What Are Inverses?

Hello, Year 4! Today, we’re going to learn about something called inverses. In maths, an inverse is like a magic partner that helps us undo what we just did.

Understanding Inverses with Addition and Subtraction

Let’s start with addition and subtraction.

  • If you add a number and then subtract the same number, you end up back where you started.

For example:

  • Start with 3.
  • Add 4:

$$3 + 4 = 7$$

  • Now, subtract 4:

$$7 – 4 = 3$$

So, the inverse of adding 4 is subtracting 4.

Understanding Inverses with Multiplication and Division

Now, let’s look at multiplication and division.

  • If you multiply a number and then divide it by the same number, you return to the original number.

For example:

  • Start with 6.
  • Multiply by 2:

$$6 \times 2 = 12$$

  • Now, divide by 2:

$$12 \div 2 = 6$$

Here, the inverse of multiplying by 2 is dividing by 2.

Key Rules about Inverses

  1. Addition and Subtraction are Inverses:
    • Adding a number and then subtracting the same number brings you back to your starting number.
  2. Multiplication and Division are Inverses:
    • Multiplying a number and then dividing by the same number brings you back to your starting number.

Tips and Tricks to Remember Inverses

  • Think of opposites: Inverses are like opposites. If one action moves you forward, the inverse brings you back.
  • Practice with pairs: If you know your addition and subtraction facts, try to practice them as pairs. For example, if you know $$5 + 3 = 8$$, then you should also remember that $$8 – 3 = 5$$.
  • Use a number line: A number line can help you visualise how addition and subtraction work together.

Questions on Inverses

Easy Level Questions

  1. What is the inverse of adding 5?
  2. What is the inverse of subtracting 2?
  3. If you have 10 and you subtract 3, what do you add back to get 10 again?
  4. What is the inverse of multiplying by 4?
  5. What is the inverse of dividing by 2?
  6. If you add 6 to 2, what do you need to subtract to get back to 2?
  7. What is 7 minus 3? What do you add to 4 to get back to 7?
  8. If you multiply by 3, what do you divide by to get back to the original number?
  9. What is 15 – 7? What do you add to 7 to get back to 15?
  10. If you start at 5 and add 5, what do you subtract to return to 5?

Medium Level Questions

  1. What is the inverse of adding 9?
  2. If you divide 20 by 4, what do you multiply by to get back to 20?
  3. If you start at 12, add 8, and then subtract what to return to 12?
  4. What is 18 divided by 3? What do you multiply by 3 to return to 18?
  5. If you subtract 4 from 10, what do you need to add to return to 10?
  6. If you multiply by 5 and then divide by 5, what do you get?
  7. What is the inverse operation of 14 + 6?
  8. What is 30 minus 15? What do you add to 15 to get 30?
  9. If you start with 25, multiply by 2, and then divide by 2, what number do you have?
  10. If you have 50 and you subtract 10, what do you add back to return to 50?

Hard Level Questions

  1. If you add 12 and then subtract 12 from your answer, what do you get?
  2. What number do you get if you multiply 6 by 4 and then divide by 4?
  3. If you subtract 15 from 45, what do you need to add to get back to 45?
  4. If you have 24 and you multiply by 3, what do you need to divide by to return to 24?
  5. What is the inverse operation of 9 x 5?
  6. If you start with 100, subtract 25, and then add what to return to 100?
  7. What is the result of (8 + 7) – 7?
  8. If you multiply a number by 10, what do you divide by to return to the original number?
  9. If you have 60 and you subtract 20, what do you add to return to 60?
  10. What is the inverse of (5 + 3) x 2 divided by 2?

Answers and Explanations

Easy Level Answers

  1. Subtracting 5.
  2. Adding 2.
  3. Add 3.
  4. Dividing by 4.
  5. Multiplying by 2.
  6. Subtract 6.
  7. 4; add 3 to 4 to get 7.
  8. Divide by 3.
  9. 8; add 7 to get back to 15.
  10. Subtract 5.

Medium Level Answers

  1. Subtracting 9.
  2. Multiply by 4.
  3. Subtract 8.
  4. 6; multiply by 3 to get back to 18.
  5. Add 4.
  6. You get the original number.
  7. Subtract 6.
  8. 15; add 15 to 15 to get 30.
  9. You have 25.
  10. Add 10.

Hard Level Answers

  1. You get the original number.
  2. You get 6.
  3. Add 15.
  4. You need to divide by 3.
  5. 9 divided by 5.
  6. Add 25.
  7. You get 8.
  8. Divide by 10.
  9. Add 20.
  10. Inverse is (5 + 3) x 2 divided by 2 gives you back the original number.

Great job, Year 4! Keep practicing inverses, and soon you’ll master them!