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Rational Numbers Practice

Solve chapter-level practice questions for Rational Numbers with reveal-only solutions and quick revision support.

Practice Set 1 — Properties

Standard form, closure, commutativity, associativity, distributivity.

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Q1.
Write −18/24 in standard form.
Q2.
Are rational numbers closed under division? Give a reason.
Q3.
Verify: 3/7 + (−6/11) + (−8/21) + (5/22) using suitable rearrangement.
Q4.
Use the distributive property to evaluate 7/5 × (−3/12) + 7/5 × 5/12.
Q5.
Name the property: 5/6 × 4/9 = 4/9 × 5/6.

Practice Set 2 — Inverses and the Number Line

Identities, additive and multiplicative inverses, numbers between two rationals.

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Q1.
Write the additive inverse of −7/9 and of 11/13.
Q2.
Write the multiplicative inverse (reciprocal) of −5/8 and of 1/6.
Q3.
Which rational number has no reciprocal?
Q4.
Find a rational number between 2/3 and 3/4.
Q5.
Find three rational numbers between 1/2 and 1.

Quick Q&A Before You Revise

Is every fraction a rational number, and is every rational number a fraction?

Every fraction with an integer numerator and non-zero integer denominator is a rational number. Every rational number can be written as such a fraction, but rational numbers also include negatives and integers written as n/1.

Why is division not associative for rational numbers?

Because (a ÷ b) ÷ c is generally not equal to a ÷ (b ÷ c). For example (8 ÷ 4) ÷ 2 = 1 but 8 ÷ (4 ÷ 2) = 4.

How many rational numbers lie between two given rational numbers?

Infinitely many. You can always take the average of the two to get one in between, then repeat with the new pairs endlessly.

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