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Operations with Integers – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 10. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Integers are whole numbers with signs: …, −2, −1, 0, 1, 2, …. Rules of signs make adding, subtracting, multiplying and dividing them easy.

Adding and subtracting

Same signs: add and keep the sign (−3 + −4 = −7).
Different signs: subtract and take the sign of the larger absolute value (−8 + 5 = −3).
Subtracting an integer = adding its opposite: 6 − (−2) = 6 + 2 = 8.

Multiplying and dividing

(+) × (+) = +, (−) × (−) = +, (+) × (−) = −.
Same rules for division; dividing by zero is not defined.
Even number of negative factors → positive product; odd number → negative.

Key terms

Integer: whole number with a sign, including zero
Additive inverse: the opposite number; a + (−a) = 0
Multiplicative identity: 1, because any number × 1 = the number

Formulas

(−a) × (−b) = ab
a − (−b) = a + b

Important questions with answers

Find (−9) + 15 − (−6).2 marks

−9 + 15 + 6 = 12.

Write the rules for the sign of a product of two integers with examples.3 marks

Positive × positive = positive (3 × 4 = 12); negative × negative = positive (−3 × −4 = 12); positive × negative = negative (3 × −4 = −12).

A submarine is at −120 m. It rises 35 m every minute. Where is it after 3 minutes, and after how many minutes will it be at −15 m? Also verify (−5) × [4 + (−3)] using the distributive property.5 marks

After 3 minutes: −120 + 3 × 35 = −120 + 105 = −15 m. So it reaches −15 m after 3 minutes. Distributive check: (−5) × [4 + (−3)] = (−5) × 1 = −5, and (−5) × 4 + (−5) × (−3) = −20 + 15 = −5 ✓.

Quick revision

Negative × negative = positive.
0 is neither positive nor negative.
Division by zero is undefined.

Exam tips

Use a number line for addition: move right for +, left for −.
Temperature below zero and debts are real-life negative integers.

Practice MCQs

−7 + 3 equals
1. −10
2. −4
3. 4
4. 10
Show answer
Answer: (b) −4. Different signs.
(−5) × (−4) equals
1. 20
2. −20
3. −9
4. 9
Show answer
Answer: (a) 20. Negative × negative = positive.
8 − (−6) equals
1. 2
2. −2
3. −14
4. 14
Show answer
Answer: (d) 14. 8 + 6.
(−36) ÷ 9 equals
1. 4
2. −4
3. −27
4. 45
Show answer
Answer: (b) −4. Different signs give negative.
(−6) × (−7) equals
1. −42
2. 42
3. −13
4. 13
Show answer
Answer: (b) 42. Negative × negative = positive.
(−1) × (−1) × (−1) × (−1) × (−1) equals
1. 1
2. −5
3. 5
4. −1
Show answer
Answer: (d) −1. Odd number of negatives.
The temperature is −3 °C at night and rises by 9 °C by noon. Noon temperature is
1. −12 °C
2. 12 °C
3. 6 °C
4. −6 °C
Show answer
Answer: (c) 6 °C. −3 + 9.
(−48) ÷ 6 × (−2) equals
1. 16
2. 4
3. −16
4. −4
Show answer
Answer: (a) 16. −8 × −2.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.