Class 7 Maths Chapter 2.3 – Distributive Property
In Class 7 Mathematics Chapter 2.3, students learn about the distributive property of multiplication over addition and subtraction. This property helps us simplify arithmetic expressions and perform calculations more easily.
Instead of multiplying a number by a complete sum or difference, we can multiply it separately by each number inside the brackets and then add or subtract the results.
For example:
5 × (4 + 3) = 5 × 4 + 5 × 3
= 20 + 15
= 35
Both methods give the same answer. Let us understand this property with simple examples, diagrams and exercise solutions.
1. What Is the Distributive Property?
The distributive property explains how multiplication works with addition and subtraction inside brackets.
Distributive Property Over Addition
When a number is multiplied by a sum, we can multiply that number by each term separately and then add the products.
a × (b + c) = a × b + a × c
For example:
4 × (6 + 3)
= 4 × 6 + 4 × 3
= 24 + 12
= 36
Check the original expression:
4 × (6 + 3) = 4 × 9 = 36
Both methods give the same result.
Distributive Property Over Subtraction
When a number is multiplied by a difference, multiply it by both numbers separately and subtract the second product from the first.
a × (b − c) = a × b − a × c
For example:
5 × (10 − 3)
= 5 × 10 − 5 × 3
= 50 − 15
= 35
Check:
5 × (10 − 3) = 5 × 7 = 35
Both methods give the same answer.
2. Understanding the Distributive Property Through Repeated Addition
Let us understand why the distributive property works.
Consider:
3 × (4 + 2)
This means three groups of (4 + 2).
We can write it as:
(4 + 2) + (4 + 2) + (4 + 2)
Now arrange the numbers:
= 4 + 2 + 4 + 2 + 4 + 2
Group the 4s and 2s:
= 4 + 4 + 4 + 2 + 2 + 2
= 3 × 4 + 3 × 2
= 12 + 6
= 18
Therefore:
3 × (4 + 2) = 3 × 4 + 3 × 2 = 18
3. Distributive Property with Larger Numbers
The distributive property is especially useful when multiplying larger numbers.
Example 1: Find 13 × 98.
Solution:
We can write 13 as 10 + 3.
13 × 98 = (10 + 3) × 98
Using the distributive property:
= 10 × 98 + 3 × 98
= 980 + 294
= 1,274
Answer: 1,274
Example 2: Find 14 × 10 − 6 × 10.
Solution:
Both terms contain multiplication by 10.
We can take 10 as a common factor.
14 × 10 − 6 × 10
= (14 − 6) × 10
= 8 × 10
= 80
Answer: 80
4. Using the Distributive Property to Make Multiplication Easier
We can break a number into convenient parts to simplify multiplication.
Example 3: Find 97 × 25.
Solution:
97 is close to 100.
Therefore, write:
97 = 100 − 3
Now:
97 × 25 = (100 − 3) × 25
Using the distributive property:
= 100 × 25 − 3 × 25
= 2,500 − 75
= 2,425
Answer: 2,425
Example 4: Find 53 × 18 if 53 × 18 = 954. Then find 63 × 18.
Solution:
We know:
53 × 18 = 954
Now write 63 as 53 + 10.
63 × 18 = (53 + 10) × 18
Using the distributive property:
= 53 × 18 + 10 × 18
= 954 + 180
= 1,134
Answer: 1,134
5. Solved Examples from the Textbook
Example 5: Find 95 × 8.
Solution:
Write 95 as 100 − 5.
95 × 8 = (100 − 5) × 8
= 100 × 8 − 5 × 8
= 800 − 40
= 760
Answer: 760
Example 6: Find 104 × 15.
Solution:
Write 104 as 100 + 4.
104 × 15 = (100 + 4) × 15
= 100 × 15 + 4 × 15
= 1,500 + 60
= 1,560
Answer: 1,560
Example 7: Find 49 × 50.
Solution:
Write 49 as 50 − 1.
