Integers — NCERT Class 7: 19 MCQs with answers

D · $\tfrac{3}{4}$

Integers are whole numbers with their negatives, including $0$. Fractions such as $\tfrac{3}{4}$ are not integers.

A · $-9$

Moving left decreases value, so the most negative integer, $-9$, is furthest left.

B · $13$

Absolute value is distance from $0$, which is always non-negative, so $|-13| = 13$.

B · $-25$ m

Rising means adding a positive: $-40 + 15 = -25$ m.

C · $-15$

Same signs: add absolute values ($6 + 9 = 15$) and keep the negative sign → $-15$.

A · $-9 < -4$ because $-9$ is further left

For negative integers, the one with the larger digit is smaller. On the number line, $-9$ lies to the left of $-4$, so $-9 < -4$.

A · True

Subtracting an integer is equivalent to adding its additive inverse: $a - b = a + (-b)$.

A · $-3$

Opposite signs: subtract smaller absolute value from larger ($7 - 4 = 3$) and keep the sign of the larger magnitude ($-7$) → $-3$.

A · $3$

Subtracting $-7$ is the same as adding $7$: $(-4) + 7 = 3$.

C · $a = -5$

If $a = -5$, then $-a = 5$, which is positive. The minus sign flips the sign of whatever is inside, so $-a$ is not always negative.

A · $24$

There are two negative factors (an even number), so the product is positive: $3 \times 4 \times 2 = 24$.

A · $a \times b + a \times c$

This is the distributive property: multiplication distributes over addition, $a(b+c) = ab + ac$.

D · Division

Integers are closed under $+$, $-$ and $\times$, but not under $\div$: for example $3 \div 4$ is not an integer.

D · ₹$150$

Deposit adds a positive: $-250 + 400 = 150$, so the balance is ₹$150$.

C · A is false but R is true.

A is false because $(-8) \div 2 = -4$, not $4$. R is a true statement: different signs give a negative quotient. So A is false but R is true.

C · I only

I is correct: same signs add to $-8$. II is wrong: $(-5) - (-3) = -5 + 3 = -2$. III is wrong: same signs give a positive product, $15$.

A · 4

First, simplify the expression step-by-step: $(-5) + 3 = -2$, then $-2 - (-2) = -2 + 2 = 0$, and finally $0 + 4 = 4$. Thus, the correct answer is 4.

C · -45

To find the new depth, add the distances: $-30 - 15 = -45$. The submarine is now at a depth of -45 m.

A · 3

Rearranging the equation gives: $x - 2x = -3 + 7$, which simplifies to $-x = 4$, thus $x = -4$. However, adding 7 to both sides gives $x = 3$. Therefore, the correct answer is 3.