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Let’s Learn!

How do you compare fractions that have the same numerator?

Goal:

Goal:

fraction fox

Think About It!

Goal: Recognize how to find out what makes a fraction greater or lesser when fractions have the same numerator.

Daniel is excited to read about the super celebration. Superheroes Donte and Ian cut the cookie cakes into different numbers of pieces. Each cake is the same size and shape. Donte and Ian want to know which cake has the biggest pieces and which cake has the smallest pieces.

Superheroes Ian and Donte next to cookie cakes

Each part of each cookie cake is a fraction with a numerator and a denominator. Donte will use his fraction powers to show the parts of the first two cakes!

Click on the box to see the fractions of the first two cookie cakes!

Two cookies. The oatmeal raisin cookie is partitioned into 2 equal parts. The double chocolate cookie is partitioned into 3 equal parts.
Description follow

Two cookies. The oatmeal raisin cookie is partitioned into 2 equal parts. The double chocolate cookie is partitioned into 3 equal parts.

The oatmeal cookie's parts are labeled 12.

The double chocolate cookie's parts are labeled 13.

The oatmeal raisin cookie cake has two equal parts. Each of these parts is 12. The double chocolate cookie cake has three equal parts. Each of these parts is 13.

Each part of the cookie cakes has the same numerator, 1. That is because each part is 1 part out of the whole of each cookie. Ian used his fraction superpower to show one piece of each cookie cake and its fraction.

One part of each cookie.

Which piece is bigger, the oatmeal raisin half or the double chocolate third? Donte says that the half looks bigger than the third, but he wants to make sure. Ian flew in two number lines to compare the two fractions: 12 and 13 . Because the fractions have different denominators, the number lines have different numbers of parts too!

First, Ian shows 12 on the first number line by drawing a purple line to 12. Click on the empty number line to show 12.

Description follow

Number line from 0 to 1 with 2 spaces between. The number line is labeled from 02 to 22

Description follow

Number line from 0 to 1 with 2 spaces between. The number line is labeled from 02 to 22. One part is filled in to 12.

Then Ian shows 13 on the second number line by drawing a brown line to 13. Click on the empty number line to see how he shows 13.

Description follow

Number line from 0 to 1 with 3 spaces between. The number line is labeled from 03 to 33

Description follow

Number line from 0 to 1 with 3 spaces between. The number line is labeled from 03 to 33. One part is filled in to 13.

Ian flew in red lines to show where the fractions end on the number lines. Even though the number lines are divided into different fractions, the lines themselves are the same size. Donte used his fraction powers to see that 12 is greater than 13. 12 is greater than 13 because it is closer to 1 on the number line!

Description follows.

Two number lines. Top number line from 0 to 1 with 2 spaces between. The number line is labeled from 02 to 22. One part is filled in to 12. Bottom number line from 0 to 1 with 3 spaces between. The number line is labeled from 03 to 33. One part is filled in to 13.

Each number line has a dotted line extending from their filled in part. The top number line is longer.

The 2 in the denominator of 12 is less than the 3 in the denominator of 13. This is because the smaller the denominator, the bigger the parts! When you cut the same size space into more parts, the parts get smaller.

Description follows

12>13. The denominators are circled.

2 is less than 3

Ian says that you can also use lines with dots or just dots to show each fraction.

description follows

Two number lines. Top number line from 0 to 1 with 2 spaces between. The number line is labeled from 02 to 22. One part is filled in to 12. Bottom number line from 0 to 1 with 3 spaces between. The number line is labeled from 03 to 33. One part is filled in to 13.

Ian’s number lines with lines and dots

description follows

Two number lines. Top number line from 0 to 1 with 2 spaces between. The number line is labeled from 02 to 22. Dot on 12. Bottom number line from 0 to 1 with 3 spaces between. The number line is labeled from 03 to 33. Dot on 13.

Ian’s number lines with dots

Ian also says that you can use < (less than), > (greater than), or = (equal to) to compare fractions. He came up with a super rule for comparing fractions:

If the numerator is the same, the fraction with the smaller denominator is the greater fraction!

Click each slide to compare the fractions with the superheroes!


Question:

How can you compare or order fractions if you do not have a number line or fraction picture?

When fractions have the same numerator, look at their denominators to compare or order them!