49 × 50 = (50 − 1) × 50
= 50 × 50 − 1 × 50
= 2,500 − 50
= 2,450
Answer: 2,450
6. Important Forms of the Distributive Property
| Property | Formula | Example |
|---|---|---|
| Multiplication over addition | a × (b + c) = a × b + a × c | 3 × (4 + 5) = 3 × 4 + 3 × 5 |
| Multiplication over subtraction | a × (b − c) = a × b − a × c | 4 × (9 − 2) = 4 × 9 − 4 × 2 |
| Taking a common factor | a × b + a × c = a × (b + c) | 5 × 7 + 5 × 3 = 5 × (7 + 3) |
| Taking a common factor from subtraction | a × b − a × c = a × (b − c) | 8 × 9 − 8 × 4 = 8 × (9 − 4) |
Class 7 Maths Chapter 2.3 – Figure It Out Solutions
Question 1. Fill in the blanks so that both sides of each expression are equal.
(a) 3 × (6 + 7) = 3 × 6 + 3 × 7
Solution:
Using the distributive property:
3 × (6 + 7) = 3 × 6 + 3 × 7
= 18 + 21 = 39
Answer: 3 × 6 + 3 × 7
(b) (8 + 3) × 4 = 8 × 4 + 3 × 4
Solution:
Multiply both terms inside the brackets by 4.
(8 + 3) × 4 = 8 × 4 + 3 × 4
= 32 + 12 = 44
Answer: 8 × 4 + 3 × 4
(c) 3 × (5 + 8) = 3 × 5 + 3 × ____
Solution:
Multiply 3 by both numbers inside the brackets.
3 × (5 + 8) = 3 × 5 + 3 × 8
Answer: 8
(d) (9 + 2) × 4 = 9 × 4 + 2 × ____
Solution:
Both terms are multiplied by 4.
(9 + 2) × 4 = 9 × 4 + 2 × 4
Answer: 4
(e) 3 × (____ + 4) = 3 × ____ + ____
Solution:
One valid completion is:
3 × (5 + 4) = 3 × 5 + 3 × 4
Answer: 5, 5 and 3 × 4
(f) (____ + 6) × 4 = 13 × 4 + ____
Solution:
The first missing number is 13. The second term must be 6 × 4.
(13 + 6) × 4 = 13 × 4 + 6 × 4
Answer: 13 and 6 × 4
(g) 3 × (____ + ____) = 3 × 5 + 3 × 2
Solution:
Compare both terms on the right side.
3 × (5 + 2) = 3 × 5 + 3 × 2
Answer: 5 and 2
(h) (____ + ____) × ____ = 2 × 4 + 3 × 4
Solution:
Both terms on the right are multiplied by 4.
(2 + 3) × 4 = 2 × 4 + 3 × 4
Answer: 2, 3 and 4
(i) 5 × (9 − 2) = 5 × 9 − 5 × ____
Solution:
Using the distributive property over subtraction:
5 × (9 − 2) = 5 × 9 − 5 × 2
Answer: 2
(j) (5 − 2) × 7 = 5 × 7 − 2 × ____
Solution:
(5 − 2) × 7 = 5 × 7 − 2 × 7
Answer: 7
(k) 5 × (8 − 3) = 5 × 8 ____ 5 × ____
Solution:
Because the expression contains subtraction, the sign between the products is minus.
5 × (8 − 3) = 5 × 8 − 5 × 3
Answer: Minus (−) and 3
(l) (8 − 3) × 7 = 8 × 7 ____ 3 × 7
Solution:
(8 − 3) × 7 = 8 × 7 − 3 × 7
Answer: Minus (−)
(m) 5 × (12 − ____) = ____ × 5 − 5 × ____
Solution:
One valid completion is:
5 × (12 − 2) = 12 × 5 − 5 × 2
Answer: 2, 12 and 2
(n) (15 − ____) × 7 = ____ × 7 − 6 × 7
Solution:
Compare the two terms on the right side.
