Question paper, Set 9

Go along the number line from $-5$ to $6$, leaving out the two ends and not missing $0$.

$-4, -3, -2, -1, 0, 1, 2, 3, 4, 5$

Answer: $-4, -3, -2, -1, 0, 1, 2, 3, 4, 5$

Jumps to the right add.

$-11 + 24 = +(24 - 11) = 13$

Answer: $13$

Adding $-59$ to $-56$ gives $-56 - 59$.

Both are negative: $-56 - 59 = -(56 + 59)$

$= -115$

Answer: $-115$

This is $-62 + 36$.

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

$-62 + 36 = -(62 - 36)$

$= -26$

Answer: $-26$

Different signs: subtract the smaller from the bigger and keep the sign of the bigger.

(i) $18 - 41 = -(41 - 18) = -23$

(ii) $-18 + 84 = +(84 - 18) = 66$

Answer: (i) $-23$, (ii) $66$

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

$-199 - 384 = -(199 + 384)$

$= -583$

Answer: $-583$

(i) $-645 + 56 = -(645 - 56) = -589$

(ii) $866 - 4804 = -(4804 - 866) = -3938$

(iii) $-772 + 809 = +(809 - 772) = 37$

(iv) $7593 + 1819 = 9412$

(v) $-87169 - 3323 = -(87169 + 3323) = -90492$

Answer: (i) $-589$, (ii) $-3938$, (iii) $37$, (iv) $9412$, (v) $-90492$

Write the smaller number under the bigger one and subtract column by column, starting from the units.

Units: $12 - 4 = 8$ (borrow 1)

Tens: $6 - 3 = 3$

Hundreds: $10 - 3 = 7$ (borrow 1)

Thousands: $3$

So $4072 - 334 = 3738$

Answer: $3738$

Rising adds: the new position is $-762 + 155$

Different signs and the bigger number $762$ is negative, so $-762 + 155 = -(762 - 155)$

Count down: $762 \to 200$ is $562$, and $200 \to 155$ is $45$

$762 - 155 = 562 + 45 = 607$

So $-762 + 155 = -607$

Answer: $-607$ m (that is, $607$ m below sea level)

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

$-657 - 8493 = -(657 + 8493)$

$= -9150$

Answer: $-9150$

Positive terms: $762 + 592 = 1354$

Negative terms: $96 + 614 = 710$

$762 + 592 - 96 - 614 = 1354 - 710$

$= 644$

Answer: $644$

Total $= 587 + 632 - 567 - 522 + 325$

Positive terms: $587 + 632 + 325 = 1544$

Negative terms: $567 + 522 = 1089$

$587 + 632 - 567 - 522 + 325 = 1544 - 1089$

$= 455$

So the five days give a profit of ₹455.

Answer: $455$, that is, a profit of ₹455

$- \times - = +$

$-5 \times -27 = +(5 \times 27) = 135$

Answer: $135$

(i) $- \times - = +$, $-4 \times -42 = 168$

(ii) $+ \times - = -$, $41 \times -9 = -369$

Answer: (i) $168$, (ii) $-369$

Sign: $- \times + = -$

$365 \times 7 = 2555$

$365 \times 80 = 29200$

$2555 + 29200 = 31755$

So $-87 \times 365 = -31755$

Answer: $-31755$

(i) $+ \times - = -$; $18 \times 5 = 90$, $18 \times 10 = 180$, $90 + 180 = 270$

So $18 \times -15 = -270$

(ii) $- \times + = -$; $264 \times 5 = 1320$, $264 \times 20 = 5280$, $1320 + 5280 = 6600$

So $-25 \times 264 = -6600$

(iii) $- \times - = +$; $112 \times 5 = 560$, $112 \times 70 = 7840$, $560 + 7840 = 8400$

So $-112 \times -75 = 8400$

Answer: (i) $-270$, (ii) $-6600$, (iii) $8400$

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

$654 \div 3 = 218$, so $\displaystyle \frac{-654}{3} = -218$

Answer: $-218$

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

$7 \div 4 = 1$ r $3$; $33 \div 4 = 8$ r $1$; $19 \div 4 = 4$ r $3$; $36 \div 4 = 9$

$7396 \div 4 = 1849$, so $\displaystyle \frac{-7396}{4} = -1849$

Answer: $-1849$

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

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

$50065 \div 5 = 10013$, so $\displaystyle \frac{-50065}{5} = -10013$

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

$6 \div 3 = 2$; $6 \div 3 = 2$; $4 \div 3 = 1$ r $1$; $18 \div 3 = 6$; $2 \div 3 = 0$ r $2$; $21 \div 3 = 7$

$664821 \div 3 = 221607$, so $\displaystyle \frac{664821}{-3} = -221607$

Answer: (i) $-10013$, (ii) $-221607$

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

(i) $3 - 79 = -(79 - 3) = -76$

(ii) $+ \times - = -$, $3 \times -79 = -237$

(iii) $-3 - 41 = -(3 + 41) = -44$

(iv) $- \times - = +$, $-3 \times -41 = 123$

(v) $\displaystyle \frac{-}{+} = -$; $53 \div 8 = 6$ r $5$; $59 \div 8 = 7$ r $3$; $31 \div 8 = 3$ r $7$; $72 \div 8 = 9$; so $\displaystyle \frac{-53912}{8} = -6739$

Answer: (i) $-76$, (ii) $-237$, (iii) $-44$, (iv) $123$, (v) $-6739$