Taking Away, and How Far Apart
There are 10 biscuits on a plate, and you eat 3. How many are left? And here is another question: Leila is 12 years old, and her brother is 7. How much older is Leila? These sound like different questions, but they are answered the same way.
How many are left?
Subtracting means taking some away. We write it with a minus sign:
- 10 - 3 = 7, said "ten minus three equals seven".
You can count what is left, or count back from 10, once for each biscuit eaten: "nine, eight, seven". On the number line, counting back is hopping to the left.
How far apart?
Now Leila and her brother. Nothing is taken away here. The question is how far apart 12 and 7 are. Find both on the number line and count the steps between them: 5. So Leila is 5 years older, and 12 - 7 = 5.
The answer to a subtracting sum is called the difference: it is how far apart the two numbers are.
For "how far apart", it is often quicker to count up from the smaller number. Many shopkeepers give change this way. Something costs 6 coins and you pay with a 10. The shopkeeper counts up from 6: "seven, eight, nine, ten", handing you a coin each time. You get 4 coins back: 10 - 6 = 4.
Subtracting undoes adding
In the Adding Is Counting On lesson, we put groups together. Subtracting pulls them apart again:
- 7 + 5 = 12, so 12 - 5 = 7 and 12 - 7 = 5.
These three sums are one family. If you know one, you know all three. That is a good way to check a subtraction: add the answer back on, and you should get the number you started with.
The order matters
With adding, the order didn't matter. With subtracting, it does. 7 - 3 is 4. But 3 - 7 means starting at 3 and going 7 steps to the left, past zero, to -4, as we saw in the Opposites lesson. So 7 - 3 and 3 - 7 are not the same.
Try it at home
- Put 15 beans on a table and take 6 away. Count what is left. Now check by adding the 6 back on.
- How many years apart are you and someone in your home? Count up from the younger age to the older one.
Answer to 1: 9 beans.
Words to know
- subtracting - taking some away, or finding how far apart two numbers are
- minus sign (-) - the sign for subtracting
- difference - the answer to a subtracting sum: how far apart two numbers are
- counting back - counting backwards, once for each thing taken away
Big idea
Subtracting tells how many are left, or how far apart two numbers are. It undoes adding: 7 + 5 = 12 means 12 - 5 = 7. Unlike adding, the order matters: 7 - 3 is 4, but 3 - 7 is -4.