(15 − 6) × 7 = 15 × 7 − 6 × 7
Answer: 6 and 15
(o) 5 × (____ − ____) = 5 × 9 − 5 × 4
Solution:
5 × (9 − 4) = 5 × 9 − 5 × 4
Answer: 9 and 4
(p) (____ − ____) × ____ = 17 × 7 − 9 × 7
Solution:
(17 − 9) × 7 = 17 × 7 − 9 × 7
Answer: 17, 9 and 7
Question 2. Compare the expressions using <, > or = without calculating their complete values.
(a) (8 − 3) × 29 ____ (3 − 8) × 29
Solution:
8 − 3 = 5, which is positive.
3 − 8 = −5, which is negative.
Multiplying a positive number by 29 gives a positive result. Multiplying a negative number by 29 gives a negative result.
Therefore:
(8 − 3) × 29 > (3 − 8) × 29
(b) 15 + 9 × 18 ____ (15 + 9) × 18
Solution:
The left side has 15 added to 9 × 18.
The right side multiplies both 15 and 9 by 18.
The right side is greater because it includes an additional 15 × 17 compared with the left side.
Answer: <
(c) 23 × (17 − 9) ____ 23 × 17 + 23 × 9
Solution:
Using the distributive property:
23 × (17 − 9) = 23 × 17 − 23 × 9
The expression on the right uses addition instead of subtraction.
Therefore, the left side is smaller.
Answer: <
(d) (34 − 28) × 42 ____ 34 × 42 − 28 × 42
Solution:
By the distributive property:
(34 − 28) × 42 = 34 × 42 − 28 × 42
Answer: =
Question 3. Find other ways to make 14 using the given pattern.
The textbook gives one example:
2 × (1 + 6) = 14
Find four other possibilities.
Solution:
Here are four valid examples:
(a) 1 × (9 + 5) = 1 × 14 = 14
(b) 2 × (3 + 4) = 2 × 7 = 14
(c) 7 × (1 + 1) = 7 × 2 = 14
(d) 14 × (1 + 0) = 14 × 1 = 14
Answer: All four expressions give 14.
Question 4. Find the sum of the numbers in each picture in at least two different ways.
(a) First picture
The picture contains five yellow squares with the number 4 and four blue circles with the number 8.
Method 1: Group equal numbers.
= 5 × 4 + 4 × 8
= 20 + 32
= 52
Method 2: Add the rows.
= (4 + 8 + 4) + (8 + 4 + 8) + (4 + 8 + 4)
= 16 + 20 + 16
= 52
Answer: 52
(b) Second picture
The picture contains eight circles showing 5 and eight circles showing 6.
Method 1: Group equal numbers.
= 8 × 5 + 8 × 6
= 40 + 48
= 88
Method 2: Group the four rows.
= 4 × (5 + 6 + 6 + 5)
= 4 × 22
= 88
Answer: 88
More Applications of the Distributive Property
Example 8: Weekly Mango Supply
Rahim supplies 9 kg of mangoes every day and Shyam supplies 11 kg every day to a market. The market operates seven days a week. Find the total mango supply in one week.
Solution:
Daily supply = 9 + 11 = 20 kg
Weekly supply = 7 × (9 + 11)
Using the distributive property:
= 7 × 9 + 7 × 11
= 63 + 77
= 140 kg
Answer: 140 kg
Example 9: Annual Savings
Binu earns ₹20,000 every month. She spends ₹5,000 on rent, ₹5,000 on food and ₹2,000 on other expenses. Find her savings at the end of one year.
Solution:
Monthly income = ₹20,000
Total monthly expenses:
= 5,000 + 5,000 + 2,000
= ₹12,000
Monthly savings:
= 20,000 − 12,000
= ₹8,000
Annual savings:
= 12 × 8,000
= ₹96,000
Answer: ₹96,000
Example 10: Snail Climbing a Post
A snail climbs 3 cm during the day and slips down 2 cm during the night. The post is 10 cm high. How many days will the snail take to reach the top?
