Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) What is the difference between the smallest and the largest two-digit whole numbers?
Perfect! Largest 2-digit: 99, Smallest 2-digit: 10. Difference = 99 - 10 = 89.
(2) Find: (6 + 4) × 3 = ?
Excellent! First solve bracket: 6 + 4 = 10, then 10 × 3 = 30.
(3) Write the name of the property of multiplication of whole numbers which satisfies a × b = b × a.
Great! The correct answer is the Commutative Property, which states: a × b = b × a.
(4) Is subtraction closed for whole numbers?
Correct! For example: 3 - 5 = -2, which is not a whole number.
(5) Fill in the blank: ? + 0 = 9876
Perfect! This shows the additive identity property: any number + 0 = that number.
(6) What is the product of the first 3 whole numbers?
Correct! First 3 whole numbers are 0, 1, 2. Product = 0 × 1 × 2 = 0.
(7) State whether 0 is the multiplicative identity.
Right! 0 is not the multiplicative identity because 0 × any number = 0, never the same number.
(8) Name the property shown: 3 + (5 + 7) = (3 + 5) + 7
Perfect! This shows that grouping doesn't change the sum.
(9) What is the identity element for multiplication of whole numbers?
Excellent! Any number × 1 = that number, so 1 is the multiplicative identity.
(10) Complete the following to show the commutative property:.
5 +
Well done! These examples show that changing the order of numbers doesn’t change the result — that’s the commutative property!
Short Answer Questions (2 Marks Each)
Answer each question in 2-3 sentences
(1) Show that addition is commutative for whole numbers using an example.
Example:
LHS=
Perfect! This shows that changing the order of addends doesn't change the sum.
(2) Using number line, show 4 + 3 and 3 + 4. What do you observe?
Now try drawing the path for 4 + 3 yourself! First click on the number 4. Drag the red dot from 4 and move it 3 spaces to the right.
Where should you end up when you add 3 to 4?
Now try drawing the path for 3 + 4 yourself! First click on the number 3. Drag the red dot from 3 and move it 4 spaces to the right.
Both give the same result:
Excellent! Both reach the same point on the number line, showing
(3) Verify the distributive property: 5 × (3 + 2) = (5 × 3) + (5 × 2)
Left side: 5 × (3 + 2) = 5 ×
Right side: (5 × 3) + (5 × 2) =
Perfect! Both sides equal 25, verifying the distributive property.
(4) Identify and name the properties used in the following:
(a) 8 + 0 = 8
Property:
(b) 6 × 1 = 6
Property:
Excellent understanding of identity properties!
(5) Find the value of using suitable property: (4 × 7) + (4 × 3)
which number can we take common from both-
we can write it as
=
Great! You can also use distributive property: 4 × (7 + 3) = 4 × 10 = 40.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Draw a number line and show the product 4 × 3 using jumps. Then show commutativity using the number line again for 3 × 4. Write your observation.
First, click on 0 on the number line.Now, drag the red dot right for 3 units and repeat it 4 times.
4 × 3 means:
The point ends at
Now try drawing the path for 3 x 4 yourself! First click on the number 0.
3 × 4 means:
Both reach the same point:
Observation:
Excellent! You've demonstrated commutativity visually using the number line.
(2) Fill in the blanks and identify the properties:
(a) 7 + ? = ? + 7
Missing numbers:
Property:
(b) ? + (12 + 4) = (? + 12) + 4
Missing number:
Property:
(c) ? × (9 + 3) = ? × 9 + ? × 3
Missing number:
Property:
(d) 6 × 1 = ?
Answer:
Property: Multiplicative
Outstanding work identifying all the properties!
(4) Use the distributive property to simplify: 12 × 25 + 12 × 75. Then verify your answer using direct multiplication.
which number can be taken common in the given expression-
Using distributive property:
12 ×
Direct verification: 12 × 25 + 12 × 75 =
Perfect! Both methods give the same answer, confirming our work.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The number of whole numbers between 1 and 100 is:
Correct! Numbers between 1 and 100 are: 2, 3, 4, ..., 99. That's 98 numbers.
(2) (3 × 4) × 2 = 3 × (4 × 2) shows:
Correct! Grouping doesn't change the product in multiplication.
(3) 6 + 0 = 6 is an example of:
Correct! 0 is the additive identity: any number + 0 = that number.
(4) Which is not a property of subtraction for whole numbers?
Correct! Subtraction has none of these properties for whole numbers.
(5) Multiplicative identity for whole numbers is:
Correct! Any number × 1 = that number, so 1 is the multiplicative identity.
(6) Which of these shows distributive property?
Correct! This shows multiplication distributing over addition.
(7) Find the value : (6 × 3) + (6 × 7) by using a property
Correct! use distributive: 6 × (3 + 7) = 6 × 10 = 60.
(8) Which of the following is not a whole number?
Correct! Whole numbers are 0, 1, 2, 3, ... Negative numbers are not whole numbers.
(9) On a number line, 0 is:
Correct! 0 is typically the starting point (origin) on a number line.
(10) Which of the following shows the commutative property?
Correct! Commutative property shows that order doesn't matter: a + b = b + a.
Property Statements Challenge
Determine whether these statements about whole number properties are True or False: