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Compare Fractions with the Same Numerator

Students will compare two fractions that share the same numerator by reasoning that when you have the same number of parts, the fraction with the larger denominator has smaller parts and is therefore smaller. For example, 1/4 < 1/2 because fourths are smaller parts than halves. Students will use models and number lines to justify their comparisons.

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Compare Fractions with the Same Numerator

Grade 3 · Comparing Fractions · question 1 of 3

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12 rungs. A star at the top.

Which of these is the least: 1/4, 1/2, 2/4 or 2/2?

How it is taught

0:00 of 3:39

When tops match, look at the bottoms.

A bigger bottom means smaller pieces.

Read it: Bigger pieces, more chocolate

Maya has 3/4 of a bar. Leo has 3/8 of the same bar. 3 pieces each — but look at how big those pieces are.

  1. See Maya's 3 shaded pieces: her bar is cut into 4.
  2. See Leo's 3 shaded pieces: his bar is cut into 8.
  3. Compare the piece size: fourths are bigger, so 3/4 is more.

Counting 3 against 3 looks even, but Leo's eighths are smaller parts of the same bar.

A whole cut into 4 has bigger parts than a whole cut into 8.

3 big fourths cover more of the bar than 3 small eighths.

Same top number, same whole: the bar cut into fewer parts has bigger parts, so 3/4 is more than 3/8.

Seeing 8 on the bottom and saying 3/8 is more, because 8 is bigger than 4.

8 on the bottom means the whole is cut into smaller parts, so 3 of them are less than 3/4.

Which is more, 2/6 or 2/8? — 2/6. A whole cut into 6 has bigger parts than a whole cut into 8, so 2/6 is more than 2/8.

1/4 vs 1/2

Imagine two chocolate bars. You eat one piece from each — but which piece is bigger?

Here's one bar split into two equal parts. We shade one part — that's one half.

Here's another bar split into four equal parts. We shade one part — that's one fourth.

Look closely. Both bars are the same size, but the fourths are smaller pieces than the halves.

Which piece is bigger?12 bar1214 bar14Same numerator → bigger denominator means smaller parts01141234141214<12ANSWER14 < 12fewer parts = bigger
Grade 3 · Same numerator, different sized parts

When the top numbers — the numerators — are the same, more pieces means smaller pieces.

Let's check on a number line from zero to one.

One fourth sits closer to zero.

One half sits farther along, halfway to one.

So one fourth is less than one half.

Same numerator? The bigger denominator means smaller parts. One fourth is less than one half!

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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