rows of ten — that's thirty squares.

Thirty out of one hundred. Same area, just smaller pieces!

Grade 4 · Why three tenths equals thirty hundredths

So three-tenths equals how many hundredths? Let's figure it out.

To turn ten into one hundred, we multiply by ten.

To keep the fraction equal, we multiply the top by ten too. Three times ten is thirty.

Three-tenths equals thirty-hundredths. Multiply the top and bottom by ten!

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

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Leads to

Add Fractions with Denominators 10 and 100

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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