Solution:
During one complete day and night, the snail gains:
3 − 2 = 1 cm
However, on the final day, the snail reaches the top before slipping back.
After seven nights, the snail has reached 7 cm.
On the eighth day, it climbs 3 cm:
7 + 3 = 10 cm
Answer: 8 days
Additional Practice Questions
Try these original questions to practise the distributive property.
Question 1. Use the distributive property to calculate.
- 6 × (10 + 4)
- 8 × (15 − 5)
- 12 × 19
- 101 × 25
- 99 × 12
Question 2. Fill in the blanks.
- 4 × (7 + 3) = 4 × 7 + 4 × ____
- 6 × (12 − 5) = 6 × 12 − 6 × ____
- (8 + 2) × 9 = 8 × 9 + ____ × 9
- 15 × 7 + 5 × 7 = (15 + ____) × 7
- 20 × 8 − 4 × 8 = (20 − ____) × 8
Question 3. Compare using <, > or =.
- 5 × (12 + 3) ____ 5 × 12 + 5 × 3
- 8 × (20 − 5) ____ 8 × 20 + 8 × 5
- (15 − 7) × 9 ____ 15 × 9 − 7 × 9
Answers to Additional Practice Questions
Question 1:
- 6 × 10 + 6 × 4 = 60 + 24 = 84
- 8 × 15 − 8 × 5 = 120 − 40 = 80
- (10 + 2) × 19 = 190 + 38 = 228
- (100 + 1) × 25 = 2,500 + 25 = 2,525
- (100 − 1) × 12 = 1,200 − 12 = 1,188
Question 2:
- 3
- 5
- 2
- 5
- 4
Question 3:
- =
- <
- =
Common Mistakes Students Should Avoid
- Multiplying only the first term: Remember to multiply every term inside the brackets.
- Using the wrong sign: When distributing over subtraction, retain the minus sign between the products.
- Forgetting the common factor: In expressions such as 8 × 9 + 8 × 4, the common factor is 8.
- Confusing addition and multiplication: The distributive property applies to multiplication over addition or subtraction.
- Not checking the answer: Calculate the original expression as a quick way to verify your result.
Quick Revision – Distributive Property
- a × (b + c) = a × b + a × c
- a × (b − c) = a × b − a × c
- a × b + a × c = a × (b + c)
- a × b − a × c = a × (b − c)
- We can split numbers into convenient parts to make multiplication easier.
- The distributive property helps us calculate mentally and simplify expressions.
Frequently Asked Questions
1. What is the distributive property in Class 7 Maths?
The distributive property states that multiplying a number by a sum or difference is the same as multiplying it by each term separately and then adding or subtracting the products.
2. What is the formula for the distributive property over addition?
The formula is a × (b + c) = a × b + a × c.
3. What is the formula for the distributive property over subtraction?
The formula is a × (b − c) = a × b − a × c.
4. How does the distributive property make multiplication easier?
It allows us to split a number into convenient parts. For example, 99 × 12 can be calculated as (100 − 1) × 12.
5. What is the common factor in an expression?
A common factor is a number or quantity that multiplies each term. For example, 5 is the common factor in 5 × 7 + 5 × 3.
6. Is the distributive property useful in everyday calculations?
Yes. It can help calculate shopping totals, quantities, savings, repeated groups and large multiplication problems.
Conclusion
The distributive property is an important concept in Class 7 Mathematics. It helps students simplify expressions, calculate large products more efficiently and understand the relationship between multiplication, addition and subtraction.
Practise the solved examples and Figure It Out questions to improve your understanding. Once you are comfortable with these rules, try the additional questions without looking at the answers.
Continue Learning Class 7 Mathematics
Explore the other sections of Class 7 Mathematics to strengthen your understanding of arithmetic expressions and mathematical operations.