High School Maths Examples and Questions

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Answers − Ratios

  1.   Share £400 in the ratio 1 : 3

(a)  Add the separate parts of the ratio to find the total number of parts
1 + 3 = 4
(b)  Divide 400 by 4 to find the value for each part: 100
(c)  Multiply each term in the ratio by 100:
1 x 100 = 100, 3 x 100 = 300

So £400 shared in the ratio 1 : 3 is £100 and £300

  2.   Divide 225 grams in the ratio 1 : 2

(a)  Add the separate parts of the ratio to find the total number of parts
1 + 2 = 3
(b)  Divide 225 by 3 to find the value for each part: 75
(c)  Multiply each term in the ratio by 75:
1 x 75 = 75, 2 x 75 = 150

So £225 shared in the ratio 1 : 2 is £75 and £150

  3.   Share £560 in the ratio 3 : 5

(a)  Add the separate parts of the ratio to find the total number of parts
3 + 5 = 8
(b)  Divide 560 by 8 to find the value for each part: 70
(c)  Multiply each term in the ratio by 70:
3 x 70 = 210, 5 x 70 = 350

So £560 shared in the ratio 3 : 5 is £210 and £350

  4.   Divide 270 kg in the ratio 2 : 7

(a)  Add the separate parts of the ratio to find the total number of parts
2 + 7 = 9
(b)  Divide 270 by 9 to find the value for each part: 30
(c)  Multiply each term in the ratio by 30:
2 x 30 = 60, 7 x 30 = 210

So 270 kg shared in the ratio 2 : 7 is 60 kg and 210 kg

  5.   Share £440 in the ratio 3 : 8

(a)  Add the separate parts of the ratio to find the total number of parts
3 + 8 = 11
(b)  Divide 440 by 11 to find the value for each part: 40
(c)  Multiply each term in the ratio by 12:
3 x 40 = 120, 8 x 40 = 320

So £440 shared in the ratio 3 : 8 is £120 and £320

  6.   The cost of a weekend break is divided between two families in the ratio of 3 : 7 the smaller share was £90. How much is the total cost of the weekend break?

(a)  Add the separate parts of the ratio to find the total number of parts
3 + 7 = 10
(b)  3/10 of the cost was £90, so 1/10 is £30
(c)  The total cost is:
10 x £30 = £300

So the total cost is £300

  7.   The cost of a holiday is divided between two families in the ratio of 3 : 8 the smaller share was £240. How much is the total cost of the holiday?

(a)  Add the separate parts of the ratio to find the total number of parts
3 + 8 = 11
(b)  3/11 of the cost was £240, so 1/11 is £80
(c)  The total cost is:
11 x £80 = £880

So the total cost is £880

  8.   The ratio of male teachers to female teachers is 2 : 7. If there are 84 female teacher, how many male teachers are there?

(a)  Add the separate parts of the ratio to find the total number of parts
2 + 7 = 9
(b)  So 7/9 are female teachers is 84, so 1/9 is 12
(c)  The number of male teachers:
2 x 12 = 24

So the total number of male teachers is 24

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