Tuesday
Tuesday: Subtracting Is Adding the Opposite
Raven writes 5 - (-3) on the Numbers Desk whiteboard. "Rocket, what is this?"
"Two minus signs," Rocket says. "Easy. Minus and minus make... 2? Or 8? Or -8?"
"What do you notice about -3 and 3?" Raven asks.
"They are opposites," Rocket says. "They make a zero pair."
Nova lowers herself until her light rests on the number line. "Taking away a negative," she says. "Which way is that hop?"
Rocket puts his finger on 5. He thinks about taking away a hop to the left. "Taking away a left hop... is a right hop!"
He hops right three times and lands on 8. "Subtracting -3 is the same as adding 3."
Raven smiles. "Now the par scores from practice will make sense."
One rule for every subtraction
Subtracting a number is the same as adding its opposite. In symbols, p - q = p + (-q).
So 5 - (-3) becomes 5 + 3, which is 8. Taking away a left hop is a right hop.
And 5 - 8 becomes 5 + (-8). Start at 5, hop 8 left, and land on -3.
The rule turns every subtraction into an addition. Then you hop the way you learned yesterday.
| Subtraction | Rewrite as adding the opposite | Hop | Answer |
|---|---|---|---|
| 5 - (-3) | 5 + 3 | right 3 from 5 | 8 |
| 5 - 8 | 5 + (-8) | left 8 from 5 | -3 |
| -4 - 6 | -4 + (-6) | left 6 from -4 | -10 |
| -2 - (-7) | -2 + 7 | right 7 from -2 | 5 |
Distance between two numbers
How far apart are -4 and 3 on the number line? Count the steps between them: 7.
You can also subtract: 3 - (-4) = 7. Or -4 - 3 = -7. The distance is the absolute value of either difference.
Distance is never negative. Write it as |3 - (-4)| = 7.
The crew uses this to find how much the thermometer changed from a morning to an evening reading.
- Write the subtraction.
- Change the minus sign to a plus sign, and flip the sign of the second number.
- Hop it out on the number line, or pair up zero pairs with counters.
- Check the sign of your answer against the picture.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
| Number sentence | True or false? |
|---|---|
| 5 - (-3) = 8 | ? |
| 5 - 8 = 3 | ? |
| -4 - 6 = -10 | ? |
| -2 - (-7) = -9 | ? |
Lay out two negative counters. You need to take away seven negatives, but there are only two.
Add five zero pairs (five positive and five negative). The value is still -2.
Now take away seven negatives. Five positive counters are left. The answer is 5.
Well done. One rule now handles every subtraction. Tomorrow you build a floor-size number line in the Numbers Lab.