NCERT Class 7 Maths Chapter 10
Operations with Integers
This chapter from Ganita Prakash Part 2 develops CBSE Class 7 students' understanding of integers and how to perform all four arithmetic operations with positive and negative numbers. Students learn the rules for adding, subtracting, multiplying, and dividing integers and apply them to real-world situations such as temperature changes, sea level measurements, and bank transactions.
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Key Terms
- Integer
- Any whole number, either positive, negative, or zero. Integers include … –3, –2, –1, 0, 1, 2, 3 … and do not include fractions or decimals.
- Absolute Value
- The distance of a number from zero on the number line, always non-negative. The absolute value of –7 is 7, and the absolute value of 7 is also 7. Written as |–7| = 7.
- Negative Integer
- An integer less than zero, located to the left of zero on a number line. Examples include –1, –5, and –100.
- Additive Inverse
- The additive inverse of any integer n is –n. Adding an integer and its additive inverse always gives zero. For example, 8 + (–8) = 0.
- Product Rule for Integers
- When multiplying two integers: positive × positive = positive, negative × negative = positive, and positive × negative = negative.
- Number Line
- A line on which every point corresponds to a real number, with positive numbers to the right of zero and negative numbers to the left. It is used to visualise and compare integers.
Frequently Asked Questions
What are integers and how are they different from whole numbers?▾
Integers include all positive whole numbers, negative numbers, and zero (… –3, –2, –1, 0, 1, 2, 3 …). Whole numbers only include zero and positive numbers (0, 1, 2, 3 …). The key difference is that integers include negative numbers while whole numbers do not.
What are the rules for multiplying integers?▾
When multiplying integers: a positive times a positive gives a positive (3 × 4 = 12), a negative times a negative gives a positive (–3 × –4 = 12), and a positive times a negative (or negative times positive) gives a negative (3 × –4 = –12).
How do you add a negative number to a positive number?▾
To add a negative number to a positive number, find the difference between their absolute values and give the result the sign of the larger absolute value. For example, 8 + (–3) = 5 (since 8 > 3, the answer is positive) and 3 + (–8) = –5 (since 8 > 3, the answer is negative).
How do you subtract integers?▾
To subtract an integer, add its additive inverse (change the sign of the number being subtracted). For example, 5 – (–3) = 5 + 3 = 8, and –4 – 6 = –4 + (–6) = –10.
What is the use of integers in real life?▾
Integers model many real-life situations: temperatures below zero (–5°C), floors below ground level in a building (B1 = –1), bank debts (–500 means you owe 500), altitude below sea level, and representing losses in business (–profit means a loss).
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