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Ratio Quiz - CBSE Class 6 Mathematics

Free practice quiz: Ratio (CBSE Class 6 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 11 multiple-choice questions on Ratio, and 11 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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What a ratio means

A ratio compares two quantities of the same kind by division, showing how many times one is of another.
The ratio of a to b is written a:b and read as 'a is to b'.
Order matters: a:b is different from b:a. Both quantities must be in the same units.

Ratio as a fraction

\[a:b=\frac{a}{b},\ b\neq 0\]

Order matters

\[a:b\neq b:a \text{ when } a\neq b\]

Common mistake: Writing the terms in the wrong order, for example giving flour to sugar when the question asks for sugar to flour.

Equivalent ratios

Multiplying or dividing both terms of a ratio by the same non-zero number gives an equivalent ratio.
Equivalent ratios show the same comparison, just like equivalent fractions.

Multiplying both terms

\[a:b=(a\times k):(b\times k),\ k\neq 0\]

Dividing both terms

\[a:b=\frac{a}{k}:\frac{b}{k},\ k\neq 0\]

Check by cross-multiplying

\[a:b=c:d \iff a\times d=b\times c\]

Common mistake: Adding the same number to both terms. This does not give an equivalent ratio. You must multiply or divide both terms.

Ratio in simplest form

A ratio is in simplest form when its two terms have no common factor other than one.
To simplify, divide both terms by their HCF.

Simplest form using HCF

\[a:b=\frac{a}{h}:\frac{b}{h},\ h=\text{HCF}(a,b)\]

Common mistake: Dividing by a common factor that is not the HCF and stopping too early. Check that the new terms share no common factor.

Finding a missing quantity

If two quantities are in ratio a:b, think of them as a equal parts and b equal parts.
Use the known quantity to find the value of one part. Then multiply to get the other quantity.

Value of one part

\[\text{one part}=\frac{x}{a} \text{ when the first quantity is } x\]

Second quantity

\[y=\frac{x}{a}\times b\]

Common mistake: Dividing the known quantity by the wrong term. Match the given quantity to its own term in the ratio.

Sharing a total in a ratio

When a total T is split in ratio a:b, there are a+b equal parts altogether.
Find one part by dividing T by a+b. Then multiply by each term to get each share.

Total number of parts

\[\text{parts}=a+b\]

First share

\[\frac{a}{a+b}\times T\]

Second share

\[\frac{b}{a+b}\times T\]

Total from one quantity

\[T=\frac{x}{a}\times(a+b)\]

Common mistake: Dividing the total by only one term of the ratio instead of by the sum of both terms.

Exam tips

Read the question carefully to see which quantity comes first in the ratio.
Check that your shares add up to the total and simplify to the given ratio.
Always give the final ratio in simplest form unless the question asks otherwise.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the ratio of 4 to 8?
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Answer: A. 1:2
The ratio of 4 to 8 is simplified by dividing both numbers by their greatest common divisor, which is 4. Therefore, 4 ÷ 4 = 1 and 8 ÷ 4 = 2, giving us a ratio of 1:2.
What is the ratio of 15 to 25 in simplest form?
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Answer: A. 3:5
Both 15 and 25 can be divided by 5. So, 15 ÷ 5 = 3 and 25 ÷ 5 = 5, resulting in the ratio of 3:5.
In a class of 30 students, the ratio of boys to girls is 2:3. How many girls are in the class?
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Answer: A. 18
The total parts of the ratio is 2 + 3 = 5 parts. Each part represents 30 ÷ 5 = 6 students. The number of girls is 3 parts × 6 students/part = 18 girls.
If the ratio of the length to the width of a rectangle is 3:2 and the width is 10 cm, what is the length?
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Answer: A. 15 cm
With a ratio of 3:2, for every 3 units of length, there is 2 units of width. If the width is 10, the length is (3/2)*10 = 15 cm.
There are 50 students in a room in the ratio 3:2 of boys to girls. How many boys are there?
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Answer: B. 30
The total parts in the ratio is 3+2=5. With 50 students, each part represents 50/5=10. Thus, boys = 3×10 = 30 boys.