Introduction for practice ratio problems:
In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Example: For every Spoon of sugar, you need 2 spoons of flour (1:2)
In our daily life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’ . If two ratios are equal, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.
In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Example: For every Spoon of sugar, you need 2 spoons of flour (1:2)
In our daily life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’ . If two ratios are equal, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.
Practice Examples for Ratio Problems:
Problem 1:
In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. suppose the bag contains totally 120 green sweets then how many red sweets are there?
Solution:
Step 1: Assign variables:
Let x = red sweets
Write the items in the ratio as a fraction.
Red / green = 4 / 5 = x / 120
Cross Multiply
4 × 120 = 5 × x
480 = 5x
480 = 5x
Isolate variable x
x = 480 / 5 = 96
x = 480 / 5 = 96
Answer: There are 96 red sweets.
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Problem 2:
There are 280 students in a certain school. If the number of boys in a school are 150. Find the ratio between
i) Number of girls to number of boys
ii) Number of boys to total number of students
Solution:
Solution:
Number of students = 280
Number of boys = 150
Number of girls = Total number of students – Total number of boys
= 280 – 150
= 130
i) Number of girls to number of boys
Number of girls: number of boys
= 130: 150
Dividing each term by 10
= 13: 15
So, ratio between girls to the boys is 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
= 150: 280
Dividing each term by 10
= 15: 28
So, ratio between boys to the students is 15 : 28
So, ratio between boys to the students is 15 : 28
Problem 3:
Length and breadth of a rectangular field are 80 m and 20 m respectively. Find the ratio of the length to the breadth of the field.
Solution:
Length of the rectangular field = 80 m
Breadth of the rectangular field = 20 m
The ratio of the length to the breadth is 80: 20
The ratio can be written as
= 80 / 20 = 4:1
Thus, the required ratio is 4:1
Practice Ratio Problems:
Practice problem 1:
Find the ratio of 24 yards to 36 yards.
Answer: 3: 4
Practice problem 2:
Find the ratio of 39 days to 30 days.
Answer: 13: 10
Practice problem 3:
Mrs. Alice earns $ 160 per month. She spends $ 8 and saves the rest. Find the ratio of her salary to savings?
Answer: 20: 1
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