Comparing Fractions and Finding Equal Ones

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What this lesson covers

  • When the bottom numbers match, the bigger top number is the bigger fraction.
  • Equivalent fractions are the same amount, written a different way.
  • 2/2, 3/3, 4/4 and 6/6 are all one whole.
  • Drawing equal parts shows when two fractions are the same.
Key idea

Same-size pieces

  • 5/8 and 3/8 are both made of eighths.
  • 5 eighths is more than 3 eighths, so 5/8 > 3/8.
  • When the bottom numbers are the same, compare the top numbers.
Key idea

Try it: compare two fractions

Worked example

Ordering fractions with the same bottom number

  • Put the top numbers in order.
FractionsSmallest to largest
4/6, 1/6, 5/61/6, 4/6, 5/6
7/12, 11/12, 2/122/12, 7/12, 11/12
3/5, 2/5, 4/52/5, 3/5, 4/5
Key idea

Many ways to write one whole

  • 2/2 means 2 out of 2 halves: the whole thing.
  • 3/3, 4/4, 6/6 and 10/10 are each one whole too.
  • When the top and bottom numbers match, it is one whole.
Key idea

Equivalent fractions

  • Cut a sandwich in half and eat 1/2.
  • Now cut each half into 3 pieces. There are 6 pieces, and you ate 3 of them: 3/6.
  • It is the same amount of sandwich, so 1/2 = 3/6.
  • Fractions that are the same amount are called equivalent.
Key idea

Try it: cut the pieces again

Worked example

Spotting equal fractions

  • Cut every piece into the same number of smaller pieces.
FractionSame asWhy
1/22/42 quarters fill a half
1/24/84 eighths fill a half
1/32/6each third cuts into 2 sixths
3/46/8each quarter cuts into 2 eighths
Key idea

Try it: the fraction wall

Common mistakes

  • 2/4 is more than 1/2 because 2 is more than 1.
    2/4 and 1/2 are the same amount. The pieces are just smaller.
  • 4/4 is four wholes.
    4/4 is all 4 quarters, which is one whole.
  • 1/2 = 2/3 because the top is one less than the bottom in both.
    Draw them. 2/3 covers more than half, so they are not equal.
  • To compare 5/8 and 3/8, look at the 8s.
    The 8s are the same, so compare the tops. 5 is more than 3.

Your turn

1

Which is the biggest: 4/10, 7/10, 2/10 or 5/10?

2

Put 5/6, 2/6 and 4/6 in order from smallest to largest.

3

Which of these is one whole: 3/4, 5/5, 1/5 or 4/5?

4

1/2 = __/8

5

Is 2/3 the same amount as 4/6?

Show answer

1. 7/10 2. 2/6, 4/6, 5/6 3. 5/5 4. 4/8 5. Yes, they are equal. Cut each third into 2 pieces and 2/3 becomes 4/6.

Summary

What to take away

  • Same bottom number: compare the tops.
  • Top and bottom the same means one whole.
  • Equivalent fractions are the same amount.
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More in Number

Numbers to 1,000: Hundreds, Tens and OnesNotesCounting in Groups, Rounding and EstimatingNotesSkip Counting, Odd and Even NumbersNotesAdding and Subtracting up to 1,000NotesMultiplying and Dividing with GroupsNotesUnit Fractions: One Equal PartNotesComparing Fractions and Finding Equal OnesNotesAdding Fractions and Finding Fractions of NumbersNotesDollars, Cents and Giving ChangeNotes

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