Integers — NCERT Class 7: quick revision, 15 bites

Integers Extend the Number Line Both Ways

Numbers don't stop at zero — they go negative.

Integers are all whole numbers together with their negatives — extending the number line infinitely in **both** directions.

Takeaway. Every integer has an opposite, and the number line never ends in either direction.

Key Terms You Must Know

Five words that unlock every integer problem.

Takeaway. Master these five terms — every integer operation is built on them.

Reading the Number Line

Right means bigger, left means smaller.

On a horizontal number line, numbers **increase to the right** and **decrease to the left**.

Takeaway. Position on the number line tells you which integer is greater.

Ordering Integers: Positive vs Negative

Negatives flip the usual ordering rules.

Takeaway. Among negatives, the one with the larger absolute value is actually smaller.

Absolute Value: Distance from Zero

Absolute value ignores the sign.

Takeaway. Absolute value measures distance, so it's always zero or positive.

Adding Integers: Same Sign vs Different Sign

Two rules cover every addition.

Takeaway. Same signs → add and keep sign; different signs → subtract and take the bigger number's sign.

Subtracting Integers = Adding the Inverse

Subtraction is just addition in disguise.

Takeaway. Never subtract — flip the sign of the second number and add.

Multiplying and Dividing Integers

Sign rules decide everything here.

Takeaway. Same signs → positive; different signs → negative.

Properties of Integer Operations

Integers obey neat algebraic rules.

Takeaway. Addition and multiplication are commutative and associative — subtraction and division are not.

The Double-Negative Trap

Two negatives don't always cancel.

Takeaway. Subtracting a negative makes the result larger, not smaller.

Don't Confuse Sign with Magnitude

−9 is smaller than −2, not bigger.

Takeaway. For negatives, bigger absolute value means smaller integer.

Integers in Real Life: Temperature

A thermometer is a number line.

Takeaway. Temperature changes are integer additions — direction of movement matches the sign.

Integers Around You

Money, altitude, and scores use integers.

Takeaway. Any quantity with two opposite directions is naturally modelled by integers.

Sign Rules in One Line

Same = plus, different = minus.

For multiplication and division: **S**ame signs give **P**ositive; **D**ifferent signs give **N**egative. Remember it as **SPDN**.

Takeaway. SPDN — Same Positive, Different Negative.

Exam Tip: Show the Sign Flip

One line saves you full marks.

Takeaway. Explicit sign-flip steps earn method marks even if the final answer slips.