SIMPLIFYING RATIOS WITH DECIMALS WORKSHEET

Problem 1 :

Express the ratio in simplest form :

(a)  0.4 : 0.5

(b) 1.3 : 1.8

(c)  0.1 : 0.9

(d)  0.2 : 0.6

(e)  0.4 : 0.2

(f)  1.4 : 0.7

(g)  0.03 : 0.15

(h)  0.02 : 0.12

(i) 0.18 : 0.06

(j)  0.05 : 0.15

Problem 2 :

Use the fact that 1 mile is approximately the same distance as 1.6 km to convert

a) 30 miles to km

b) 21 miles to km

c)  80 km to miles

d)  20 km to miles

(a)   Solution :

0.4 : 0.5

On both parts of the ratio, we have only one digit after the decimal. So, we multiply both parts of the ratio by 10.

=  0.4(10) : 0.5(10)

=  4 : 5

(b)  Solution :

1.3 : 1.8

Multiply both parts of ratio by 10, we get

=  1.3(10) : 1.8(10)

=  13 : 18

It is not possible to simplify hereafter, so the answer is 13 : 18.

(c)  Solution :

0.1 : 0.9

Multiply both parts of ratio by 10, we get

=  0.1(10) : 0.9(10)

=  1 : 9

So, the answer is 1 : 9.

(d)  Solution :

0.2 : 0.6

Multiply both parts of ratio by 10, we get

=  0.2(10) : 0.6(10)

=  2 : 6

=  2/6

=  1/3

So, the answer is 1 : 3.

(e)   Solution :

0.4 : 0.2

Multiply both parts of ratio by 10, we get

=  0.4(10) : 0.2(10)

=  4 : 2

=  4/2

=  2/1

So, the answer is 2 : 1.

(f)  Solution :

1.4 : 0.7

Multiply both parts of ratio by 10, we get

=  1.4(10) : 0.7(10)

=  14 : 7

=  14/7

=  2/1

So, the answer is 2 : 1.

(g)  Solution :

0.03 : 0.15

Multiply both parts of ratio by 100, we get

=  0.03(100) : 0.15(100)

=  3 : 2

=  4/2

=  2/1

So, the answer is 2 : 1.

(h)  Solution :

0.02 : 0.12

Multiply both parts of ratio by 100, we get

=  0.02(100) : 0.12(100)

=  2 : 12

=  2/12

=  1/6

So, the answer is 1 : 6.

(i)  Solution :

0.18 : 0.06

Multiply both parts of ratio by 100, we get

=  0.18(100) : 0.06(100)

=  18 : 6

=  18/6

=  3/1

So, the answer is 3 : 1.

(j)  Solution :

0.05 : 0.15

Multiply both parts of ratio by 100, we get

=  0.05(100) : 0.15(100)

=  5 : 15

=  5/15

=  1/3

So, the answer is 1 : 3.

Problem 2 :

Use the fact that 1 mile is approximately the same distance as 1.6 km to convert

a) 30 miles to km

b) 21 miles to km

c)  80 km to miles

d)  20 km to miles

Solution :

1 mile = 1.6 km -----(1)

a) 30 miles to km

Multiplying (1) by 30 on both sides

30 miles = 1.6 x 30 km

= 48 km

b) 21 miles to km

Multiplying (1) by 21 on both sides

21 miles = 1.6 x 21

= 33.6 km

c)  80 km to miles

From (1),

1 mile = 1.6 km

1 km = 1/1.6 mile

1 km = 0.625 miles ------(2)

Multiplying (2) by 80 on both sides

80 km = 0.625 x 80 miles

= 50 miles

d)  20 km to miles

Multiplying (2) by 20 on both sides

20 km = 0.625 x 20 miles

= 12.5 miles

Problem 3 :

If £1 is worth of $1.60 convert

a) £15 to dollars

b) $8 to pounds

Solution :

The value of £1 = $1.60 -------(1)

a) £15 to dollars

To find the value of £15, we will multiply (1) by 15 on both sides.

£1 x 15 = $1.60 x 15

£15 = $24

b) $8 to pounds

To convert dollars to pounds, we have to find the value of $1 in pounds.

$1.60 = £1

$1 = £1/1.60

$1 = £0.625 ------(2)

Multiplying (2) by 8 on both sides, we get

$1 x 8 = £0.625 x 8

$8 = £5

Problem 4 :

If 25 floppy disc cost $5.50. Calculate the cost of 11 floppy discs.

Solution :

Cost of 25 floppy disc = $5.50

Cost of 1 floppy disc = 5.50/25

= $0.22

Cost of 1 floppy disc = $0.22

Cost of 11 floppy disc = 0.22 x 11

= $2.42

Problem 5 :

Anna has 75 pence. Rashid has £1.20. What is the ratio of Rashid's money to Anna's money ?

Solution :

100 pence = £1

Amount Anna has = 75 pence

Amount Rashid has = £1.20

Converting into pence,

1.20 x 100 ==> 120 pence

Ratio between Rashid's money to Anna's money

= 120 : 75

= 120/75

= 24/15

= 8/5

So, the ratio between their money is 8 : 5.

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