Properties of Multiplication under Integers

Q. A shopkeeper earns a profit of ₹ 1 by selling one pen and incurs a loss of 40 paise by selling a pencil. If she sells 70 pens, then how many pencils does she have to sell if there is no profit or loss in the transaction.

1. 175
2. 174
3. 170
4. 185

Q. Which of the following statement is true?

1. There does not exist an integer b such that for $a>1$, $a\times b=b\times a=b$
2. The product of a positive and a negative integer is positive.
3. Subtraction follows commutative property.
4. All are false.

Q. In a cricket match, a coin is tossed to decide which team will decide to bat or ball first. What is the probability that team A will get to decide whether to bat or ball first in a match between teams A and B?

1. $1$
2. $\frac{1}{6}$
3. $\frac{1}{3}$
4. $\frac{1}{2}$

Q. 5 masons built a wall in 2 days. If the wall has to be built in a single day, how many masons should be employed?

1. 9 masons
2. 12 masons
3. 8 masons
4. 10 masons

Q. Find the product, using suitable properties:
$(-41)\times 102$

Q.

Kali runs $10$ laps around a track each day.

Each lap around the track is $400$ meters.

How many days will it take Kali to run a total of $12$ kilometers?

Q. Find the following products:
$(-12)\times (-11)\times \left(10\right)$

Q. Find the product, using suitable properties:
$25\times (-50)+(-50)\times (-32)$

Q. You throw two dice together and noted the sum of the digits of both the dice. The probability of getting 13 as the sum is .

1. $0$
2. $1$
3. $\frac{1}{3}$

Q. Solve the following using suitable property.

$81\times (-3)+81\times 4$

1. 566
2. 162
3. 81
4. 567

Q.

The teacher distributes $4$ laddoos per student on Childrens Day . Can you tell how many laddoos are needed , given the number of students ? ( Use $S$ for the number of students ).

Q.

You picked a card at random from a deck of 52, noted the suit of the card, and then replaced the card. You repeated this experiment 99 more times. Your observations are as shown below.

$$\begin{array}{cc}Suit& Frequency\\ Spades& 23\\ Diamond& 26\\ Club& 21\\ Heart& 30\end{array}$$

Find the probability of drawing
(i) Spades
ii) Diamonds
(iii) Clubs
(iv) Hearts.
Show that the sum of these probabilities is 1. [4 MARKS]

Q.

Write $2$subtraction facts for each addition fact.

$29574+126=29700$

Q.

Product of odd numbers of an integer is always $\left(\_\_\_\_\_\right)$

Q. A child has a die whose six faces show the letters as given below:
The die is thrown once.



(i) What is the probability of getting A?
(i) What is the probability of getting B?

Q. How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?
I. A can fill the tank in $6$ minutes.
II. B can empty the full tank in $8$ minutes.

1. I alone sufficient while II alone not sufficient to answer
2. II alone sufficient while I alone not sufficient to answer
3. Either I or II alone sufficient to answer
4. Both I and II are not sufficient to answer
5. Both I and II are sufficient to answer

Q. Find the product of $125\times 40\times 8\times 25$ suitable rearrangement

Q.

Solve using properties of integers:

$\frac{(3+2)+5+2\times (3+5)}{2\times 3+2\times 5+3+(2+5)}=?$

1. $5$
2. $1$
3. $2$
4. $10$

Q.

You picked a card at random from a deck of 52, noted the suit of the card, and then replaced the card. You repeated this experiment 99 more times. Your observations are as shown below.

$$\begin{array}{cc}\text{Suit}& \text{Frequency}\\ \text{Spades}& 23\\ \text{Diamond}& 26\\ \text{Club}& 21\\ \text{Heart}& 30\end{array}$$

Find the probability of drawing
(i) Spades
ii) Diamonds
(iii) Clubs
(iv) Hearts.
Show that the sum of these probabilities is 1. [4 MARKS]

Q.

Solve the given equation by the systematic method$:$

$x-25=30$

Q.

$\left(-5\right)\times \left(-6\right)\times \left(-7\right)=\_\_$

Q. Enter the number that can replace ${}^{\prime }{x}^{\prime }$ in the following equation:
$12\times 35=12\times x-12\times 15$

1. 50

Q. In a cricket match, a coin is tossed to decide which team will decide to bat or ball first. What is the probability that team A will get to decide whether to bat or ball first in a match between teams A and B?

1. $1$
2. $\frac{1}{6}$
3. $\frac{1}{3}$
4. $\frac{1}{2}$

Q. 10 × (–12) + (–12) × (–30) = ?

1. -240
2. 462
3. 240
4. -462

Q. Find the value of:
-32 $\times$ 12 = ___
12 $\times$ (-32) = ___

1. 496, -496
2. 382, 382
3. -384, -384
4. 384, 384

Q. $a\times (b\times c)=$

1. (a×b)×c
2. ab+ac
3. ab+bc

Q. $12\times (2+1)=$

1. 12×2+12×1
2. 12×2
3. 12×2×1
4. 12×2+1

Q.

$\begin{array}{cc}\text{Properties of multiplication of integers}& \text{Representation}\\ 1).\text{Distributive Property}& a).a\times b=b\times a\\ 2).\text{Commutative Property}& b).a\times (b\times c)=(a\times b)\times c\\ 3).\text{Associative Property}& c).a\times (b+c)=(a\times b)+(a\times c)\end{array}$

Pick the option which shows the correct match.

1. $1-a;2-b;3-c$

2. $1-b;2-a;3-c$

3. $1-c;2-b;3-a$

4. $1-c;2-a;3-b$

Q.

Compute and choose the relations that are correct.

1. $5\times (8+10)=10\times (8+5)$

2. $12\times (6-3)=(12\times 6)-(12\times 3)$

3. $(8+10)\times 15>8+(10\times 15)$

4. $(-11)\times (-3)\times \left(2\right)=-66$

Q. Solve using suitable properties of integers under multiplication:
(-4 x 0) x 676 + 32 = ?

1. 32