# Free Integers 03 Practice Test - 7th grade

### Question 1

A car travelled 60 km towards the north direction from a point A. From there, it travelled 100 km in the south direction. How far is the car from point A now?

40 km South

40 km North

160 km South

160 km North

#### SOLUTION

Solution :A

Let's assume a car travelling toward North as positive and South as negative.

+60 + (- 100) = - 40. The car is 40 km South from point A.

### Question 2

The product of three negative integers is a

#### SOLUTION

Solution :The product of three negative integers is negative.

For example, −2×−1×−3=−6

### Question 3

Fill in the blank.

#### SOLUTION

Solution :Let the number in blank be x.

According to question,x + 23 = 0

So, x = 0 - 23 = - 23

### Question 4

For any integer b, b ÷ (-1) is ______.

b

1

−b

Not defined

#### SOLUTION

Solution :C

Here, for any integer b,

b−1=−b.

### Question 5

Which of the following statements is not true?

The sum of two integers is always an integer.

The difference of two integers is always an integer.

Sum of four integers can never be zero.

-14 > - 8 - (-7)

#### SOLUTION

Solution :C and D

We know that addition and subtraction of integers follow closure property. So, the first two statements are correct.

Consider four integers 3, 5, -6, -2.

The sum of these integers

= 3 + 5 + (-6) + (-2) = 0

Here,

-8 - (-7) = -1 then,

-1 > -14

Therefore, statement iii and iv are not true.

### Question 6

State whether true or false: For all non-zero integers 'a' and 'b', a×b is always greater than either a or b.** **

True

False

#### SOLUTION

Solution :B

It is not always true. If one of the integers a is negative and the other one b is positive, then their product will be a negative integer, which is less than b.

Let's take an example: -4, 8

=−4×8

=−32

=−32<8

### Question 7

Arrange the following in ascending order.

i. 21×(−34)×(−12)

ii. (7×8)−9

iii. 7×(8−9)

iv. 21×(−34)×(12)

i < ii < iii < iv

ii < iii < i < iv

iv < i < iii < ii

iv < iii < ii < i

#### SOLUTION

Solution :D

Here,

21×(−34)×(−12)=8568

(7×8)−9=47

7×(8−9)=−7

21×(−34)×(12)=−8568

∴−8568<−7<47<8568

### Question 8

If x % y = x + y - xy, then 13 % 7 =

#### SOLUTION

Solution :Given, x % y = x + y - xy

Therefore, x = 13 and y = 7

13 % 7 = 13 + 7 - 13 × 7 = -71

### Question 9

The number zero is an integer. The sign of this number is

Positive

Negative

Does not have any sign

Sometimes positive, sometimes negative.

#### SOLUTION

Solution :C

Zero has no sign. It is neither positive nor negative.

### Question 10

By what number should −240 be divided to obtain 16?

15

-30

30

#### SOLUTION

Solution :A

Let the number be a.

⇒ 16=−240a

⇒ a=−24016=−15

Hence, -240 should be divided by -15 to obtain 16.