SIMPLIFYING RATIOS INVOLVING DECIMALS

In the following exercises, write each ratio as a fraction.

Problem 1 :

6.4 to 0.8

Solution :

6.4: 0.8

Multiply both parts of ratio by 10, we get

= 6.4(10): 0.8(10)

= 64: 8

= 64/8

Dividing both numerator and denominator by 8, we get

= 8/1

So, the answer is 8:1.

Problem 2 :

1.26 to 4.2

Solution :

1.26 : 4.2

In 1.26, we have two digits after the decimal, in 4.2 we have one digit after the decimal. So, multiply both parts by 100.

= 1.26(100) : 4.2(100)

= 126 : 420

= 63/210

= 21/70

= 7/10

So, the answer is 7:10.

Problem 3 :

0.56 to 2.8

Solution :

0.56 : 2.8

Multiply both parts by 100, we get

= 0.56(100) : 2.8(100)

= 56 : 280

Dividing both parts by 28, we get

= 2 :10

Dividing both parts by 2, we get

= 1 : 5

So, the answer is 1 : 5.

Problem 4 :

$1.21 to $0.44

Solution :

1.21 : 0.44

Multiply both parts of ratio by 100, we get

= 1.21(100) : 0.44(100)

= 121 : 44

= 121/44

Dividing both parts by 11, we get

= 11/4

So, the answer is 11 : 4.                               

Problem 5 :

$1.38 to $0.69

Solution :

1.38 : 0.69

Multiply both parts of ratio by 100, we get

= 1.38(100) : 0.69(100)

= 138 : 69

= 138/69

= 2/1

So, the answer is 2:1. 

Problem 6 :

Soap bars at 8 for $8.69

Solution :

The ratio is 8 : 8.69

Problem 7 :

Soap bars at 4 for $3.39

Solution :

By writing it as ratio, we get

= 4 : 3.39

Multiply both parts by 100, we get

= 4(100) : 3.39(100)

= 400 : 339

Problem 8 :

Women’s sports socks at 6 pairs for $7.99

Solution :

= 6 : 7.99

Multiply both parts by 100, we get

= 6(100) : 7.99(100)

= 600 : 799

So, the required ratio is 600 : 799.

Problem 9 :

Men’s dress socks at 3 pairs for $8.49

Solution :

= 3 : 8.49

Multiply both parts by 100, we get

= 3(100) : 8.49(100)

= 300 : 849

= 100 : 283

So, the required ratio is 100 : 283.

Problem 10 :

Snack packs of cookies at 12 for $5.79

Solution :

= 12 : 5.79

Multiplying both parts by 100, we get

= 12(100) : 5.79(100)

= 1200 : 579

= 400 : 193

The ratio is 400 : 193.

Problem 11 :

Granola bars at 5 for $3.69

Solution :

= 5 : 3.69

Multiplying both parts by 100, we get

= 5(100) : 3.69(100)

= 500 : 369

Problem 12 :

CD-RW discs at 25 for $14.99

Solution :

= 25 : 14.99

Multiply both parts by 100.

= 25(100) : 1499

= 2500 : 1499

Problem 13 :

CDs at 50 for $4.49

Solution :

= 50 : 4.49

Multiply both parts by 100.

= 50(100) : 4.49(100)

= 5000 : 449

So, the required ratio is 5000 : 449.

Problem 14 :

The grocery store has a special on macaroni and cheese. The price is $3.87 for 3 boxes. How much does each box cost?

Solution :

= 3.87 : 3

Multiplying both parts by 100, we get

= 3.87(100) : 3(100)

= 387 : 300

Dividing by 3 on both sides.

= 129 : 100

So, the required ratio is 129 : 100.

Problem 15 :

Which costs more per issue, an 18 issue subscription for $40.50 or a 12 issue subscription for $33.60 ?

Solution :

Cost of 18 issue = $40.50

Cost of 1 issue = 40.50/18

= $2.25

Cost of 12 issue = $33.60

Cost of 1 issue = 33.60/12

= $2.8

$2.25 is lesser.

Problem 16 :

A scale model of an airplane has a width of 13.5 inches. The scale of the model is 1 inch = 8 feet. What is the width of the actual airplane ?

a)  110 ft   b)  108 ft     c)  104 ft    d)  115 ft

Solution :

Scale mode of width = 13.5 inches

1 inch = 8 feet

13.5 inches = 13.5 x 8

= 108 feet

So, option b is correct.

Problem 17 :

Ana earns $6.80 per hour when she works on weekdays. She earns twice that amount per hour when she works on weekends. If Ana worked 4 hours on Tuesday, 4 hours on Thursday and 5 hours on Saturday, then how much did she earn ?

Solution :

Number of hours she is working in the weekdays = 4 + 4

= 8

Number of hours she is working in the weekends = 5

Amount she earns on weekdays = $6.80 per hour

Amount she earns on weekends = 2(6.80)

= $13.6

= 8(6.80) + 5(13.6)

= 54.4 + 68

= $122.4

So, she earns $122.4.