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Explain the concept of composing and decomposing 10 for addition with examples.

Mathematics

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Answers

2 parts
a
17
b
11
12
13

Step-by-step solution

3 steps

Part a· 3 steps

To calculate 9+89 + 8 mentally

  1. Decompose one of the numbers to make 10 with the other.

    We can decompose 8 into 1 and 7.

    9+8=9+(1+7)9 + 8 = 9 + (1 + 7)
  2. Add 9 and 1 to make 10.

    (9+1)+7=10+7(9 + 1) + 7 = 10 + 7
  3. Add 10 and 7.

    10+7=1710 + 7 = \boxed{17}

Part b11

To use composition and decomposition of 10 for addition when the sum is more than 10

The strategy is to decompose one of the addends to compose a 10 with the other addend. Then, add the remaining part.

  • For 8+38 + 3: Decompose 3 into 2 and 1. Add 2 to 8 to make 10. Then add the remaining 1.
8+3=8+(2+1)=(8+2)+1=10+1=118 + 3 = 8 + (2 + 1) = (8 + 2) + 1 = 10 + 1 = \boxed{11}
  • For 4+84 + 8: Decompose 8 into 6 and 2. Add 6 to 4 to make 10. Then add the remaining 2.
4+8=4+(6+2)=(4+6)+2=10+2=124 + 8 = 4 + (6 + 2) = (4 + 6) + 2 = 10 + 2 = \boxed{12}
  • For 6+76 + 7: Decompose 7 into 4 and 3. Add 4 to 6 to make 10. Then add the remaining 3.
6+7=6+(4+3)=(6+4)+3=10+3=136 + 7 = 6 + (4 + 3) = (6 + 4) + 3 = 10 + 3 = \boxed{13}
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