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Solve the following addition problems using the regrouping method: a) 65 + 52, b) 76 + 63, c) 86 + 65

Mathematics

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Answers

3 parts
a

117\text{117}

b

139\text{139}

c

151\text{151}

Step-by-step solution

13 steps

Here are the solutions for the addition problems:

Part a· 4 steps

65+5265 + 52

  1. Separate into tens and ones.

    65=665 = 6 tens and 5 ones.
    52=552 = 5 tens and 2 ones.

  2. Add the ones and tens separately.

    Total ones: 5+2=75 + 2 = 7 ones.
    Total tens: 6+5=116 + 5 = 11 tens.

  3. Regroup the tens.

    Since there are 11 tens, we can regroup 10 tens into 1 hundred.
    11 tens =1= 1 hundred and 1 ten.

  4. Combine the regrouped values.

    We have 1 hundred, 1 ten, and 7 ones.

    100+10+7=117100 + 10 + 7 = 117

    The sum is 117\boxed{\text{117}}.

Part b

139\text{139}

76+6376 + 63

  1. Separate into tens and ones.

    76=776 = 7 tens and 6 ones.
    63=663 = 6 tens and 3 ones.

  2. Add the ones and tens separately.

    Total ones: 6+3=96 + 3 = 9 ones.
    Total tens: 7+6=137 + 6 = 13 tens.

  3. Regroup the tens.

    Since there are 13 tens, we can regroup 10 tens into 1 hundred.
    13 tens =1= 1 hundred and 3 tens.

  4. Combine the regrouped values.

    We have 1 hundred, 3 tens, and 9 ones.

    100+30+9=139100 + 30 + 9 = 139

    The sum is 139\boxed{\text{139}}.

Part c

151\text{151}

86+6586 + 65

  1. Separate into tens and ones.

    86=886 = 8 tens and 6 ones.
    65=665 = 6 tens and 5 ones.

  2. Add the ones and tens separately.

    Total ones: 6+5=116 + 5 = 11 ones.
    Total tens: 8+6=148 + 6 = 14 tens.

  3. Regroup the ones.

    Since there are 11 ones, we can regroup 10 ones into 1 ten.
    11 ones =1= 1 ten and 1 one.

  4. Regroup the tens.

    We started with 14 tens and added 1 ten from the regrouped ones, making a total of 14+1=1514 + 1 = 15 tens.
    Since there are 15 tens, we can regroup 10 tens into 1 hundred.
    15 tens =1= 1 hundred and 5 tens.

  5. Combine the regrouped values.

    We have 1 hundred, 5 tens, and 1 one.

    100+50+1=151100 + 50 + 1 = 151

    The sum is 151\boxed{\text{151}}.

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