Question paper, Set 8

Jumps to the left subtract.

$10 - 24 = -(24 - 10) = -14$

Answer: $-14$

Jumps to the left subtract and jumps to the right add.

$9 - 14 = -(14 - 9) = -5$

$-5 + 11 = +(11 - 5) = 6$

You finish at $6$.

Answer: $6$

Both are negative: add them and keep the $-$ sign.

$-17 - 84 = -(17 + 84)$

$= -101$

Answer: $-101$

The signs are different: subtract the smaller from the bigger and keep the sign of the bigger.

$29 - 58 = -(58 - 29)$

$= -29$

Answer: $-29$

Going up adds.

$-3 + 14 = +(14 - 3) = 11$

Answer: Floor $11$

(i) $-588 + 795 = +(795 - 588) = 207$

(ii) $-758 - 52 = -(758 + 52) = -810$

Answer: (i) $207$, (ii) $-810$

Profit $= +2527$, loss $= -3761$

$2527 - 3761 = -(3761 - 2527) = -1234$

The answer is $-1234$: a loss of ₹1234.

Answer: $-1234$, that is, a loss of ₹1234

Subtract column by column from the units, borrowing when the top digit is smaller.

(i) Units: $5 - 2 = 3$; Tens: $17 - 8 = 9$ (borrow 1); Hundreds: $13 - 6 = 7$ (borrow 1); Thousands: $3$; so $4475 - 682 = 3793$

(ii) Units: $15 - 9 = 6$ (borrow 1); Tens: $11 - 4 = 7$ (borrow 1); Hundreds: $12 - 4 = 8$ (borrow 1); Thousands: $16 - 7 = 9$ (borrow 1); Ten thousands: $2$; so $37325 - 7449 = 29876$

(iii) Units: $8 - 7 = 1$; Tens: $11 - 4 = 7$ (borrow 1); Hundreds: $9 - 0 = 9$ (borrow 1); Thousands: $14 - 5 = 9$ (borrow 1); Ten thousands: $8$; so $95018 - 5047 = 89971$

Answer: (i) $3793$, (ii) $29876$, (iii) $89971$

Different signs and the bigger number $812$ is negative, so $577 - 812 = -(812 - 577)$

Count down: $812 \to 600$ is $212$, and $600 \to 577$ is $23$

$812 - 577 = 212 + 23 = 235$

So $577 - 812 = -235$

Answer: $-235$

Different signs and the bigger number $1281$ is negative, so $-1281 + 703 = -(1281 - 703)$

Count down: $1281 \to 800$ is $481$, and $800 \to 703$ is $97$

$1281 - 703 = 481 + 97 = 578$

So $-1281 + 703 = -578$

Answer: $-578$

Positive terms: $148 + 605 = 753$

Negative terms: $65 + 15 = 80$

$-65 + 148 - 15 + 605 = 753 - 80$

$= 673$

Answer: $673$

(i) Positive terms: $788 + 849 = 1637$

Negative terms: $818 + 887 = 1705$

$788 - 818 + 849 - 887 = 1637 - 1705$

$= -(1705 - 1637) = -68$

(ii) Positive terms: $4765 + 6332 = 11097$

Negative term: $7085$

$4765 + 6332 - 7085 = 11097 - 7085$

$= 4012$

Answer: (i) $-68$, (ii) $4012$

$- \times + = -$

$-4 \times 44 = -(4 \times 44) = -176$

Answer: $-176$

$22 \times 11 = 242$; only the sign changes, by the rule.

(i) $+ \times + = +$, so $22 \times 11 = 242$

(ii) $- \times - = +$, so $-22 \times -11 = 242$

(iii) $+ \times - = -$, so $22 \times -11 = -242$

(iv) $- \times + = -$, so $-22 \times 11 = -242$

Answer: (i) $242$, (ii) $242$, (iii) $-242$, (iv) $-242$

(i) $- \times + = -$; $35 \times 7 = 245$, $35 \times 10 = 350$, $245 + 350 = 595$

So $-17 \times 35 = -595$

(ii) $- \times - = +$; $441 \times 7 = 3087$, $441 \times 90 = 39690$, $3087 + 39690 = 42777$

So $-97 \times -441 = 42777$

(iii) $+ \times - = -$; $934 \times 7 = 6538$, $934 \times 20 = 18680$, $6538 + 18680 = 25218$

So $934 \times -27 = -25218$

Answer: (i) $-595$, (ii) $42777$, (iii) $-25218$

$\displaystyle \frac{-}{-} = +$

So $\displaystyle \frac{-2058}{-2}$ is positive.

Answer: Positive

$\displaystyle \frac{+}{-} = -$

$8 \div 7 = 1$ r $1$; $14 \div 7 = 2$; $4 \div 7 = 0$ r $4$; $49 \div 7 = 7$

$8449 \div 7 = 1207$, so $\displaystyle \frac{8449}{-7} = -1207$

Answer: $-1207$

(i) $\displaystyle \frac{+}{-} = -$

$12 \div 3 = 4$; $0 \div 3 = 0$; $2 \div 3 = 0$ r $2$; $27 \div 3 = 9$

$12027 \div 3 = 4009$, so $\displaystyle \frac{12027}{-3} = -4009$

(ii) $\displaystyle \frac{-}{-} = +$

$3 \div 3 = 1$; $9 \div 3 = 3$; $0 \div 3 = 0$; $4 \div 3 = 1$ r $1$; $19 \div 3 = 6$ r $1$; $15 \div 3 = 5$

$390495 \div 3 = 130165$, so $\displaystyle \frac{-390495}{-3} = 130165$

Answer: (i) $-4009$, (ii) $130165$

(i) Addition, same signs: add and keep $-$: $-3 - 59 = -(3 + 59) = -62$

(ii) Multiplication: $- \times - = +$, so $-3 \times -59 = 177$

Answer: (i) $-62$, (ii) $177$

Addition uses the addition rule; multiplication and division use the sign rule.

(i) $9 - 28 = -(28 - 9) = -19$

(ii) $+ \times - = -$, $9 \times -28 = -252$

(iii) $-6 - 34 = -(6 + 34) = -40$

(iv) $- \times - = +$, $-6 \times -34 = 204$

(v) $\displaystyle \frac{-}{+} = -$; $25 \div 7 = 3$ r $4$; $47 \div 7 = 6$ r $5$; $55 \div 7 = 7$ r $6$; $63 \div 7 = 9$; so $\displaystyle \frac{-25753}{7} = -3679$

Answer: (i) $-19$, (ii) $-252$, (iii) $-40$, (iv) $204$, (v) $-3679$