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Facts About Division and Multiplication in Maths

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Key properties rules formulas and solved examples of division and multiplication

Multiplication and division are basic knowledge for school students. Multiplication is the process of calculating the product of two or more numbers. It is a basic arithmetic operation that is frequently used in everyday life. When we need to combine groups of equivalent size, we employ multiplication. Division is the separating of a large group into smaller groups so that each group has an equal number of things. In Mathematics, it is an operation used for equal grouping and equal sharing. In this article, we will introduce you to some well-known multiplication and division facts.


What are Multiplication and Division Facts?

The numbers that are being multiplied are referred to as factors, and the outcome of the multiplication is referred to as the product.


In division, the dividend is the number being divided, the divisor is the number dividing it, and the quotient is the outcome of the division.


Multiplication and Division


Multiplication and Division


Division and Multiplication-related Facts

  • You can write a multiplication fact simply by writing out a multiplication calculation. For example: 12 × 12 = 144, 3 × 6 = 18 and 8 × 5 = 40

  • You can also write multiplication facts using different methods of multiplication. For example, repeated addition is a way of finding multiplication facts by repeatedly adding a number until you reach the answer. 2 × 5 is the same as 2 + 2 + 2 + 2 + 2 = 10. The multiplication fact in that case is 10.

  • If the dividend is ‘zero’ then any number as a divisor will give the quotient as ‘zero’.

Example: If ‘zero’ sweets are to be distributed among 8 children, naturally no one will get any sweets.

  • If the divisor is ‘1’ then any dividend will have the quotient equal to itself.

Example: There are 15 sweets; each child is to get 1 sweet. How many children get sweets?

Division of 15 by 1


Division of 15 by 1


Multiplication and Division Drills

Q1. At a zoo, there are 45 deer. Find out the total number of legs of all the deer.

Ans: There are a total of 45 deer. We know that each deer will have 4 legs.

Therefore, the total number of legs deer will have will be equal to the:

$= 45 \times 4$
= 180.

Hence, 180 will be the total number of legs of all the deer.


Q2. Write two multiplication for each division:

(i) 15 ÷ 3 = 5

Ans: The two multiplication for it will be: 5 × 3 = 15 and 3 × 5 = 15

(ii) 3 ÷ 3 = 1

Ans: The two multiplication for it will be: 1 × 3 = 3 and 3 × 1 = 3


Practice Questions

Q1. Write two multiplication for each division:

(i) 21 ÷ 3 = 7

(ii) 30 ÷ 3 = 10

(iii) 33 ÷ 3 = 11

Ans:

(i) 7 × 3 = 21 and 3 × 7 = 21

(ii) 10 × 3 = 30 and 3 × 10 = 30

(iii) 11 × 3 = 33 and 3 × 11 = 33


Q2. Write two divisions for each multiplication:

(i) 6 × 3 = 18 (Ans: 18 ÷ 3 = 6 and 18 ÷ 6 = 3)

(ii) 2 × 3 = 6 (Ans: 6 ÷ 2 = 3 and 6 ÷ 3 = 2)

(iii) 9 × 3 = 27 (Ans: 27 ÷ 9 = 3 and 27 ÷ 3 = 9)

(iv) 12 × 3 = 36 (Ans: 36 ÷ 3 = 12 and 36 ÷ 12 = 3)

(v) 8 × 3 = 24 (Ans: 24 ÷ 3 = 8 and 24 ÷ 8 = 3)


Summary

In this article, we have learned about multiplication which is a mathematical operation that conveys the fundamental concept of repeated addition of the same integer. Later, we also learned about division sentences, as it is a basic mathematical operation in which a bigger number is divided into smaller groups with the same number of components. In the end, we have seen some practice problems based on the facts. We hope you have a clear picture of the facts on multiplication and division. Practise further to enhance your understanding of the topic.

FAQs on Facts About Division and Multiplication in Maths

1. What is the relationship between multiplication and division?

Multiplication and division are inverse operations, meaning they undo each other. If a × b = c, then c ÷ b = a and c ÷ a = b. For example:

  • 6 × 4 = 24
  • 24 ÷ 4 = 6
  • 24 ÷ 6 = 4
This inverse relationship is a key fact in arithmetic and helps in checking answers.

2. What is the formula for multiplication?

The basic formula for multiplication is Product = Multiplicand × Multiplier. In symbols:

  • a × b = c
Here, a and b are factors, and c is the product. For example, 7 × 5 = 35, where 35 is the product.

3. What is the formula for division?

The standard division formula is Dividend ÷ Divisor = Quotient. In symbols:

  • a ÷ b = c
Here, a is the dividend, b is the divisor, and c is the quotient. For example, 20 ÷ 4 = 5.

4. How do you solve multiplication step by step?

To solve multiplication, multiply each digit and add the results according to place value. For example, solve 23 × 4:

  • Step 1: Multiply ones: 4 × 3 = 12 (write 2, carry 1)
  • Step 2: Multiply tens: 4 × 2 = 8, plus 1 = 9
  • Final answer: 92
This method is called the standard multiplication algorithm.

5. How do you solve division step by step?

To solve division, divide step by step using long division or basic facts. For example, solve 36 ÷ 6:

  • Ask: How many times does 6 go into 36?
  • 6 × 6 = 36
  • So, 36 ÷ 6 = 6
This process finds the quotient by using multiplication facts.

6. What are the properties of multiplication?

Multiplication has four main properties: commutative, associative, distributive, and identity.

  • Commutative: a × b = b × a
  • Associative: (a × b) × c = a × (b × c)
  • Distributive: a × (b + c) = ab + ac
  • Identity: a × 1 = a
These properties help simplify calculations.

7. What are the basic rules of division?

The key rules of division include dividing by 1, zero rules, and inverse facts. Important rules are:

  • a ÷ 1 = a
  • 0 ÷ a = 0 (if a ≠ 0)
  • Division by 0 is undefined
Division is not commutative, meaning a ÷ b ≠ b ÷ a in most cases.

8. What is the difference between multiplication and division?

Multiplication combines equal groups, while division separates a quantity into equal parts. In simple terms:

  • Multiplication finds the total of equal groups (e.g., 4 × 3 = 12).
  • Division splits a total into equal groups (e.g., 12 ÷ 3 = 4).
They are inverse operations but perform opposite actions.

9. How are multiplication and division used in real life?

Multiplication and division are used to calculate totals, rates, and equal sharing in everyday life. Examples include:

  • Finding total cost: 5 items × $3 = $15
  • Sharing money equally: $20 ÷ 4 = $5 each
  • Calculating speed: distance ÷ time
These operations are essential in budgeting, shopping, travel, and measurements.

10. What are common mistakes in multiplication and division?

Common mistakes in multiplication and division include place value errors and incorrect use of zero. Frequent errors are:

  • Forgetting to carry in multiplication
  • Misplacing digits in long division
  • Dividing by 0, which is undefined
  • Ignoring remainders when required
Carefully checking steps and using inverse operations helps avoid these mistakes.