Equivalent Expressions and Number Sequences
Primary 6 · Mathematics
Equivalent Expressions and Number Sequences
Lesson 1 of 5
15 min
Let's begin
Mugisha goes to the school shop to buy exercise books at 300 Frw each, and one pen for 500 Frw. He has not decided yet how many books to buy. Can we still write down what he will pay? Yes: we let a letter stand for the number of books. That letter turns a sentence into a short piece of algebra.
A letter such as n, x or a can stand for a number we do not know yet, or a number that can change. It is called a variable. An algebraic expression is made of numbers, letters and operation signs, but has no "=" sign. For example: n + 5, 3a, 2x − 1, 4(y + 2).
Mugisha's cost for n books and one pen is 300n + 500 Frw.
| Words | Expression |
|---|---|
| 5 more than a number x | x + 5 |
| 3 times a number x | 3x |
| 8 less than m | m − 8 |
| half of k | k ÷ 2 |
| twice the sum of a and 4 | 2(a + 4) |
In the expression 4x + 7 there are two terms, 4x and 7. The number in front of the letter, 4, is the coefficient of x. A term with no letter, like 7, is called a constant.
To evaluate an expression, put the number in place of the letter and work it out.
Worked example 1
Find 3x + 4 when x = 5.
3 × 5 + 4 = 15 + 4 = 19.
Worked example 2
If a = 2 and b = 7, find 4a + b and 2(a + b).
4a + b = 4 × 2 + 7 = 8 + 7 = 15.
2(a + b) = 2 × (2 + 7) = 2 × 9 = 18.
Worked example 3
Mugisha buys 6 books. Cost = 300 × 6 + 500 = 1 800 + 500 = 2 300 Frw.
When an expression is set equal to a number, you get an equation, and you can find the unknown. Do the same thing to both sides to keep them balanced.
x + 7 = 15. Take 7 from both sides: x = 15 − 7 = 8.
3(x + 1) = 9. Divide both sides by 3: x + 1 = 3. Take 1 from both sides: x = 2.
5x + 5 = x + 25. Take x from both sides: 4x + 5 = 25. Take 5 from both sides: 4x = 20. Divide by 4: x = 5.
Tip
An expression is like a machine with an empty slot. Put a number into the slot for the letter, and the machine gives you an answer.
Answers
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Quick check
Match each sentence to its expression.
Tap one on the left, then its partner on the right.
