11. With different signs, subtract the sizes; don't add them. 23 and 12 subtracted, with the sign of the one further from 0: 11.

(−13) + 27 + (−8): the negatives make −□ together; adding 27 gives □. Fill in each blank

21, 6. Gather the negatives first: −13 and −8 make −21. Then 27 + (−21) = 6.

(−1/2) + 2/5 = □ Answer in simplest form

−1/10. Common denominator first, then subtract as the signs differ, keeping the sign of the one further from 0: −1/10, in lowest terms.

Directed numbers · Ages 12–13

Adding directed numbers

Same signs: add. Different: subtract, take the further one's sign.

How to do it

Method

Same signs: add. Different: subtract, take the further one's sign

(−7) + 3 = −4

Another way

Walk the number line

From −7, 3 steps right, to −4

In full

Same signs: add the sizes and keep the sign, (−3) + (−5) = −8. Different signs: subtract the sizes and take the sign of the number further from 0, (−7) + 3 = −4. Or walk along the number line: start at the first number, go right to add a positive, left to add a negative; (−7) + 3 starts at −7 and goes 3 right, reaching −4. Both ways always agree. With several numbers, gather the negatives first, then add the positives.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
(−12) + 23 =
Show the answer and working
Answer: 11
With different signs, subtract the sizes; don't add them. 23 and 12 subtracted, with the sign of the one further from 0: 11.
Example 2
(−13) + 27 + (−8): the negatives make − together; adding 27 gives .
Fill in each blank
Show the answer and working
Answer: 21, 6
Gather the negatives first: −13 and −8 make −21. Then 27 + (−21) = 6.
Example 3
(−12) + 25 =
Answer in simplest form
Show the answer and working
Answer: −110
Common denominator first, then subtract as the signs differ, keeping the sign of the one further from 0: −110, in lowest terms.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.14 + (−10) =
Answer:
2.(−2) + 55 =
Answer:
3.(−9) + 16 + (−15): the negatives make − together; adding 16 gives .
Fill in each blank
Answer:
4.(−34) + 56 =
Answer in simplest form
Answer:
5.(+2.5) + (+5.9) =
Answer:

All the answers

1. 4
2. 53
3. 24, −8
4. 112
5. 8.4

Free worksheet: Adding directed numbersWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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