What is Inverse?

Hello, Year 4! Today, we’re going to learn about something called multiplication using the inverse. But first, let’s understand what inverse means.

The inverse is the opposite of something. In maths, the inverse of multiplication is division. This means that if you multiply a number and then divide it by the same number, you will get back to where you started!

Example of Inverse

Imagine you have 3 bags with 4 apples in each. You can write this as:

$$3 \times 4 = 12$$

Now, if you want to find out how many bags you have if you only know the total number of apples, you can use division, which is the inverse of multiplication:

$$12 \div 4 = 3$$

This tells us that if we have 12 apples and each bag holds 4 apples, we have 3 bags.

Why Use Inverse?

Using the inverse helps us check our work. If we multiply and then divide, we can make sure our answers are correct.

Key Rules

  1. Inverse Relationship: Remember that multiplication and division are opposites.
  2. Checking Work: You can check your multiplication by using division.
  3. Equal Values: Multiplying and then dividing by the same number gives you the original number.

Tips and Tricks

  • Think of Real-Life Examples: Use things like fruit, toys, or books. How many groups do you have? How many items are in each group?
  • Practice with Simple Numbers: Start with small numbers to make it easier.
  • Use Arrays: Drawing arrays can help you visualise multiplication and its inverse.

Questions

Easy Level Questions

  1. What is the inverse of 5 x 2?
  2. If you have 10 cookies and put them into 2 bags, how many cookies are in each bag?
  3. 6 x 3 = ? What is the inverse?
  4. If you divide 15 by 5, what do you get?
  5. 4 x 2 = ? What is the inverse operation?
  6. How many groups of 3 are in 9?
  7. If you have 24 apples and you want to divide them into bags of 6, how many bags do you have?
  8. What is the result of 8 ÷ 4?
  9. If 7 x 2 = ?, what is the inverse?
  10. How many 5s are in 20?

Medium Level Questions

  1. 12 x 6 = ? What is its inverse?
  2. If you have 36 pencils and you put them into packs of 9, how many packs do you have?
  3. What is the result of 25 ÷ 5?
  4. If 4 x 5 = ?, what is the inverse operation?
  5. How many sets of 4 are in 32?
  6. 15 ÷ 3 = ?
  7. If 6 x 4 = ?, what is the inverse operation?
  8. How many 8s are in 64?
  9. 20 ÷ 4 = ?
  10. If 10 x 10 = ?, what is the inverse?

Hard Level Questions

  1. 14 x 7 = ? What is its inverse?
  2. If you have 84 marbles and you want to divide them into groups of 12, how many groups do you have?
  3. What is 56 ÷ 7?
  4. If 9 x 9 = ?, what is the inverse operation?
  5. How many groups of 6 are in 54?
  6. 27 ÷ 3 = ?
  7. If 11 x 5 = ?, what is the inverse?
  8. How many 9s are in 81?
  9. 48 ÷ 6 = ?
  10. If 18 x 2 = ?, what is the inverse operation?

Answers with Explanations

Easy Level Answers

  1. 2 (Inverse is 5 ÷ 2)
  2. 5 cookies (10 ÷ 2 = 5)
  3. 18 (Inverse is 6 ÷ 3)
  4. 3 (15 ÷ 5 = 3)
  5. 8 (Inverse is 4 ÷ 2)
  6. 3 (9 ÷ 3 = 3)
  7. 4 bags (24 ÷ 6 = 4)
  8. 2 (4 ÷ 4 = 1)
  9. 14 (Inverse is 7 ÷ 2)
  10. 4 (20 ÷ 5 = 4)

Medium Level Answers

  1. 72 (Inverse is 72 ÷ 6)
  2. 4 packs (36 ÷ 9 = 4)
  3. 5 (25 ÷ 5 = 5)
  4. 20 (Inverse is 4 ÷ 5)
  5. 8 (32 ÷ 4 = 8)
  6. 5 (15 ÷ 3 = 5)
  7. 24 (Inverse is 6 ÷ 4)
  8. 8 (64 ÷ 8 = 8)
  9. 5 (20 ÷ 4 = 5)
  10. 100 (Inverse is 10 ÷ 10)

Hard Level Answers

  1. 98 (Inverse is 14 ÷ 7)
  2. 7 groups (84 ÷ 12 = 7)
  3. 8 (56 ÷ 7 = 8)
  4. 81 (Inverse is 9 ÷ 9)
  5. 9 (54 ÷ 6 = 9)
  6. 9 (27 ÷ 3 = 9)
  7. 55 (Inverse is 11 ÷ 5)
  8. 9 (81 ÷ 9 = 9)
  9. 8 (48 ÷ 6 = 8)
  10. 36 (Inverse is 18 ÷ 2)

Now, go ahead and practice! Remember, understanding the inverse of multiplication helps you become a better mathematician. Happy learning!