In this article, you will learn about the problems of ratios in the simplest form. We know that a ratio needs to be expressed always in its lowest terms or simplest form. A Ratio will be in the simplest form if the first term and the second term are consequent and have no common factors other than 1. In order to write a ratio in the simplest form, sometimes we need to find out the Highest Common Factor of the terms and divide each term by the HCF.
6th Grade Math Students can practice at their own pace and gradually move on to difficult level problems on the topic too. On this page, you will learn about solved example problems on reducing ratios to lowest forms, etc. all explained step by step.
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Problems on Expressing Given Ratios in Simplest Form | Ratios in Simplest Form Questions and Answers
Problem 1:
A shirt costs Rs.64 another cost is Rs.32. Find the Ratio in the simplest form?
Solution:Â
Given that,
The cost of the shirts is 64: 32.
Now, we need to find the ratio in the simplest form.
Next, find the HCF. The Highest Common Factor of 64 and 32 is 32.
Then the ratio is (64/32) : (32/32)= 2: 1.
Therefore, the ratio in the simplest form is 2: 1.
Problem 2:
Find the ratio of the following in the simplest form. The following is 3m 5cm to 35cm.
Solution:
Given that, the value is 3m 5cm to 35cm.
Now, we will find the ratio in simplest form.
We know that, 1 meter = 100 cm.
So, 3m 5cm = 3 x 100cm + 5 cm = 305cm.
Thus, the ratio is 3m 5cm: 35cm = 305cm : 35cm
= 305/35 = 61/7
Hence, the final ratio in simplest form is 61: 7.
Problem 3:
Ryan earned 4000 and paid 500 as income tax and spent $1500 on household expenses. Find the ratio of
(i) Income tax to income
(ii) Household Expenses to income
(iii) Savings to Earnings
Solution:Â
As given in the question,
Ryan’s total income is Rs.4000.
He paid to income is Rs.500.
He spent Rs.1500 on household Expenses.
Now, you have to find the ratios of the following,
(i)Income tax to Income
The amount used to paid income tax is rs.500.
So, the income tax to income ratio is 500/4000.
The Highest Common Factor of 500, 4000 is 500.
then (500/500) / ( 4000/500) = 1 / 8.
The ratio in the simplest form of income tax to income is 1:8.
(ii) Household Expense to Income
The amount used for the household expense is Rs. 1500
Now, we will find the household expense to income ratio that is 1500/4000.
The highest common factor of 1500, and 4000 is 500.
Then the ratio is (1500/ 500) / (4000/500) = 3/8.
Thus, the simplest ratio of household expenses is 3:8.
(iii) Savings to Earnings
Now, we will find the savings to earnings ratio.
So, the Savings = Income – (Expense + income)
Substitute the values, we get
Savings = 4000-(1500+500) = 4000 – 2000 = 2000.
The savings amount is 2000.
The savings to earnings ratio is 2000/4000.
The Highest Common Factor of 2000, and 4000 is 2000.
Then, the ratio is (2000/2000) /(4000/2000) = 1/2 = 1:2.
Hence, the ratio of Savings to Earnings is 1:2.
Problem 4:
Find the ratio of 81cm to 2.70m in the simplest form.
Solution:
As given in the question, the value is 81 cm to 2.70m.
Now, we have to find the ratio in the simplest form.
We know that 1meter = 100 cm.
So, 2.01m= 2 x 100cm + 1 cm = 270cm.
Thus, the ratio is 81cm to 270cm = 9/30
Hence, the final ratio in the simplest form of 81cm to 2.70 m is 9cm: 30cm.
Problem 5:
The height of a 1.5m shrub to the height of a 6m tree. Find the simplest form of ratio?
Solution :
As given in the question,
The height of a shrub is 1.5m.
The height of a tree is 6m.
So, the shrub to tree ratio is 1.5m: 6m.
Now, multiply both sides by 10, we get
The shrub to tree ratio is 15: 60.
