Integers: The Complete Number System: 18 MCQs with answers

B · $\frac{3}{4}$

Integers are whole numbers with negatives and zero; fractions like $\frac{3}{4}$ are not integers.

B · $0$

Zero is the only integer that is neither positive nor negative.

A · $-9$

Smaller integers sit further left; $-9$ is the smallest of these.

C · $13$

Absolute value is distance from zero, so $|-13| = 13$.

C · $-6$ and $6$

Opposites are the same distance from zero on opposite sides, like $-6$ and $6$.

B · $-10$

Same signs: add absolute values ($4+6=10$) and keep the negative sign.

A · True

Zero is the only integer that is neither positive nor negative.

D · $3$

$(-2) + 5 = 3$: different signs, subtract $2$ from $5$, take the positive sign.

A · $-5$

Different signs: $9-4=5$, and the negative term has larger absolute value, so the result is $-5$.

C · $-3$

Rewrite as $5 + (-8)$; different signs give $-3$.

B · $10$

Two minus signs combine into a plus: $7 + 3 = 10$.

D · $12$

Same signs multiply to a positive: $(-3)\times(-4)=12$.

D · $-4$

Different signs give a negative quotient: $(-20)\div 5 = -4$.

C · $-14$

BODMAS: multiply first, $3\times(-4)=-12$, then $(-2)+(-12)=-14$.

A · $-5 < 3$ and $|-5| > |3|$

The number line orders $-5$ below $3$, but absolute value measures size, so $|-5|=5 > 3$.

B · $\$150$

$(-200) + 350 = 150$: different signs, $350-200=150$, sign of the larger absolute value.

D · -6

First, convert the subtraction of $-2$ into addition: $(-3) + 5 + 2 + (-4)$. Now, perform the addition step-by-step: $(-3) + 5 = 2$, then $2 + 2 = 4$, and finally $4 + (-4) = 0$. Thus, the final result is $-6$.

D · 10

First, substitute the values: $2 imes (3 - (-4)) + (-5) \div (-1)$. This simplifies to $2 imes (3 + 4) + 5$. Next, calculate $3 + 4 = 7$, so $2 imes 7 + 5 = 14 + 5 = 19$. Therefore, the final result is $10$.