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Introduction Quiz - CBSE Class 7 Mathematics

Free practice quiz: Introduction (CBSE Class 7 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 18 multiple-choice questions on Introduction, and 18 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 Is a Rational Number

A rational number can be written as p/q, where p and q are integers and q is not zero.
All integers, whole numbers, natural numbers and fractions are rational. A whole number n can be written as n/1.
Terminating or repeating decimals are rational. Numbers like √7 or π are not rational.

Definition

\[\frac{p}{q},\; p,q \in \mathbb{Z},\; q \neq 0\]

Integer as rational

\[n = \frac{n}{1}\]

Sign rule

\[\frac{-a}{b} = \frac{a}{-b} = -\frac{a}{b}\]

Common mistake: Thinking negative numbers or decimals cannot be rational. Negative fractions and terminating or repeating decimals are all rational.

Equivalent Forms and Simplest Form

Multiplying or dividing the numerator and denominator by the same non-zero number gives an equivalent rational number.
A rational number is in simplest form when the HCF of the numerator and denominator is 1.
To change p/q into a decimal, divide p by q using long division.

Equivalent form

\[\frac{p}{q} = \frac{p \times m}{q \times m},\; m \neq 0\]

Simplest form (h = HCF of p and q)

\[\frac{p}{q} = \frac{p \div h}{q \div h}\]

Common mistake: Dividing by a common factor that is not the HCF and stopping early. Always check that no common factor remains.

Adding and Subtracting Rational Numbers

With the same denominator, add or subtract the numerators and keep the denominator.
With different denominators, first rewrite both using the LCM of the denominators. Then add or subtract.

Same denominator

\[\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}\]

Different denominators

\[\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}\]

Subtraction

\[\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}\]

Common mistake: Adding numerators and denominators separately, like a/b + c/d = (a+c)/(b+d). This is wrong.

Multiplying, Dividing and Reciprocals

To multiply, multiply the numerators together and the denominators together. Then simplify.
The reciprocal of a/b is b/a, where a is not zero. A number times its reciprocal equals 1.
To divide, multiply the first number by the reciprocal of the second number.

Multiplication

\[\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}\]

Reciprocal

\[\frac{a}{b} \times \frac{b}{a} = 1,\; a \neq 0\]

Division

\[\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\]

Common mistake: Taking the reciprocal of the first number instead of the second when dividing. Flip only the divisor.

Infinitely Many Rationals Between Two

Between any two different rational numbers there are infinitely many rational numbers.
One rational number between a and b is their average. You can repeat this again and again.

Average lies between a and b

\[a < \frac{a+b}{2} < b \text{ when } a < b\]

Common mistake: Thinking there are no rational numbers between two consecutive integers, or only a fixed number of them.

Exam tips

Always reduce your final answer to simplest form before matching it with the options.
Cancel common factors across numerators and denominators before multiplying to keep the numbers small.
Check that the denominator is never zero, because p/0 is not defined.

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

Sample questions

What is a rational number?
Show answer
Answer: A. A number that can be expressed as a fraction
Rational numbers are numbers that can be expressed as a ratio of two integers.
Which fraction represents the same value as 0.5?
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Answer: B. 1/2
The decimal 0.5 is equivalent to the fraction 1/2.
Which of these pairs of numbers are both rational?
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Answer: C. 1.5 and 7/3
1.5 is a rational number as it can be expressed as 3/2 and 7/3 is already a fraction.
Which of these is an example of a whole number that is also a rational number?
Show answer
Answer: A. 7
Whole numbers are also rational numbers as they can be represented as fractions with 1 as the denominator.
If a = 1/3 and b = 1/6, find the value of a/b.
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Answer: A. 2
To find a/b, multiply a by the reciprocal of b: (1/3) × (6/1) = 2.

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