# Free Whole Numbers Subjective Test 01 Practice Test - 6th grade

Define whole numbers. [1 MARK]

#### SOLUTION

Solution :

All natural numbers including '0' form the whole numbers in mathematics. Whole numbers are the basic counting numbers. Whole numbers include positive integers along with 0.

Find three predecessors and successors of 444. [2 MARKS]

#### SOLUTION

Solution :

Predecessor: 1 Mark
Successor: 1 Mark

Predecessor = Number - 1
the three predecessors of 444 are:

444 - 1 = 443,
443 - 1 = 442 and
442 - 1 = 441

Successor = Number +1
the three successors of 444 are:

444 + 1 = 445,
445 + 1 = 446 and
446 + 1 = 447

Why addition and multiplication follow the property of closure, but not subtraction and division? Explain with examples. [2 MARKS]

#### SOLUTION

Solution :

Solution: 1 Mark
Example: 1 Mark

When we perform the arithmetic operations like addition and subtraction on whole numbers, the result is also a whole number. For e.g. Let us take two numbers as 12 and 16. When we perform addition,

12 + 16 = 28

When we perform multiplication,

12 × 16 = 192; the result of above operations is a whole number.

Whereas when we subtract these numbers, the result may or may not be a whole number.

E.g. 16 - 12 = 4, 4 is a whole number but 12 - 16 = -4, -4 is not a whole number.

Similarly, 16÷12 = 1.33, this is again not a whole number.

A typist types 45 words in 15 minutes and takes a 5-minute break to align the paper. How many words will he type in one and half hours? [3 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks

One and half hours = 60 + 30 = 90 min

In 15 minutes, he types 45 words
He takes 5 minutes of break to align the paper.
So, the total number of words typed by him in 20 minutes = 45

Now, 90=(20+20+20+20)+10

So, in 80 minutes he can type 45 × 4 = 180 words

The number of words he can type in the next 10 minutes= 4515× 10=30

So, total number of words he will type = 180 + 30 = 210 words.

Rohit worked for 2 weeks and made Rs.26700 from the first week and Rs.32800 from the second week. His deductions were Rs. 3900. Shikhar worked at the same place for 2 weeks and made 27300 from the first week and Rs. 31600 from the second week. His deductions were Rs.4100. What is the difference in their pay cheques? Who earned more and by how much? [3 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks

In two weeks, Rohit's total income = Rs. (26700 + 32800) = Rs. 59500

In two weeks, Shikhar's total income = Rs. (27300 + 31600) = Rs.58900

So, after deduction Rohit's income = Rs. 59500 - 3900 = Rs.55600

After deduction Shikhar's income = Rs (58900 - 4100) = Rs. 54800.

The difference in the incomes = Rs. (55600 - 54800) = Rs.800

Hence, Rohit's income is Rs. 800 more than Shikhar's income.

Find the value of the following, using suitable properties:

a) 406×516

b) 8 ×291×125
[3 MARKS]

#### SOLUTION

Solution :

Steps: 1×2=2 Marks

a) By distributive law

406×516 = (400 + 6)×(500 + 16)
= 200000 + 96 + 6400 + 3000 = 2,09,496

b) By distributive law
8 ×291×125=(4×2)×(290+1)×(25× 5)=(25× 4)×(5×2)×(290+1)
= 100 × 10 × (290+1) = 1000 × (290+1)
= 290000 + 1000 = 291000

Mahesh found a bicycle in a sale for Rs 2500 but it required a new brake cable and brake oil to make it work perfectly. He bought brake cable for Rs.82 and brake oil for Rs.20, fixed it up and then sold it to his neighbour for Rs. 3500. How much profit did he make on that deal? [4 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks
Formula: 1 Mark

Mahesh bought a bicycle for Rs. 2500.

Repairing cost = Rs. (82 + 20) = 80+2+20 = 100+2 = Rs.102

Total expenses on the bicycle = Rs. (2500 + 102) = 2500+100+2 = 2600+2 = Rs.2602

Profit = (Selling Price - Cost Price) = Rs. (3500 - 2602) = 3500-2600-2 = 900-2 = Rs. 898

Study the following number patterns:

45×9+2=407

456×9+3=4107

4567×9+4=41107

Find the next 2 lines.
[4 MARKS]

#### SOLUTION

Solution :

Application: 2 Marks
Steps: 1 Mark

This pattern is like this:-

45×9+2=407

456×9+3=4107

4567×9+4=41107

For next three lines, it would be like this-
As we can see in the pattern, the number of digits is incremented by 1, and the units digit is the successor of the previous number.
Also, the number which we are adding to the product is incremented by 1.

Using distributive property we can make the calculations simpler for the following,

45678×9+5=45678×(101)+5
=45678045678+5=411107

456789×9+6=456789×(101)+6
=4567890456789+6=4111107

Vineet wrote a sequence of numbers in which every odd number is 7 less than the previous number, and every even number is 2 more than the previous one. The first term of the sequence is 100. Find the 5th term. [4 MARKS]

#### SOLUTION

Solution :

Steps: 3 Marks

Given that:
The first term of the sequence = 100.
Now every odd number is 7 less than the previous one and every even number is 2 more than the previous one.
So the second term=100 + 2 = 102
Third term = 102 - 7 = 95
Fourth term = 95 + 2 = 97
Fifth term = 97 - 7 = 90
Hence, the fifth term of the sequence is 90.

Solve these problems:

a) Arjun’s new car payment will be Rs.28800 each month for five years. What is the total payment?

b) In a game of cards, Suresh and Ramesh are making addition problems. The cards are lying below: The winner of the game is one who makes the question with the largest number as the answer. Suresh eventually got the largest number as result and won the game.

What was the strategy followed by Suresh? (Operation is done on two-digit numbers without repetition)
[4 MARKS]

#### SOLUTION

Solution :

Steps: 1 ×2 = 2 Marks 