Next, find the HCF. So, the Highest Common Factor of 15 and 60 is 15.
Then (15/15) :(60/15) = 1:4.
Thus, the ratio in simplest form is 1:4.
Problem 6:
The top speed of a car is 150 km h-1 to the top speed of a formula. One car is 350 km h-1. What is the simplest form ratio?
Solution:
Given that,
The ratio of speed is 150: 350.
We will find the ratio in the simplest form.
But, first, we have to find the Highest Common Factor.
The HCF of 150 and 350 is 50.
So, the ratio is (150/50) : ( 350/50) = 3: 7
Thus, the ratio in the simplest form of 150, and 350 is 3:7.
Problem 7:
What are the following ratios in the same units and then express them in their smallest form?
(i) 5 kg : 100 gm
(ii) 5 cm : 0.7 m
(iii) 2 m : 80 cm
(iv) 4 hour : 60 minutes
Solution:
As given in the question,
(i) 5 kg : 200 gm
Now, we need to find the ratio in the simplest form.
we know that 1 kg=1000 gm.
5000 gm: 100 gm = 50gm :2gm
By dividing with 2. we get,
50/2 : 2/2 = 25:1
So, the simplest form ratio is 25:1.
(ii) 5cm : 0.7m
We know that 1m=100 cm.
So, the value is 5cm: 70m.
Now, divide by 5 into both sides.
Then, the value is 1: 14
Thus, the ratio in simplest form is 1:14.
(iii) 2 m : 80 cm
we know that 1m=100 cm.
200 cm:80 cm
20 cm:8 cm
Now, Divide with 2, we get
20/2 cm:8/2 cm =10 :4
So, the simplest form ratio is 10cm: 4cm.
(iv) 4 hour : 60 minutes
we know that 1 hour = 60 minutes.
So, it will be 240 minutes:40 minutes
By dividing with 40 we get,
then the ratio is 240/40 : 40/40 = 6:1.
Hence, the ratio in the simplest ratio is 6:1.
Problem 8:
The following are the ratios. What is the simplest form ratios,
(i) 500 kg : 0.1 quintal
(ii) 50 paise : 1 Rupee
(iii) 300 m : 6 km
(iv) 4 hours : 1 day
Solution:Â
As given in the question,
(i) 500 kg: 0.1 quintal
we know that 1 quintal=1000 kg
So, the value is 500 kg:100 kg
Now, divide with 50 we get,
500/50 : 100/50 = 10:2.
So, the ratio in simplest form is 10:2.
(ii) 50 paise : 1 Rupee
we all know that 1 rupee=100 paise.
So, 50 paise:100 paise
Divide with 50, we get
Hence the ratio is 1 paise:2 paise.
(iii) 300 m: 6 km
we know that 1 km=1000 m.
300 m: 6000 m = 3m:60m.
Now, dividing by 3. we get,
3/3:60/3
Thus, the simplest form ratio is 1:20.
(iv) 4 hours : 1 day
we know that 1 day=24 hour.
4 hours: 24 hours
By dividing with 4, we get
Hence, the final ratio is 1:6.
Problem 9:
What is the simplest form of ratio? If the height of an insect is 2mm to the height of a rat which is 10 cm.
Solution:
As given in the question,
The height of an insect is 2mm.
The height of a rat is 10cm.
Now, we need to find the ratio in the simplest form.
As both the measurements are in different units, first make their units the same.
So, we know that, 1mm = 0.1cm.
Now, the value is 2mm = 0.2cm.
The insect to rat ratio is 0.2 cm: 10cm.
Now, Multiply both sides by 10, we get
0.2 x 10 : 10 x 10 = 2 :100
Next, the Highest Common factor of 2 and 100 is 2.
Then the value is (2/2) : (100/2)= 1cm: 50cm.
So, the ratio in the simplest form of 2mm and 10cm is 1cm: 50cm.