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Math · Grade 3 Math

Chapter 5: Fractions as Numbers

Comparing Fractions With the Same Bottom

Same size pieces, so just count them.

Lesson
6
Time
About 12 minutes
0 of 7 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

If two fractions have the same denominator, the pieces are the same size.

So just count them

5/8 is more than 3/8, because 5 pieces beats 3 pieces of the same size.

Why this is safe

It only works because the pieces match. That is what makes counting fair.

Same-sized pieces, so count them

Comparing 3/8 and 5/8 is easy because both are made of eighths. Five pieces is more than three pieces when the pieces are identical, so 5/8 > 3/8. With the same bottom number, the top numbers decide.

Why this is the easy case

It is the only case where you can compare tops directly, and it works precisely because the piece size is fixed. As soon as the bottoms differ, comparing tops is meaningless — 1/2 is bigger than 3/8 even though 1 is smaller than 3.

Check on the number line

Put both fractions on the same number line, cut into eighths. The one further right is bigger. Whenever a fraction comparison feels uncertain, drawing the line settles it, and it never lies.

Step 2: Try It Yourself

Tap and try it out.

Keep both denominators the same and change the top numbers.
5/8
3/8
015/83/8

5/8 is greater than 3/8.

The pieces are the same size, so more pieces means more.

Step 3: Watch an Example

One step at a time.

Watch Leo Compare Eighths

Leo compares 5/8 and 3/8.

  1. Step 1

    He checks the denominators first: both 8, so the pieces match.

Step 4: Your Turn

Practice makes it stick.

Two Bars

Problem 1 of 2

Which is bigger, 4/6 or 5/6?

The Race

Problem 2 of 2

Ana ran 3/5 of a lap and Leo ran 4/5. Who ran further?

Same Bottom Number

1 of 3

Which is bigger, 2/7 or 5/7?

2 of 3

Which is bigger, 7/8 or 6/8?

3 of 3

Why can you just count when the denominators match?

Step 5: Quick Check

Show what you know.

Question 1 of 2

Which is bigger, 3/4 or 1/4?

Question 2 of 2

When does counting the top numbers work?

What You Learned

  • Same denominator means same-size pieces.
  • So the bigger numerator wins.
  • That only works when the pieces match.