Comparing Fractions and Finding the Whole

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What this lesson covers

  • A half is 1 of 2 equal parts, a third 1 of 3, a quarter 1 of 4.
  • More parts means smaller parts: halves beat thirds, thirds beat quarters.
  • Fractions that cover the same amount are equivalent, like 2/4 and 1/2.
  • If you know one part, you can find the whole.
Key idea

One of the equal parts

  • The bottom number says how many equal parts make the whole.
FractionNameEqual parts in the whole
1/2a half2
1/3a third3
1/4a quarter4
Key idea

More parts, smaller parts

  • Share one pizza between 2 people: big slices.
  • Share the same pizza between 4 people: smaller slices.
  • So 1/2 is bigger than 1/3, and 1/3 is bigger than 1/4.
  • This only works when the wholes are the same size.
Key idea

Try it: compare two fractions

Worked example

Compare two fractions

  • Same bottom number: count the parts. 3/4 is more than 1/4.
  • Same top number: fewer parts means bigger parts. 1/3 is more than 1/4.
PairBiggerWhy
1/2 and 1/41/2halves are bigger pieces
1/3 and 1/41/3thirds are bigger pieces
2/3 and 1/32/3more pieces of the same size
2/4 and 1/2neitherthey are equivalent
Worked example

A fraction of a set, in groups

  • 12 eggs sit in a carton in 2 rows of 6. Half is one row: 6 eggs.
  • For a quarter, make 4 equal groups of 3. A quarter of 12 is 3.
  • For a third, make 3 equal groups of 4. A third of 12 is 4.
  • Use the rows and groups you can see. No need to share one at a time.
FindGroupsAnswer
1/2 of 122 groups of 66
1/3 of 123 groups of 44
1/4 of 124 groups of 33
1/4 of 204 groups of 55
Key idea

Try it: split a set into equal groups

Worked example

Find the whole from one part

  • If half is 5, the whole is two halves: 5 + 5 = 10.
  • If a quarter is 3 shells, the whole is four quarters: 3 + 3 + 3 + 3 = 12.
  • If a third of a ribbon is 10 cm, the whole ribbon is 10 + 10 + 10 = 30 cm.
PartCopies to make the wholeWhole
1/2 is 5210
1/3 is 10 cm330 cm
1/4 is 3412
Key idea

Maths blocks

Common mistakes

  • 1/4 is bigger than 1/3, because 4 is bigger than 3.
    More parts means smaller parts. 1/3 is bigger than 1/4.
  • If half is 6, the whole is 3.
    Half is one of two equal parts. Double it: the whole is 12.
  • To find a quarter, halve once.
    A quarter is half of a half, so halve twice. Half of 16 is 8, and half of 8 is 4.

Your turn

1

Which is bigger, 1/2 or 1/3?

2

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

3

What is 1/4 of 20?

4

1/3 of a bag of lollies is 4 lollies. How many lollies are in the whole bag?

5

Half a fence is 9 m long. How long is the whole fence?

Show answer

1. 1/2 2. 3/4 3. 5 4. 12 5. 18 m

Summary

What to take away

  • More parts means smaller parts.
  • 2/4 and 1/2 are equivalent.
  • Use groups to find a fraction of a set.
  • Copy the part to rebuild the whole.
Report a mistake

More in Number

Numbers to 120: Read, Write and CompareNotesGroups of Ten and Where Numbers Sit on a LineNotesRounding, Skip Counting, Odd and EvenNotesAdding and Taking Away: Facts to 20 and TensNotesStory Problems: Adding and Taking Away to 100NotesTimes and Share: 2s, 5s and 10sNotesHalves, Thirds and QuartersNotesComparing Fractions and Finding the WholeNotesNZ Coins and Notes: Count and Make MoneyNotes

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