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Maths · Grade 6 · Set A
Two Ways to Write the Same Thing
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A
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Goal: 15 min
Score/ 12
Remember: The same number can be written two ways. Test a number to be sure.

Breaking a product apart

1
The dots show 4 × (3 + 5). Count them as two groups: 4 × 3 + 4 × 5 = dots in all.
2
5(x + 8) = 5x +
3
3x + x + 3x = x
4
Which is the same as 7(2x + 9)?
14x + 914x + 639x + 1614x + 16
5
35 + 7x is equal to 7(5 + x).
TrueFalse
6
4(x + 3) is the same as 4x + 3.
TrueFalse

Factor and combine

7
6 + 18y = 6(1 + y)
8
Join each expression to the same thing written another way.
  1. 12(n + 4)
  2. 23n + n
  3. 32 + 3n + 4
  4. 45(2n)
  • A4n
  • B3n + 6
  • C10n
  • D2n + 8
9
The dots show two groups of 2 rows. Which expression is the total number of dots?
2(5 + 3)2 × 5 + 32 + 5 + 35 × 3 + 2
10
Test x = 4. What is 2(x + 6) when x = 4? Answer:
11
3 + x + 4 + 3x = + 4x

Stretch

12
Which expression is NOT equal to 12x + 18?
6(2x + 3)3(4x + 6)12(x + 18)2(6x + 9)
13
Write an expression that is equal to 3(x + 2). Show how you know.
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Answer key · Set A
Two Ways to Write the Same Thing
132 4 × 3 = 12 and 4 × 5 = 20. 12 + 20 = 32, the same as 4 × 8.
240 Multiply the 5 by each part inside: 5 × x = 5x and 5 × 8 = 40.
37 3x, x (which is 1x) and 3x: 3 + 1 + 3 = 7.
414x + 63 7 × 2x = 14x and 7 × 9 = 63. Multiply both parts inside the bracket.
5True 7 × 5 = 35 and 7 × x = 7x, so 7(5 + x) = 35 + 7x. Testing numbers agrees.
6False The 4 multiplies both parts: 4(x + 3) = 4x + 12. The table shows the two writings give different numbers.
73 6 × 3y = 18y, so 18y = 6 × 3y.
81-D, 2-A, 3-B, 4-C Break the bracket apart, add the n terms, and add the plain numbers.
92(5 + 3) There are 2 rows, and each row has 5 + 3 dots: 2(5 + 3) = 16.
1020 4 + 6 = 10, and 2 × 10 = 20.
117 Add the plain numbers: 3 + 4 = 7. Add the x terms: x + 3x = 4x.
1212(x + 18) 12(x + 18) = 12x + 216. The other three all give 12x + 18.
13Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.