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Year 4AC9M4N03

Fractions of a Whole

Find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation.

Read this first

A fraction is a way to name part of a whole. The pieces must all be the same size.

One half, one quarter and one eighth1/21/41/8

More pieces means each piece is smaller. One eighth is the smallest here.

Words you need

Numerator
The top number. It counts the pieces you have.
Denominator
The bottom number. It says how many equal pieces the whole was cut into.
Whole
The full thing, before you cut it up.

Worked example

e.g. A cake is cut into 8 equal pieces. You take 3. What fraction did you take?
  1. The cake was cut into 8 pieces. So the bottom number is 8.
    A cake cut into eight piecescake
  2. You took 3 pieces. So the top number is 3.
    Three of the eight pieces taken3/8
  3. You took three eighths.

Bottom number first: how many pieces in all. Then top: how many you have.

Practice

The pictures fade as you go. By the last few you are on your own.

1What fraction is shaded?with a picture
Two of four parts shaded?
Answer24\tfrac{2}{4}, which is the same as 12\tfrac{1}{2}. Four pieces in all, two shaded.
2Which is bigger: 14\tfrac{1}{4} or 18\tfrac{1}{8}?with a picture
One quarter next to one eighth1/41/8
Answer14\tfrac{1}{4} is bigger. Cutting into 4 gives bigger pieces than cutting into 8.
3A pizza is cut into 4 equal slices. You eat 3. What fraction did you eat?with a hint
Need a hint?

How many slices in all? That is the bottom number.

Answer34\tfrac{3}{4}.
4How many quarters make one whole?with a hint
Need a hint?

Look at a bar cut into 4. How many pieces to fill it?

Answer4. Four quarters make one whole, so 44=1\tfrac{4}{4} = 1.
5What fraction of a whole is 5 pieces out of 8?on your own
Answer58\tfrac{5}{8}.
6Which is smaller: 12\tfrac{1}{2} or 18\tfrac{1}{8}?on your own
Answer18\tfrac{1}{8}.
7How many eighths make one half?on your own
Answer4, because 48=12\tfrac{4}{8} = \tfrac{1}{2}.

Think about it

1
Why must the pieces be the same size?
One good answerIf one piece is bigger, you cannot say how much you have. A quarter only means something when all four pieces match.
2
Sam says 18\tfrac{1}{8} is bigger than 14\tfrac{1}{4} because 8 is bigger than 4. What would you tell him?
One good answerThe bottom number says how many pieces the whole was cut into. More pieces means each one is smaller. So 18\tfrac{1}{8} is smaller.
3
What does it mean when the top and bottom numbers are the same, like 55\tfrac{5}{5}?
One good answerYou have every piece. That is one whole.

Common mistakes

Cutting a shape into pieces that are not equal and calling them quarters.
Fractions only work when every piece is the same size.
Thinking a bigger bottom number means a bigger fraction.
It means more pieces, so each piece is smaller.
Mixing up the top and bottom numbers.
Bottom is how many pieces in all. Top is how many you have.
Next step
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