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Negative numbers in real life

Temperature, height, money; distance between two numbers · Foundations · 24 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Write it as a sum
  2. Work it out
  3. Check

The steps for It is -4°C. It warms up 9 degrees. What is the temperature now?. Every solution names its steps, so you always know what comes next.

Worked examples

It is -4°C. It warms up 9 degrees. What is the temperature now? Easy

The question

Question: It is −4°C.

It warms up 9 degrees.

What is the temperature now?

1 Write it as a sum

We start at −4.

Warms up means up: add 9.

−4 + 9

Below zero is negative.

−4°C: below zero
warms up 9 → + 9

2 Work it out

Start at −4.

Go up 9.

We pass 0.

Careful!

We start at −4, not at 4.

Keep the minus sign.

Careful: not 4 + 9 = 13 ✗

We land on 5°C.

= 5°C

So the answer is 5°C: 5 degrees above zero.

3 Check

Let's check: go back.

5 minus 9 is −4, where we started.

So the answer is right!

5 − 9 = −4

Let's look back.

First: write it as a sum.

Then: work it out.

Last: check.

Answer
= 5°C

▶ Watch it solved

It is -2°C. It gets 5 degrees colder. What is the temperature now? Medium

The question

Question: It is −2°C.

It gets 5 degrees colder.

What is the temperature now?

1 Write it as a sum

We start at −2.

Colder means down: take away 5.

−2 − 5

Below zero is negative.

−2°C: below zero
colder 5 → − 5

2 Work it out

Start at −2.

Go down 5.

Careful!

Colder from below zero goes further down.

The number gets more negative.

Careful: not −2 − 5 = 3 ✗

We land on −7°C.

= −7°C

So the answer is −7°C: 7 degrees below zero.

3 Check

Let's check: go back.

−7 plus 5 is −2, where we started.

So the answer is right!

−7 + 5 = −2

Let's look back.

First: write it as a sum.

Then: work it out.

Last: check.

Answer
= −7°C

▶ Watch it solved

The high was 4°C and the low was -10°C. What is the difference? Harder

The question

Question: what is the difference between 4°C and −10°C?

difference between 4°C and −10°C

The difference is how far apart the two numbers are.

It is never negative.

difference = how far apart

1 Mark both numbers

On the number line: −10 and 4.

We go from the smaller one, −10, up to the bigger one, 4.

2 Bigger minus smaller

The bigger one minus the smaller one: 4 minus −10.

= 4 − (−10)

Taking away a negative is the same as adding.

Minus minus 10 is plus 10.

= 4 + 10

Careful!

Do not drop the minus sign of −10.

−10 is below zero, so it is further away.

Careful: not 4 − 10 = -6 ✗

4 plus 10 is 14°C.

= 14°C

So the difference is 14 degrees.

3 Check

Let's check in two parts.

From −10 up to 0 is 10.

From 0 up to 4 is 4.

10 plus 4 is 14.

So the answer is right!

−10 to 0: 10, 0 to 4: 4, 10 + 4 = 14

Let's look back.

First: mark both numbers.

Then: bigger minus smaller.

Last: check.

Answer
= 14°C

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. It is -4°C. It warms up 9 degrees. What is the temperature now?
    Answer
    = 5°C
  2. It is 3°C. It gets 8 degrees colder. What is the temperature now?
    Answer
    = −5°C
  3. It is -6°C. It warms up 4 degrees. What is the temperature now?
    Answer
    = −2°C
  4. A diver is at -12 m. She goes up 5 m. Where is she now?
    Answer
    = −7 m
  5. A bird is at 6 m. It dives 9 m. Where is it now?
    Answer
    = −3 m
  6. Ana has $20 and spends $35. What is her balance?
    Answer
    = −$15
  7. distance between -3 and 5
    Answer
    = 8
  8. distance between -6 and 2
    Answer
    = 8
  9. distance between 0 and -7
    Answer
    = 7

Medium

  1. It is -2°C. It gets 5 degrees colder. What is the temperature now?
    Answer
    = −7°C
  2. It is -11°F. It rises 15 degrees. What is the temperature now?
    Answer
    = 4°F
  3. The temperature is 5°C. It drops 12 degrees. What is the temperature now?
    Answer
    = −7°C
  4. A submarine is at -40 m. It sinks 25 m. Where is it now?
    Answer
    = −65 m
  5. Leo owes $15 and earns $40. How much does he have now?
    Answer
    = $25
  6. Mia owes $8 and spends $12. What is her balance?
    Answer
    = −$20
  7. difference between 6°C and -3°C
    Answer
    = 9°C
  8. difference between -2°F and 9°F
    Answer
    = 11°F
  9. distance between -9 and -4
    Answer
    = 5

Harder

  1. The high was 4°C and the low was -10°C. What is the difference?
    Answer
    = 14°C
  2. A diver is at -18 m. She swims up 18 m. Where is she now?
    Answer
    = 0 m
  3. Sam owes $25 and is paid $18. How much does he have now?
    Answer
    = −$7
  4. distance between -14 and 11
    Answer
    = 25
  5. It is -15°C. It warms up 7 degrees. What is the temperature now?
    Answer
    = −8°C
  6. difference between -12°C and -5°C
    Answer
    = 7°C