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6th Grade > Mathematics

WHOLE NUMBERS MCQs

Total Questions : 50 | Page 4 of 5 pages
Question 31.


Is it possible to find the largest whole number on the number line? [1 MARKS]


 Discuss Question
Answer: Option A. ->
:


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


Question 32.


Using suitable properties, find the value of following:


Simplify:  


a) 126×55+126×45


b) 89×48
c) 49×12
[3 MARKS]


 Discuss Question
Answer: Option A. ->
:

Each option: 1 Mark
By using distributive property we can simplify the problem
a×(b+c)=(a+b)×(a+c)

a×(bc)=(ab)×(ac)


a)126×55+126×45
126(55+45)=126×100=12600.


b)  89×48=(901)×(502)
=450018050+2=4272.
c) 49×12=(501)×(10+2)
=500+100102=588. 


Question 33.


Michel owes Rs. 3, Steve owes Rs. 5 but Cooper doesn't owe anything. Each of them has Rs. 13 in their pocket presently. Place these people on the number line and find who is poorest and who is richest. [3 MARKS]


 Discuss Question
Answer: Option A. ->
:

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.


Michel Owes Rs. 3, Steve Owes Rs. 5 But Cooper Doesn't Owe A...


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


Michel Owes Rs. 3, Steve Owes Rs. 5 But Cooper Doesn't Owe A...


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.


Question 34.


Does division follow the associative law? Explain it with help of examples. [3 MARKS]


 Discuss Question
Answer: Option A. ->
:

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.


Question 35.


What are whole numbers? How are they different from natural numbers? Are all natural numbers whole numbers? Explain. [2 MARKS]


 Discuss Question
Answer: Option A. ->
:

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.


Question 36.


State the property of closure of whole numbers. Do all the arithmetic operations follow this property? If not, why? [2 MARKS]


 Discuss Question
Answer: Option A. ->
:

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.


Question 37.


A restaurant provides a buffet lunch and dinner for Rs. 650 & Rs. 850 respectively. For a day, the maximum handling capacity of the restaurant is 1000 people and for the lunch, it is 450. Find total income of the restaurant per day. [4 MARKS]


 Discuss Question
Answer: Option A. ->
:

Steps: 3 Marks
Answer: 1 Mark
The total capacity of restaurant = 1000.


Lunch income =450 × 650
= 292500


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


Dinner income =550 × 850
= 467500


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


Question 38.


A milkman sold milk at two different rates depending on how much water he added to them. One of the types in which he added no water, he sold it for ₹ 101 per kilogram. The one in which he added water he sold it for ₹ 81 per kilogram. He sold 4 kilograms of pure milk and 9 kilograms in which water was added. Find his net monthly income.  [4 MARKS]


 Discuss Question
Answer: Option A. ->
:

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
His net income = 101×4 + 81×9 = (100+1)×4 + (80 + 1)×(10-1)
= 400 + 4 + 800 - 80 + 10- 1 = 1133


Question 39.


Determine the sum of the four number as given below:
(a) successor of 32
(b) predecessor of 49
(c) predecessor of the predecessor of 56
(d) successor of the successor of 67.
[4 MARKS]

 


 Discuss Question
Answer: Option A. ->
:
Each Option: 0.5 Marks
Answer: 2 Marks
a) Successor of 32=32+1 =33
b) Predecessor of 49 = 49 -1 =48
c) Predecessor of 56 = 56 -1 =55
Predecessor of 55 = 55 -1 =54
Predecessor of  predecessor of 56 =54
d) Successor of 67 = 67 +1 = 68
and successor of 68 = 68 +1 = 69.
Successor of successor of 67 = 69.
Required sum = 33 + 48 + 54 + 69 = 204
Question 40.


John used the calculator to find the product 1499 and 319. He multiplied 319 with the successor of 1499 instead. How much should be subtracted to get the correct answer? [4 MARKS]


 Discuss Question
Answer: Option A. ->
:
Steps: 3 Marks
Answer: 1 Mark
John had to find the product of the numbers 1499 and 319. 
Instead, he multiplied 319 with the successor of 1499 which is 1500
Now,1500×319 = 1500×(300+20-1) = 450000+30000-1500=478500
1499×319 = (1500-1)×(300+20-1) = 450000 + 30000 - 1500 - 300 - 20 + 1=478181
The difference = 478500-478181= 319
Hence 319 should be subtracted from product to get the correct answer.

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