Free Whole Numbers Subjective Test 02 Practice Test - 6th grade 

No, it is not possible to find the largest number on the number line because every number has a successor in the number line.

Whole numbers: 1 Mark
Explanation: 1 Mark

All the counting numbers are called natural numbers (i.e. 1,2,3,4...). These natural numbers along with 0 form the group of whole numbers. All the natural numbers are also whole numbers but all the whole numbers are not natural numbers.

Property: 1 Mark
Reason: 1 Mark

A set of numbers is said to be closed for a specific mathematical operation if the result obtained when an operation is performed on any two numbers in the set, is itself a member of the set. 

Only addition and multiplication operations on whole numbers satisfy the property of closure because  when we perform this operation on whole numbers, the result also lies in the set of whole numbers.

But when we perform division on whole numbers, the result may be a whole number or a fraction.

So, it doesn't satisfy the property of closure. Similarly, for subtraction of two whole numbers, the result which we get maybe a positive number or negative number which clearly does not satisfy the property of closure.

Example:-
1) 3 + 4 = 7

Here 3 and 4 are whole numbers.

The addition of 3 and 4 which is 7 is also a whole number.

So, property of closure is true for addition.

(2) 4 - 3 = 1

Here, 4 and 3 are whole numbers and 1 is also a whole number.

So the property is true.

But 3 - 4 = -1

Here 3 and 4 are whole numbers.

The subtraction of 3 and 4 is -1 which is not a whole number.

(3) 1) 30 x 7 = 210
Here 30 and 7 are whole numbers.

The multiplication of 30 and 7 which is 210 is also a whole number.

So property of closure for multiplication is true.

(4) Note : Property of closure is not always true for division.

Example : 45 ÷ 0 = not defined
As division with zero is not possible.

Answer: 1 Mark
Example: 2 Marks

No, the "Associative Law" states that it doesn't matter how we group the numbers (i.e. which we calculate first) we will get same result. 

a $÷$ (b $÷$ c) ≠ (a $÷$ b) $÷$c (except in a few special cases)

Let assume a = 48, b = 16 and c = 2

48 $÷$ (16 $÷$ 2) = 48 $÷$ 8 = 6;

But (48 $÷$ 16) $÷$ 2 = 3 $÷$ 2 = 1.5

This example illustrates how division doesn't follow the associative property.

Regrouping the numbers resulted in two different answers.
So division does not follow the associative law.

Number Line: 1 Mark
Steps: 1 Mark
Answer: 1 Mark

Money in the pocket can be taken as positive. Then the money owed will be negative.Presently Steve has Rs.13 but he owes Rs. 5. Hence, money he actually has =13-5 = 8. The given number line shows the money Steve has.

Similarly, Michel owes Rs. 3, Hence actual money Michel has =Rs. 13 - Rs. 3 = Rs. 10

Cooper has Rs.13.

As we know that the number on the left side is smaller than the number on the right side, we can hence conclude that Steve is poorest and Cooper is richest.

Each option: 1 Mark

By using distributive property we can simplify the problem
$a\times (b+c)$=$(a+b)\times (a+c)$
$a\times (b-c)$=$(a-b)\times (a-c)$

a)$126\times 55+126\times 45$
$126(55+45)=126\times 100=12600$.

b) $89\times 48=(90-1)\times (50-2)$
$=4500-180-50+2=4272.$

c) $49\times 12=(50-1)\times (10+2)$
$=500+100-10-2=588.$ 

Concept: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Given that :
The cost of pure milk = ₹ 101 per kilogram
The cost of milk in which water was added= ₹ 81 per kilogram
Amount of pure milk he sold = 4 kilograms
Amount of impure milk he sold = 9 kilograms
$\therefore$ His net income = 101$\times$4 + 81$\times$9 = (100+1)$\times$4 + (80 + 1)$\times$(10-1)
= 400 + 4 + 800 - 80 + 10- 1 = ₹ 1133

Steps: 3 Marks
Answer: 1 Mark

The total capacity of restaurant = 1000.

Lunch income =450 $\times$ 650
= 292500

No. of people in dinner =1000 - 450 = 550

Dinner income =550 $\times$ 850
= 467500

So, total income for a day = 292500 + 467500 = Rs.760000.