Negative numbers Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Negative numbers questions. See exactly how to solve problems on adding directed numbers, number line, adding a negative, adding two negatives.

adding directed numbersnumber lineadding a negativeadding two negativesadding to a negativecrossing zero
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Work out −3+5-3 + 5.

Worked solution

  1. Start on the number line

    begin at −3\text{begin at } -3

    Start at −3. Adding a positive number means moving to the right.

  2. Move 5 to the right

    −3→+52-3\xrightarrow{+5}2

    Count 5 steps right: −3, −2, −1, 0, 1, 2.

  3. State the answer

    −3+5=2-3+5=2

    So the answer is 2.

Answer
22
Question 2
1 markeasy
Work out 4+(−7)4 + (-7).

Worked solution

  1. Adding a negative means subtracting

    4+(−7)=4−74+(-7)=4-7

    Adding −7 is the same as subtracting 7, so we move left from 4.

  2. Count 7 to the left

    4→−7−34\xrightarrow{-7}-3

    From 4 go left 7 steps, crossing zero: 4,3,2,1,0,−1,−2,−3.

  3. State the answer

    4+(−7)=−34+(-7)=-3

    So the answer is −3.

Answer
−3-3
Question 3
1 markeasy
Work out −2+(−6)-2 + (-6).

Worked solution

  1. Both numbers are negative

    −2+(−6)=−2−6-2+(-6)=-2-6

    Adding −6 is subtracting 6, so we go further into the negatives.

  2. Combine the amounts

    2+6=82+6=8

    The two negative amounts add to 8, and the answer stays negative.

  3. State the answer

    −2+(−6)=−8-2+(-6)=-8

    So the answer is −8.

Answer
−8-8
Question 4
1 markeasy
Work out −7+10-7 + 10.

Worked solution

  1. Adding a positive moves right

    begin at −7\text{begin at } -7

    Start at −7. Adding a positive means moving to the right.

  2. Move 10 to the right

    −7→+103-7\xrightarrow{+10}3

    From −7, 7 steps reach 0, then 3 more reach 3.

  3. State the answer

    −7+10=3-7+10=3

    So the answer is 3.

Answer
33
Question 5
1 markeasy
Work out −9+(−1)-9 + (-1).

Worked solution

  1. Adding a negative means subtracting

    −9+(−1)=−9−1-9+(-1)=-9-1

    Adding −1 is subtracting 1, going further negative.

  2. Combine the amounts

    9+1=109+1=10

    The negatives add to 10, staying negative.

  3. State the answer

    −9+(−1)=−10-9+(-1)=-10

    So the answer is −10.

Answer
−10-10

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