PRACTICE TEST ON WHOLE NUMBERS GRADE 6

Example 1 :

Write 4738 in word form.

Solution :

Mention 4738 in place value.

Now, we write 4738 in word form.

Four Thousand Seven Hundred and Thirty Eight.

Example 2 :

What number is represented by the digit 4 in 86482 ?

Solution :

Mention 86482 in place value.

Here the digit 4 in 86482 is represented as 4 hundred (or) 400.

Example 3 :

What is the difference between 895 and 2718 ?

Solution :

First number = 895 ---(1)

second number = 2718 ---(2)

Subtract (1) from (2),

= 2718 - 895

Difference = 1823

Example 4 :

Round off 48526 to the nearest 100.

Solution :

To round a number to the nearest 100, check the tens digit to decide whether to round up or round down. 

Here 48526 has a 2 as its tens digit, which is 4 or less.

So, we round down 48526 nearer to 100 as 48500.

Example 5 :

Find an approximate value for 106 × 295.

Solution :

106 × 295 = 31270

To round a number to the nearest 10000, check the thousands digit to decide whether to round up or round down. 

Here 31270 has a 1 as its thousands digit, which is 4 or less.

So, we round down 31270 nearer to 10000 as 30000.

Example 6 :

Calculate 123 × 36

Solution :

Multiply the numbers,

123 × 36 = 4428

Example 7 :

How many buses would be required to transport 329 students if each bus holds a maximum of 47 students ?

Solution :

Given,

Total students = 329

Maximum students in each bus = 47

Number of buses = (Total students)/Maximum students in each bus

= (329)/47

Required buses = 7 

Example 8 :

Simplify the following :

a) 20 × 33 × 5     

b) 125 × 7 × 8

Solution :

a) Multiply the numbers,

20 × 33 × 5 = 3300

b) Multiply the numbers,

125 × 7 × 8 = 7000

Example 9 :

A class contains 14 boys and 15 girls. If each student is given 13 pencils, how many pencils are given out altogether ?

Solution :

Given,

Number of boys and girls in class = (14 + 15)

= 29 students

Number of pencils given to each student = 13 pencils

Total pencils = No. of. boys and girls × No. of. pencils given to each student

= 29(13)

= 377 pencils

Example 10 :

If a baker sells 24 dozen rolls at 15 cents each, how much many does he receive ?

Solution :

1 dozen = 12

Number of rolls = 24(12)

= 288 rolls

1 cent = $0.01

15 cents = $0.15

Cost of 1 roll = $0.15

Total cost = Number of rolls × cost of 1 roll

= 288(0.15)

= 43.2

So, he is receiving $43.2.

Example 11 :

Find 1834 - 712 + 78.

Solution :

= 1834 - 712 + 78

= 1122 + 78

= 1200

Example 12 :

Find the 9^th square number.

Solution :

The 1^st square number is 1 × 1 = 1

The 2^nd square number is 2 × 2 = 2

The 3^rd square number is 3 × 3 = 9

Similarly,

The 9^th square number is 9 × 9 = 81

Example 13 :

A woman has €255 in her purse. She gives €35 to each of her five children. How much money does she left ?

Solution :

Amount she has in her purse = €255

Each child gets = €35

Amount distributed = 35(5)

= 175

Amount she has left = 255 - 175

= €80

Example 14 :

Find the sum of the first five square numbers.

Solution :

The formula to calculate the first n square numbers is

S_n = [n(n + 1)(2n + 1)]/6

Here n = 5

S₅ = [5(5 + 1)(2(5) + 1)]/6

= [(30)(11)]/6

= 330/6

S₅ = 55

Example 15 :

Find :  a) 3⁶     b) 8³

Solution :

a)

3⁶ = 3 × 3 × 3 × 3 × 3 × 3

= 729

b)

8³ = 8 × 8 × 8

= 512

Example 16 :

Simplify :

a) 7 × 4 - 18 ÷ 2

b) 20 - (8 - 4) × 3

c) (31 - 11)/12 ÷ 6

d) (8 + 14 ÷ 2)/12 ÷ 4

Solution :

a)

By BODMAS rule,

= 7 × 4 - 18 ÷ 2

= 28 - 9

= 19

b)

By BODMAS rule,

= 20 - (8 - 4) × 3

= 20 - 4 × 3

= 20 - 12

= 8

c)

By BODMAS rule,

 = (31 - 11)/12 ÷ 6

= 20/2

= 10

d)

By BODMAS rule,

= (8 + 14 ÷ 2)/12 ÷ 4

= (8 + 7)/3

= 15/3

= 5

Example 17 :

Insert brackets into the following to make a true statement :

a) 4 × 2 + 3 - 5 = 15

b) 20 ÷ 4 + 1 + 5 = 2

Solution :

a)

By BODMAS rule,

4 × (2 + 3) - 5 = 15

b)

By BODMAS rule,

20 ÷ (4 + 1 + 5) = 2