Grade 7 Mathematics
Rational numbers include positive numbers, negative numbers, zero, fractions, and decimals. You can add, subtract, multiply, and divide them using special rules!
Key insight: Negative numbers follow patterns. Once you learn the rules, you can solve ANY problem!
Same Signs: Add the numbers, keep the sign
(-5) + (-3) = -8 | 5 + 3 = 8
Different Signs: Subtract the numbers, keep sign of larger absolute value
(-7) + 4 = -3 | 7 + (-4) = 3
Think: Adding positives moves RIGHT, adding negatives moves LEFT
Change to ADDING THE OPPOSITE!
5 - (-3) = 5 + 3 = 8
-4 - 7 = -4 + (-7) = -11
-6 - (-2) = -6 + 2 = -4
Tip: "Keep, Change, Change" - Keep the first number, Change subtraction to addition, Change the sign of the second number.
| Signs | Result | Multiply Example | Divide Example |
|---|---|---|---|
| Positive x Positive | Positive | 4 x 5 = 20 | 20 / 5 = 4 |
| Negative x Negative | Positive | (-4) x (-5) = 20 | (-20) / (-5) = 4 |
| Positive x Negative | Negative | 4 x (-5) = -20 | 20 / (-5) = -4 |
| Negative x Positive | Negative | (-4) x 5 = -20 | (-20) / 5 = -4 |
Same signs = POSITIVE | Different signs = NEGATIVE
WRONG: (-3) + (-5) = 8 because "two negatives make a positive"
RIGHT: The "two negatives = positive" rule is ONLY for multiplying and dividing! For adding: (-3) + (-5) = -8 (adding two debts makes more debt!)
The sign rules are the same! Just apply normal fraction/decimal operations.
Fractions:
(-1/2) + (-1/4) = (-2/4) + (-1/4) = -3/4
(-2/3) x (3/5) = -6/15 = -2/5
Decimals:
(-3.5) + 1.2 = -2.3
(-2.4) x (-1.5) = 3.6
1. Solve these addition problems:
a) (-9) + (-4) =
b) (-12) + 7 =
c) 8 + (-15) =
2. Solve these subtraction problems (Remember: Keep, Change, Change!):
a) 6 - (-4) = 6 + ___ =
b) (-5) - 8 = (-5) + ___ =
c) (-7) - (-3) = (-7) + ___ =
3. Solve these multiplication and division problems:
a) (-6) x 5 =
b) (-8) x (-4) =
c) (-36) / 9 =
d) (-42) / (-7) =
4. Solve with fractions and decimals:
a) (-1/2) + 3/4 =
b) (-2/3) x (-3/4) =
c) (-4.5) + 2.3 =
d) (-3.2) x 1.5 =