SME
Grade 7 Math · Problem type
Adding with counters
Use this for “Show 3 + (−5) with counters.”
Diagram
3 + (−5) = −2
3 zero pairs make 0.
2 negative counters left: −2.
This is an example. Type your own values to start a new problem.
a
+
(
b
)
=
r
Formulas
r
=
a
+
b
(sum
=
first
number
+
second
number)
−2 = 3 + (−5)
Assumptions
•
A + counter is +1 and a − counter is −1.
•
A + and a − together make a zero pair: 0. The counters left over are the sum.
•
The sign of the sum is the sign of the counters left over.
Step-by-step
WE KNOW
a = 3 (first number), b = −5 (second number)
FIND
sum (r)
Step 1 · Find sum (r)
Use r = a + b (sum = first number + second number)
Pair
each
+
counter
with
a
−
counter;
each
pair
is
0.
The
counters
left
over
are
the
sum.
r
=
3
+
(−5)
r
=
−2
Check
Put the numbers back in. Both sides should match.
−2 = 3 + (−5) ✓
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Operations with positive and negative rational numbers
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Subtracting signed numbers
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Related lessons
Operations with positive and negative rational numbers
Main lesson
Subtracting signed numbers
Use this for “−3 − 8” and “How many feet higher is 1,640 ft than −212 ft?”
Multiplying and dividing signed numbers
Use this for “(−6)(−4)” and “54 ÷ (−9)”.
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.