Maths from Beginner to Advanced · Lesson 2

Addition and Subtraction

In Lesson 1 you met numbers and the + sign. Now we'll look properly at adding and taking away, picture both on a number line, and discover how the two are connected.

Addition Means Combining

Addition means putting quantities together to find how many there are altogether.

Suppose you have 6 cats:

Six cats.

Then 3 more cats arrive:

Six cats, and three more arrive.

Count them all and there are nine cats. So:

6+3=9

Counting every object works, but it gets slow with bigger numbers. There's a picture that makes adding much quicker.

The Number Line

A number line is the whole numbers laid out in order along a line, like steps along a path. Each step to the right is one more; each step to the left is one less.

The numbers 0 to 10. Moving right, the numbers get bigger; moving left, they get smaller.

Adding on the Number Line

To work out 6+3, start at 6. Adding 3 means taking 3 steps to the right:

Start at 6 and move 3 steps right: 6 → 7 → 8 → 9. Adding moves right.

You finish at 9, the same answer you got by counting the cats:

6+3=9
Key idea

On a number line, adding moves to the right. The number you add tells you how many steps to take.

Subtraction

Subtraction has two everyday meanings, and both are useful:

  1. Taking something away — how many are left?
  2. Finding the difference — how much bigger is one amount than another?

Taking away

Suppose you have ₹10 and spend ₹4. How much money is left? You started with 10, and 4 was taken away:

10−4=6

You have ₹6 left. The − sign is read as "minus".

Finding the difference

Now suppose you have 10 marbles and a friend has 4. How many more do you have? Nothing is being taken away this time — we're comparing two amounts. But it's the same calculation:

10−4=6

You have 6 more marbles. We say the difference between 10 and 4 is 6.

Subtracting on the Number Line

If adding moves right, subtracting moves the other way. To work out 10−4, start at 10 and take 4 steps to the left:

Start at 10 and move 4 steps left: 10 → 9 → 8 → 7 → 6. Subtracting moves left.

Four steps left from 10 lands on 6, so:

10−4=6
Key idea

On a number line, subtracting moves to the left. The number you subtract tells you how many steps to take.

Opposite Operations

Look at these two facts side by side:

6+4=10
10−4=6

In the first, we start at 6 and add 4 to reach 10. In the second, we start at 10 and take the same 4 away — and we're back at 6. Subtracting 4 undoes adding 4.

On the number line it's easy to see why: adding 4 is four steps right, and subtracting 4 is four steps left, straight back to where you started.

Because each one undoes the other, addition and subtraction are called inverse operations — "inverse" simply means opposite.

Key idea

Addition and subtraction are inverse operations: one undoes the other. If 6+4=10, then 10−4=6.

Tip

This gives you a free way to check your answers. After working out a subtraction, add your answer back on. If you get to the number you started with, you're right.

Longer Calculations

Sometimes a calculation has several + and − signs in a row. When that happens, work from left to right, one step at a time, just like reading a sentence. For example:

5+4−3

First, 5+4=9. Then take 3 away from that result: 9−3=6. On a number line, that's 4 steps right from 5, then 3 steps left.

Recap

What you learned
  • Addition means combining quantities. On a number line, it moves right.
  • Subtraction means taking away, or finding the difference between two amounts. On a number line, it moves left.
  • Addition and subtraction are inverse operations — each one undoes the other.
  • With several + and − signs, work from left to right.

Your Turn

Your turn

Try each one on your own. Sketch a number line if it helps, and use the inverse-operation trick to check your subtractions.

  1. 18+7=?
  2. 25−9=?
  3. 12+8−5=?
  4. Thinking question: You have ₹50. You buy something for ₹18. How much money is left?
  5. Slightly tricky: 20−7+4=?