What are fractions?

What are fractions? exercise

• Help identify the shapes that show $\frac1 4$.

  Hints

  First, work out the denominator - bottom number. How many parts are there?

  To show $\frac1 4$ the shape needs to be divided into 4 equal parts.

  Next, work out the numerator - top number. To find this you need to count the number of equal parts shaded.

  To find $\frac1 4$ 1 part out of 4 needs to be shaded.

  In this example there are 5 equal parts. So the denominator - bottom number is 5.

  There is 1 part shaded. So our numerator - top number is 1.

  1 out of 5 is shaded. $\frac1 5$

  Solution

  To identify a $\frac1 4$ it needs to have 4 equal parts and 1 of the 4 needs to be shaded.

  The circle and triangle show $\frac1 4$ shaded in because there are 4 equal parts and 1 part is shaded in.

• How much cake has been eaten?

  Hints

  First, count how many slices are missing from the cake.

  This will give you the numerator - top number.

  Count how many equal slices the cake has been split into.

  This will give you the denominator - bottom number.

  In this example we can see that this cake was split into 4 equal parts.

  There are 3 slices missing. So $\frac3 4$ of this cake has been eaten.

  Solution

  When working out the denominator (bottom number), we count how many equal parts the cake had been split into.

  When working out the numerator (top number), we count to see how many slices were missing.

• Help Axel and Tank identify what fractions of the chocolate, pizza and pie are left.

  Hints

  First, count how many equal parts it has been split into. This will give you the denominator - bottom number.

  Next, count the amount of parts that are left. This will give you the numerator - top number.

  In this example, we can see that there are 6 equal parts.

  2 parts have been eaten, so there are 4 pieces left.

  This gives us the fraction $\frac4 6$.

  Solution

  $\frac1 4$ - 4 equal parts with 1 part highlighted or left over.

  $\frac2 3$ - 3 equal parts with 2 parts highlighted or left over.

  $\frac2 5$ - 5 equal parts with 2 parts highlighted or left over.

• Can you help match the fractions and answers?

  Hints

  To help find the fractions of amounts, we can look at the denominator - bottom number. This will tell us how many equal groups the total number has been split into.

  Look at the numerator - top number. This will tell you how many of those equal groups you need.

  For example, if there are 9 counters and you need to find $\frac1 3$; you would split the 9 into 3 equal groups. 1 group = 3 and would represent $\frac1 3$. 2 groups = 6 and would represent $\frac2 3$.

  In this example there are 12 sweets.

  If we want to find $\frac1 3$, we need to divide the whole amount 12 by 3 - the denominator - bottom number. This tells us how many equal groups we need.

  12 $\div$ 3 = 4

  Solution

  To find fractions of amounts we look at the denominator. This will tell us how many equal groups to split the items/objects into.

  The numerator tells us how many of the groups we need.

  $\frac1 4$ = 5 . We look at the amount of cards which is 25. Then we divide 25 by the denominator (bottom number). This gives us 5.

  $\frac1 5$ = 2 . We look at the total number of counters which is 10. We then divide 10 by the denominator (bottom number) which is 5. 10 divided by 5 = 2.

  $\frac2 3$ = 4 . 6 cards divided by the denominator 3 gives us 2. We then multiply this by the numerator as we want 2 of the groups $\frac2 3$. 2 x 2 = 4.

  $\frac1 2$ = 6 . 12 counters divided by the denominator 2 = 6

• Can you work out which images show $\frac1 3$ shaded?

  Hints

  The denominator is 3. This means that we are looking for a shape that has 3 equal parts.

  The numerator - top number, tells us how many of those parts are shaded.

  In this example it is showing 3 out of 4 squares are shaded.

  The image consists of a rectangle spilt into 4 equal parts. The 4 will be our denominator which is the bottom number.

  3 parts have been shaded in. 3 will be our numerator which is the top number of a fraction.

  Solution

  First, we must count the equal parts the shape has been split into.

  We are looking for a shape that has 3 equal parts.

  Next, we must find a shape where 1 part of the 3 is shaded.

  All the highlighted shapes in the above image show $\frac1 3$.

• Can you help Axel and Tank work out what they have left?

  Hints

  The denominator - bottom number tells us how many equal parts the whole has been split into.

  The numerator - top number tell us the number of parts it represents.

  Solution

  What fraction of the cake has been eaten? $\frac3 4$

  What fraction of the cake is left? $\frac1 4$

  There are 16 cards in total.

  There are 4 blue cards, 4 pink cards and 8 green cards.

  What fraction of cards are blue? $\frac1 4$

  There are 10 counters in total. 5 out of 10 counters are yellow.

  The fraction of yellow counters is $\frac1 2$.