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Maths · Grade 6 · Set C
Same Number, Two Ways: More
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C
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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 6 × (5 + 3). Count them as two groups: 6 × 5 + 6 × 3 = dots in all.
2
9(x + 7) = 9x +
3
4n + 6n + n = n
4
Which is the same as 11(3n + 4)?
33n + 4433n + 414n + 153n + 44
5
Which is the same as 5(2n − 3)?
10n − 310n − 157n − 152n − 15

Factor and combine

6
14 + 21y = 7(2 + y)
7
24n + 16 = 8(n + 2)
8
6x + 9 is equal to 3(2x + 3).
TrueFalse
9
2(x + 5) + 3x is equal to 5x + 5.
TrueFalse
10
Join each expression to the same thing written another way.
  1. 15(a + 2) + a
  2. 23a + 2(a + 1)
  3. 34(a + 1) − 4
  4. 42a + 7 + 3a + 3
  • A5a + 10
  • B6a + 10
  • C5a + 2
  • D4a

Use it, then explain it

11
Test x = 6. What is 4(x + 3) + 2x when x = 6? Answer:
12
A garden is 4 meters wide and x + 5 meters long. Which expression is its area?
x + 204x + 54(x + 5)4 + x + 5
13
Which expression is NOT equal to 18x + 12?
2(9x + 6)3(6x + 4)6(3x + 2)6(3x + 12)
14
Mia says 4(x + 2) and 4x + 2 are the same. Write how you could show her she is wrong.
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Answer key · Set C
Same Number, Two Ways: More
148 6 × 5 = 30 and 6 × 3 = 18. 30 + 18 = 48, the same as 6 × 8.
263 Multiply the 9 by each part inside: 9 × x = 9x and 9 × 7 = 63.
311 4n, 6n and n (which is 1n): 4 + 6 + 1 = 11.
433n + 44 11 × 3n = 33n and 11 × 4 = 44. Multiply both parts inside the bracket.
510n − 15 5 × 2n = 10n and 5 × 3 = 15. Multiply both parts inside the bracket, and keep the minus.
63 7 × 3y = 21y, so 21y = 7 × 3y. And 7 × 2 = 14.
73 8 × 3n = 24n, so 24n = 8 × 3n. And 8 × 2 = 16.
8True 3 × 2x = 6x and 3 × 3 = 9, so 3(2x + 3) = 6x + 9. Testing numbers agrees.
9False 2(x + 5) = 2x + 10. Then 2x + 10 + 3x = 5x + 10, not 5x + 5. The table shows different numbers.
101-B, 2-C, 3-D, 4-A Break the bracket apart first, then add the a terms and the plain numbers.
1148 6 + 3 = 9 and 4 × 9 = 36. Then 2 × 6 = 12. 36 + 12 = 48.
124(x + 5) Area is width times length: 4 × (x + 5), written 4(x + 5). The 4 multiplies both parts.
136(3x + 12) 6(3x + 12) = 18x + 72. The other three all give 18x + 12.
14Your own words: a grown-up reads it.
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