Egypt Primary 6 Mathematics, Week 7: Rewriting an expression in an equivalent form

Real-life and equivalent expressions

Week 7 · Expressions in real life and equivalent expressions · 3 lessons

Rewriting an expression in an equivalent form

Discover Mathematics P6: Term 1, Unit 3, Lessons 6–7

GoalUse the distributive property and like terms to write an equivalent expression.

New words

expand · multiply every term inside brackets, like 2(x + 3) = 2x + 6combine like terms · add the coefficients of terms with the same lettersimplify · write an expression with fewer terms

Explanation

We can rewrite an expression without changing its value. Tool 1, the distributive property: the number outside the brackets multiplies every term inside, so 3(x + 4) = 3x + 12. A picture of 3 rows with x and 4 shows it. Tool 2, combining like terms: add the coefficients, so 4x + 2x + 5 = 6x + 5. It works backwards too: 6x + 12 = 6(x + 2). Watch for two traps: x + x = 2x (not x²), and 2(x + 3) = 2x + 6 (not 2x + 3, because the 2 multiplies the 3 as well).

Right	Wrong
x + x = 2x	x + x = x²
2(x + 3) = 2x + 6	2(x + 3) = 2x + 3

Worked examples

3(x + 4) is 3 rows, each with x and 4. All together there are 3 x’s and 3 fours: 3x + 12.

x	3	10
4x + 2x + 5	23	65
6x + 5	23	65

Combine like terms: 4x + 2x + 5 = 6x + 5. Check with x = 3: 12 + 6 + 5 = 23 and 18 + 5 = 23.

x	5	1
6x + 12	42	18
6(x + 2)	42	18

Working backwards: 6x + 12 = 6(x + 2), because 6 goes into both terms. Check with x = 5: 30 + 12 = 42 and 6 × 7 = 42.

Class activity

Rewrite it. A grown-up chooses an expression such as 5(n + 2) or 3a + 4a + 1. Rewrite it in an equivalent form, then prove your answer by testing two numbers. Try to find a number where a wrong rewrite fails.

Practice

Expand 5(n + 2).

Simplify 3a + 4a.

Simplify 8x + 3 + 2x.

Are 4(x + 1) and 4x + 1 equivalent? Test x = 2.

Write 9y + 18 as 9 times a sum.