SME
Grade 7 Math · Problem type
Multiplying and dividing signed numbers
Use this for “(−6)(−4)” and “54 ÷ (−9)”.
Diagram
Different signs: the answer is negative.
This is an example. Type your own values to start a new problem.
a
First number
example
b
Second number
example
r
Product
worked out (not typed)
d
Quotient
worked out (not typed)
Formulas
r
=
a
×
b
(product
=
first
number
×
second
number)
−12 = −3 × 4
d
=
a
÷
b
(quotient
=
first
number
÷
second
number)
−
3
4
=
−3
÷
4
Assumptions
•
Multiply or divide the sizes, then find the sign from the table.
•
Same signs give a positive answer; different signs give a negative one.
•
Dividing by a number is multiplying by its reciprocal, so the sign rule is the same.
Step-by-step
WE KNOW
a = −3 (first number), b = 4 (second number)
FIND
product (r), quotient (d)
Step 1 · Find product (r)
Use r = a × b (product = first number × second number)
Multiply the sizes; same signs give a positive answer, different signs a negative one.
r
=
−3
×
4
r
=
−12
Step 2 · Find quotient (d)
Use d = a ÷ b (quotient = first number ÷ second number)
Divide the sizes; the sign rule is the same as for multiplying.
d
=
−
3
4
d
=
−
3
4
Check
Put the numbers back in. Both sides should match.
−12 = −3 × 4 ✓
−
3
4
=
−3
÷
4
✓
Topic check
See what you know: 5 questions on this topic
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Related lessons
Operations with positive and negative rational numbers
Main lesson
Adding with counters
Use this for “Show 3 + (−5) with counters.”
Subtracting signed numbers
Use this for “−3 − 8” and “How many feet higher is 1,640 ft than −212 ft?”
Fractions as decimals
Use this for “Write 3/8 as a decimal” or “Which decimal is closest to 13/16?”
The sign of the answer
Use this for “Is (−5) × (−7) positive or negative?” before working it out.