Ratios and fractions

The Maths Habit

Which bars are more than half pink?

ANo: less than halfBYesCExactly half

Each box is one part. How many parts altogether?

5
7
9

Ratio
Compares one part with another part.
pinkwhitepink : white
Fraction
Compares one part with the whole.
pinkpinkwhole
Whole
All the parts together.
whole

redblue
first+second=all parts
red=the partall parts
  1. 1Draw the bar.One box for each part. Shade the first group.
  2. 2Add the parts.This is the whole.
  3. 3Write the fraction.The part on the top. All the parts on the bottom.

The ratio of red to blue is 2 : 3. What fraction of the counters are red?

1Draw the bar.
redblue
2Add the parts.
2+3=5
3Write the fraction.
red=25

The ratio of apples to pears is 3 : 4. What fraction of the fruit is apples?

1Draw the bar.
applespears
2Add the parts.
3+4=7
3Write the fraction.
apples=37

The ratio of red to blue is 2 : 3. What fraction of the counters are red?

1Draw the bar.
redblue
2Add the parts.
2+3=5
3Write the fraction.
red=25
12first+second=all parts3the partall parts

The ratio of boys to girls is 1 : 4. What fraction of the children are girls?

1Draw the bar.
boysgirls
2Add the parts.
1+4=5
3Write the fraction.
girls=45

The ratio of red to blue is 2 : 3. What fraction of the counters are red?

1Draw the bar.
redblue
2Add the parts.
2+3=5
3Write the fraction.
red=25
12first+second=all parts3the partall parts

The ratio of wins to losses is 5 : 2. What fraction of the games are wins?

1Draw the bar.
winslosses
2Add the parts.
5+2=7
3Write the fraction.
wins=57

The ratio of red to blue is 2 : 3. What fraction of the counters are red?

1Draw the bar.
redblue
2Add the parts.
2+3=5
3Write the fraction.
red=25
12first+second=all parts3the partall parts

The ratio of hens to ducks is 3 : 5. What fraction of the birds are ducks?

1Draw the bar.
hensducks
2Add the parts.
3+5=8
3Write the fraction.
ducks=58

12first+second=all parts3the partall parts

1The ratio of sand to cement is 2 : 7. What fraction of the mix is sand?

1
sandcement
2
2+7=9
3
sand=29

2The ratio of tea to coffee is 4 : 3. What fraction of the drinks are coffee?

1
teacoffee
2
4+3=7
3
coffee=37

3The ratio of pens to pencils is 3 : 2. What fraction of the pens and pencils are pens?

1
penspencils
2
3+2=5
3
pens=35

4The ratio of cars to vans is 2 : 5. What fraction of the vehicles are vans?

1
carsvans
2
2+5=7
3
vans=57

How many boxes are not shaded?

5
3
4

redblue
all parts−shaded=rest
red : blue=shaded:rest
  1. 1Draw the bar.The bottom number tells you how many boxes. Shade the top number of boxes.
  2. 2Find the rest.All the parts take away the shaded parts.
  3. 3Write the ratio.Shaded parts : the rest.

38 of the counters are red. The rest are blue. Write the ratio of red to blue.

1Draw the bar.
redblue
2Find the rest.
8−3=5
3Write the ratio.
red : blue=3:5

25 of the sweets are green. The rest are yellow. Write the ratio of green to yellow.

1Draw the bar.
greenyellow
2Find the rest.
5−2=3
3Write the ratio.
green : yellow=2:3

38 of the counters are red. The rest are blue. Write the ratio of red to blue.

1Draw the bar.
redblue
2Find the rest.
8−3=5
3Write the ratio.
red : blue=3:5
12all parts−shaded=rest3shaded:rest

16 of the vehicles are vans. The rest are cars. Write the ratio of vans to cars.

1Draw the bar.
vanscars
2Find the rest.
6−1=5
3Write the ratio.
vans : cars=1:5

38 of the counters are red. The rest are blue. Write the ratio of red to blue.

1Draw the bar.
redblue
2Find the rest.
8−3=5
3Write the ratio.
red : blue=3:5
12all parts−shaded=rest3shaded:rest

47 of the shirts are white. The rest are black. Write the ratio of black to white.

1Draw the bar.
whiteblack
2Find the rest.
7−4=3
3Write the ratio.
black : white=3:4

38 of the counters are red. The rest are blue. Write the ratio of red to blue.

1Draw the bar.
redblue
2Find the rest.
8−3=5
3Write the ratio.
red : blue=3:5
12all parts−shaded=rest3shaded:rest

710 of the seats are full. The rest are empty. Write the ratio of full to empty.

1Draw the bar.
fullempty
2Find the rest.
10−7=3
3Write the ratio.
full : empty=7:3

Ratios and fractions worksheet, page 1

Ratios and fractions worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. Red to blue is 2 : 3, so 25 are red.

    Right

  2. Red to blue is 1 : 2, so 12 are red.

    Wrong: 13

  3. 34 are red, the rest blue, so red to blue is 3 : 4.

    Wrong: 3 : 1

  4. Red to blue is 4 : 1, so 15 are blue.

    Right

  5. 27 are red, the rest blue, so red to blue is 2 : 5.

    Right

  1. Red to blue to green is 1 : 2 : 3. What fraction of the counters are green?

    12

  2. The ratio of boys to girls is 6 : 4. What fraction of the class are boys? Give it in its simplest form.

    35

  3. 14 of the pens are red and 12 are blue. The rest are black. Write the ratio of red to blue to black.

    1 : 2 : 1

  1. The ratio of pink to white is 2 : 5. What fraction of the beads are pink?

    27
    pinkwhite1Drawthe bar.2Addthe parts.+=3Writethe fraction.pink=

  2. 38 of the pens are black. The rest are blue. Write the ratio of black to blue.

    3 : 5
    1Drawthe bar.2Findthe rest.−=3Writethe ratio.black : blue=:

  3. Cats to dogs is 4 : 5. What fraction of the animals are dogs?

    59
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