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Maths · Grade 6 · Set B
Same Number, Two Ways
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B
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Goal: 15 min
Score/ 13
Remember: The same number can be written two ways. Test a number to be sure.

Breaking a product apart

1
The dots show 3 × (4 + 2). Count them as two groups: 3 × 4 + 3 × 2 = dots in all.
2
6(x + 5) = 6x +
3
2x + 5x + x = x
4
Which is the same as 4(3x + 8)?
12x + 87x + 1212x + 3212x + 12
5
Each bar is x + 4 long. There are 3 bars. Which expression is the total length?
3x + 43(x + 4)x + 12x + 4 + 3
6
9 + 3x is equal to 3(3 + x).
TrueFalse
7
x + x + x is the same as x + 3.
TrueFalse

Factor and combine

8
8 + 12y = 4(2 + y)
9
Join each expression to the same thing written another way.
  1. 13(n + 5)
  2. 24n + 2n
  3. 31 + 6n + 3
  4. 42(4n)
  • A3n + 15
  • B6n
  • C6n + 4
  • D8n
10
The dots show two groups of 3 rows. Which expression is the total number of dots?
3 × 4 + 64 × 6 + 33 + 4 + 63(4 + 6)
11
Test x = 5. What is 3(x + 4) when x = 5? Answer:
12
2 + x + 5 + 2x = + 3x

Stretch

13
Which expression is NOT equal to 8x + 24?
8(x + 24)8(x + 3)4(2x + 6)2(4x + 12)
14
Write an expression that is equal to 2(x + 6). Show how you know.
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Answer key · Set B
Same Number, Two Ways
118 3 × 4 = 12 and 3 × 2 = 6. 12 + 6 = 18, the same as 3 × 6.
230 Multiply the 6 by each part inside: 6 × x = 6x and 6 × 5 = 30.
38 2x, 5x and x (which is 1x): 2 + 5 + 1 = 8.
412x + 32 4 × 3x = 12x and 4 × 8 = 32. Multiply both parts inside the bracket.
53(x + 4) Each bar is x + 4 long, and there are 3 of them: 3(x + 4). The 3 multiplies both x and 4.
6True 3 × 3 = 9 and 3 × x = 3x, so 3(3 + x) = 9 + 3x. Testing numbers agrees.
7False x + x + x is 3 groups of x, which is 3x. Adding 3 to x is a different thing, and the table shows different numbers.
83 4 × 3y = 12y, so 12y = 4 × 3y. And 4 × 2 = 8.
91-A, 2-B, 3-C, 4-D Break the bracket apart, add the n terms, and add the plain numbers.
103(4 + 6) There are 3 rows, and each row has 4 + 6 dots: 3(4 + 6) = 30.
1127 5 + 4 = 9, and 3 × 9 = 27.
127 Add the plain numbers: 2 + 5 = 7. Add the x terms: x + 2x = 3x.
138(x + 24) 8(x + 24) = 8x + 192. The other three all give 8x + 24.
14Your own words: a grown-up reads it.
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