SME
Grade 7 Math · The Number System
Operations with positive and negative rational numbers
Use this for “Find −3.45 + 5,” and other sums of positive and negative decimals and fractions.
Diagram
−3.45 + 5 = 1.55
Start at −3.45 and move 5 to the right.
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)
1.55 = −3.45 + 5
Assumptions
•
Start at the first number. A positive number jumps right; a negative one jumps left.
•
Adding a negative number is the same as subtracting its opposite.
•
A number and its opposite add to 0.
•
Decimals and fractions jump the same way as whole numbers.
Step-by-step
WE KNOW
a = −3.45 (first number), b = 5 (second number)
FIND
sum (r)
Step 1 · Find sum (r)
Use r = a + b (sum = first number + second number)
Start at the first number; a positive number jumps right, a negative one left.
r
=
−3.45
+
5
r
=
1.55
Check
Put the numbers back in. Both sides should match.
1.55 = −3.45 + 5 ✓
Topic check
See what you know: 5 questions on this topic
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More problem types
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?”
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.