seegongsik
Grade 3 (age 8-9)

grade 3 Introduction to Fractions

A fraction names some of the equal parts that one whole has been split into. Cut a pizza into 4 equal slices and eat 1 of them, and you have eaten one fourth of the pizza, written ¼. The denominator under the bar tells how many equal parts the whole was cut into, the numerator on top tells how many of those parts you have, and the bigger the denominator, the smaller each part. Change the number of slices and the number of shaded slices to see the same fraction on the pizza and on the bars.

What Is a Fraction?

🍕 One Pizza, Four Slices
①Cut one pizza into 4 slices that are all the same size
②If you eat 1 slice, you have eaten 1 of the 4 equal slices
③That amount is read one fourth and written ¼
④If the slices were different sizes, 1 slice out of 4 would not be one fourth

Fractions on a Pizza

4
1
💡 Numerator and Denominator
①The denominator is the number under the bar; it shows how many equal parts the whole was cut into
②The numerator is the number above the bar; it shows how many of those parts are chosen
③The more slices you cut the pizza into, the bigger the denominator and the smaller each slice
④Raise the numerator until it equals the denominator and the whole pizza is shaded; the fraction is then 1

Fractions on Bars

📏 Reading the Bars
①The blue bar at the top is the whole, 1, and the middle bar splits it into as many equal parts as the denominator
②The green bar at the bottom carries the shaded length over, and the dashed line shows how far along the whole the fraction reaches
③With the same denominator, the bigger numerator gives the bigger fraction: 3/4 is longer than 1/4
④With the same numerator, the bigger denominator gives the smaller fraction: 1/8 is shorter than 1/4
⑤The % next to the green bar writes the same amount as a percent, which you will learn about in a later grade

Summary

Parts of a Fraction
numeratordenominator
The numerator on top counts the chosen parts; the denominator below counts all the equal parts
Unit Fractions
12, 13, 14 ...
A fraction with numerator 1 is the size of a single part
Fractions Equal to 1
denominatordenominator = 1
When the numerator equals the denominator, you have the whole, which is 1
🎯 Summary
①A fraction tells how many of the equal parts of a whole you have
②The denominator goes below the bar and the numerator above it
③With the same denominator, the bigger numerator means the bigger fraction
④The bigger the denominator, the smaller each part
⑤When the numerator equals the denominator the fraction is 1, and when the numerator is 0 it is 0

Examples and Unit Test

Example 1
A pizza is cut into 4 equal slices and 1 slice is shaded. What fraction of the pizza is shaded?
1
The total number of slices, 4, is the denominator, and the number of shaded slices, 1, is the numerator.
2
Denominator 4 and numerator 1 make one fourth, written ¼.
▸ 14 (one fourth)
The denominator counts all the slices; the numerator counts the shaded ones.
Example 2
Which is greater, 3/5 or 2/5?
1
Both fractions have denominator 5, so every slice is the same size.
2
3 slices of that size are more than 2 slices, so 3/5 is greater.
▸ 35 (three fifths)
When the denominators match, the slices match, so you only compare the numerators.
Unit Test
Which number is equal to 6/6?
①0
②16
③1
④6
▸ ③ 1
1
The numerator and the denominator are both 6, so you have all 6 of the 6 slices.
2
Having the whole means 6/6 equals 1.
← Previous
Division Basics
Next →
Rounding Numbers

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