Substituting integers into expressions
Variables, coefficients, like terms, substitution, formulae and word formulae. Numbers below zero: comparing, on the number line, and calculating with signs. Read one part at a time and tap “I know this”. Then test yourself in the quiz.
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The language of algebra
| Term | Meaning | In 3x + 5 |
|---|---|---|
| variable | a letter for an unknown number | x |
| coefficient | the number in front of the variable | 3 |
| constant | a number without a letter | 5 |
| term | parts separated by + or − | 3x and 5 |
- 3x means 3 × x.
- Like terms have the same letter and can be added: 4a + 2a = 6a. But 4a + 2b stays as it is.
Substitution and formulae
Substitute the number for the letter: if x = 4, then 3x + 5 = 3 × 4 + 5 = 17. With integers: x = −2 → 3 × (−2) + 5 = −1.
A formula is a rule with letters: perimeter of a square P = 4s. If s = 6 cm, P = 24 cm.
A word formula gives the rule in words: cost of a taxi trip = R15 plus R8 for every km. With letters: C = 15 + 8k. For 12 km: C = 15 + 8 × 12 = R111.
A number sentence from words: “I think of a number, multiply it by 4 and add 3; the answer is 31.” → 4 × □ + 3 = 31, so □ = 7 (31 − 3 = 28; 28 ÷ 4 = 7).
Positive and negative
Integers are the numbers …, −3, −2, −1, 0, 1, 2, 3, …: the whole numbers (0, 1, 2, 3, …) and their negatives. Negative numbers are less than 0, like temperatures below freezing.
- On a number line left is always smaller: −7 < −3.
- The opposite of 5 is −5; their sum is 0.
Calculating with integers
| Rule | Example |
|---|---|
| plus a negative = minus | 5 + (−3) = 2 |
| minus a negative = plus | 5 − (−3) = 8 |
| same signs × or ÷ → positive | (−4) × (−3) = 12 |
| different signs × or ÷ → negative | (−4) × 3 = −12 |
- On the number line: adding a positive number moves you right; subtracting a positive number moves you left.
- −3 + (−4) = −7: start at −3 and move 4 to the left.
- −2 − 5 = −7: start at −2 and move 5 to the left.
- −6 + 9 = 3: start at −6 and move 9 to the right.
Think of money: −3 is a debt of R3. If someone takes your debt away, you are better off: −(−3) = +3.
Remember this and test yourself
- A variable is a letter for an unknown.
- Negative numbers are less than 0.
- 3x = 3 × x; 3 is the coefficient.
- Left on the number line is smaller.
- Only like terms can be added.
- Minus a negative = plus.
Write these points in your book. Read them again the night before the test.
Apples with apples: 4a + 2a = 6a, but apples and bananas (a and b) stay apart.
Important words
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Match column A to column B
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Now the real quiz!
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Take the quiz: Substituting integers into expressions- Let your child work the examples on paper and explain them to you.
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Follows CAPS for Grade 7 Mathematics. Always check your teacher’s notes and textbook too.