## Aug 11, 2009

### Ratio - Simple word problems worksheet

1) Find the ratio of 36 yards to 48 yards.

Solution:

36 yards : 48 yards
= 36 : 48
Dividing both numbers by 2 (to avoid more steps we can also divide it by GCD)
= 18 : 24
Dividing both numbers by 2
= 9 : 12
Dividing both numbers by 3
= 3 : 4
This is the simplest form which is not reducible further.
36 yards : 48 yards = 3 : 4

2) Find the ratio of 65 days to 50 days.

Solution:

65 days : 50 days
65 : 50
Dividing both numbers by 5
13 : 10
This is the simplest form.
65 days : 50 days = 13 : 10

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Practice questions:

Find the ratio of
i) 200 m to 600 m

ii) 350 bags to 500 bags
iii) 25 feet to 125 feet
iv) 150 pencils to 225 pencils
v) 69 km to 96 km
vi) 22 yards to 77 yards
vii) 36 hours to 60 hours
viii) \$64 to \$48
ix) 121 inches to 99 inches

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3) Find the ratio of 36 hours to 2 days.

Solution:
1 day = 24 hours
2 days = 2 * 24 = 48 hours
36 hours : 2 days
= 36 hours : 48 hours
= 36 : 48
Dividing by 6 ( Use 2 to divide if not familiar with 6 )
= 6 : 8
Dividing by 2
= 3 : 4

4) Find the ratio of \$2.50 to 75 cents.

Solution:1 dollar = 100 cents
2.50 dollar = 2.50 * 100 = 250 cents
\$2.50 to 75 cents
= 250 cents : 75 cents
= 250 : 75
Dividing by 25
= 10 : 3

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Practice questions:

Find the ratio of
i) 12 inches to 3 feet
ii) 12 feet to 7 yards
iii) \$1.25 to half a dollar
iv) 8 quarters to 5 nickels
v) 36 pints to 4 gallons
vi) 20 ounces to 1.5 pounds
vii) 45 cm to 2 meter
viii) 3 hours 20 minutes to 2 hours 10 minutes
ix) 1250 feet to 1 mile
x) 12 cm to 1.2 cm

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5) There are 250 students in a certain school. If the number of boys in a school are 120. Find the ratio between
i) number of girls to number of boys
ii) number of boys to total number of students
iii) number of students to number of girls

Solution:

Number of students = 250
Number of boys = 120
Number of girls = Total number of students – Total number of boys
= 250 – 120
= 130

i) Number of girls to number of boys
= number of girls : number of boys
= 130 : 120
Dividing each term by 10
= 13 : 12
So, ratio between girls to the boys is 13 : 12

ii) Number of boys to total number of students
= number of boys : number of students
= 120 : 250
Dividing each term by 10
= 12 : 25
So, ratio between boys to the students is 12 : 25

iii) Number of students to number of girls
= number of students : number of girls
= 250 : 130
Dividing each term by 10
= 25 : 13
So, ratio between students to the girls is 25 : 13

6) Mr. Mac has 12 white balls, 15 black balls and 18 green balls. Find the ratio of
i) Black balls to white balls
ii) White balls to total number of balls
iii) Black balls to white balls to green balls

Solution:

Number of white balls = 12
Number of black balls = 15
Number of green balls = 18
Total number of balls = 12 + 15 + 18
= 45

i) Black balls to white balls
= black balls : white balls
= 15 : 12
Dividing each term by 3
= 5 : 4
So, the ratio of black balls to white balls is 5 : 4

ii) White balls to total number of balls
= white balls : total number of balls
= 12 : 45
Dividing each term by 3
= 4 : 15
So, the ratio of white balls to total number of balls is 4 : 15

iii) Black balls to white balls to green balls
= black balls : white balls : green balls
= 15 : 12 : 18
Dividing each term by 3
= 5 : 4 : 6
So, the ratio of black balls to white balls to green balls is 5 : 4 : 6

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Practice questions:

i) Mrs. Alice earns \$ 1200 per month. She spends \$ 800 and saves the rest. Find the ratio of her salary to savings ?
ii) Anne scored 40 points out of 50. Find the ratio between the number of points scored to total number of points.
iii) In grade six, 36 students were passed. Total students in a class are 48. Find the ratio of passed students to the failed students.