WRITE THE GIVEN RATIOS IN SIMPLEST FORM

Write each ratio as a fraction in simplest form, using a colon, and using the word “to”.

Problem 1 :

3 sailboats to 6 motorboats

Solution :

Ratio between sail boats to motorboats = 3 : 6

Dividing both parts by 3, we get

= (3/3) : (6/3)

= 1 : 2

Problem 2 :

4 tulips to 9 daffodils

Solution :

Ratio between tupils to daffodils = 4 : 9

It cannot be simplified further.

= 4 : 9

Problem 3 :

5 baseballs to 25 softballs

Solution :

Ratio between baseballs to softballs.

= 5 : 25

Dividing both parts by 5.

= (5/5) : 25/5)

= 1 : 5

Problem 4 :

2 days out of 8 days

Solution :

Ratio between days out to total days.

= 2 : 8

Dividing both parts by 2, we get

= (2/2) : 8/2)

= 1 : 4

Problem 5 :

6 poodles out of 18 dogs

Solution :

Ratio between number of poodles to total dogs.

= 6 : 18

Dividing both parts by 6, we get

= (6/6) : 18/6)

= 1 : 3

Problem 6 :

10 yellow eggs out of 12 colored eggs

Solution :

Ratio between yellow eggs to coloured eggs.

= 10 : 12

Dividing both parts by 2, we get

= (10/2) : (12/2)

= 5 : 6

Problem 7 :

12 sheets of paper out of 28

Solution :

Ratio between two sheets.

= 12 : 28

Dividing both parts by 4, we get

= (12/4) : (28/4)

= 3 : 7

Problem 8 :

18 hours out of 24 hours

Solution :

Ratio between number of hours he is out to total hours.

= 18 : 24

Dividing both parts by 3, we get

= 2 : 3

Problem 9 :

16 elms out of 20 trees

Solution :

Ratio between number of elms out of total trees.

= 15 : 24

Dividing both parts by 3, we get

= 5 : 8

Problem 10 :

15 trumpets to 9 trombones

Solution :

Ratio between no of trumpets to trombones

= 15 : 9

Dividing both parts by 3, we get

= (15/3) : (9/3)

= 5 : 3

Problem 11 :

5 ducks to 30 geese

Solution :

Ratio between ducks to geese.

= 5 : 30

Dividing both parts by 5, we get

= (5/5) : 30/5)

= 1 : 6

Problem 12 :

14 lions to 10 tigers

Solution :

Ratio between lions and tigers.

= 14 : 10

Dividing by 2, we get

= (14/2) : (10/2)

= 7 : 5

Problem 13 :

6 sodas out of 16 drinks

Solution :

Ratio between sodas to total number of drinks.

= 6 : 10

Dividing by 2 on both sides.

= 3 : 5

Problem 14 :

20 blue jays out of 35 birds

Solution :

Ratio between blue jays to total number of birds.

= 20 : 35

Dividing each part by 5, we get

= (20/5) : (35/5)

= 4 : 7

Problem 15 :

An office opens at 9 am and closes at 5 pm with a lunch interval of 30 minutes. What is the ratio of lunch interval to the total period in office ?

Solution :

Time difference between 9 am to 5 pm = 5 + 12

= 17

= 17 - 9

= 8 hours

Lunch interval = 30 minutes

= 1/2 hour

Ratio :

= 1/2 : 8

= 1 : 16

Problem 16 :

The length of a steel tape for measurements of building is 10 m and its width is 2.4 cm. Waht is the ratio of its length to width?

Solution :

Length = 10 m

Width = 2.4 cm

1 m = 100 cm

10 m = 10 x 100

= 1000 cm

Ratio between length to width = 1000 : 2.4

= (1000/2.4) x (10/10)

= 10000/24

= 5000/12

= 2500/6

= 1250/3

= 1250 : 3

Problem 17 :

The number of boys and girls in a school are 1168 and 1095 respectively. Express the ratio of the number of boys to that of girls in the simplest form.

Solution :

Number of boys to girls = 1168 : 1095

= 1168/1095

Greatest common factor of 1168 and 1095 = 73

= 1168 ÷ 73 / 1095 ÷ 73

= 16 / 15

So, the required form of ratio is 16 : 15.

Problem 18 :

Manoj weight is 36 kg. His brother weight is 2 kg more. Find the ratio of weight of Manoj's brother to Manoj.

Solution :

Weight of Manoj = 36 kg

Weight of Manoj's brother = 36 + 2

= 38 kg

= 36 : 38

= 18 : 19

So, the required ratio is 18 : 19.