3.4 Self-Check

The more you practice, the more your skills improve. Below are some exercises that will help you continue to develop your ability and check to make sure you understand the concepts discussed in this unit. Be sure to write your work out in your math notebook so that you can refer to it later if necessary.

Exercise symbolExercise 1: Adding it Up

(a) sum with, 3 , summands 24.08 plus 68.2 plus 105.59

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Answer

(a) multiline equation line 1 separator 21 times four full stop times 01 times eight line 2 six eight .2 line 3 separator plus plus 105.59 low line line 4 197.87

Estimate:equation sequence sum with, 3 , summands 25 plus 70 plus 105 equals sum with, 3 , summands 25 plus 105 plus 70 equals 200; this is close to the answer you calculated.

(b) 198.22 plus 32.8

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Answer

(b) multiline equation line 1 11 times 91 times 81 times .2 two line 2 separator plus 32.8 low line line 3 two 31 .0 two

Estimate: 200 plus 33 equals 233; this is close to the answer you calculated.

(c) sum with, 3 , summands 35.4 plus 292.56 plus 29.35

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Answer

(c) sum with, 3 , summands 35.4 plus 292.56 plus 29.35 equals 357.31

Estimate: 35 + 300 + 30 = 365; this is close to the answer you calculated.

(d) sum with, 3 , summands 1027 plus 2.95 plus 329.6

Solution symbol

Answer

(d) sum with, 3 , summands 1027 plus 2.95 plus 329.6 equals 1359.55

Estimate: 1030 + 3 + 330 = 1363: this is close to the answer you calculated.

Exercise symbolExercise 2: Subtracting

For each subtraction problem, calculate the difference on paper, then use an estimate to check if your answer is reasonable. Check your work by using addition.

183.72 minus 65.68

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Answer

(a) multiline equation line 1 one times 87 times 31 full stop 76 times 21 line 2 full stop separator minus 65 full stop separator 68 low line line 3 one one eight full stop zero four

Estimate:185 minus 65 equals 120; this is close to the answer you calculated.

Check using addition: 118.04 plus 65.68 equals 183.72

(b) 245.06 minus 20.2

Solution symbol

Answer

(b) multiline equation line 1 24 times 54 full stop 01 six line 2 full stop separator minus 20 full stop separator two low line line 3 two two four full stop eight six

Estimate: 250 minus 20 equals 230; this is close to the answer you calculated.

Check using addition: 20.2 plus 224.86 equals 245.06.

(c) 305.6 minus 90.07

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Answer

(c) 305.6 minus 90.07 equals 215.53

Estimate: 300 minus 90 equals 210; this is close to the answer you calculated.

Check using addition: 90.07 plus 215.53 equals 305.6.

(d) 7230 minus 321.6

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Answer

(d) 7230 minus 321.6 equals 6908.4

Estimate: 7200 minus 300 equals 6900 semicolon this is close to the answer you calculated.

Check using addition: 321.6 plus 6908.4 equals 7230.

Exercise symbolExercise 3: Multiplying

Carry out these calculations and then use an estimate to check whether your answer is reasonable.

(a) 422 times normal x times 38

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Answer

(a) multiline equation line 1 422 line 2 separator multiplication 38 low line line 3 3376 line 4 plus plus 12660 low line line 5 16036

Estimate:400 times normal x times 40 equals 16000; this is close to the answer you calculated.

Carry out these calculations and then use an estimate to check whether your answer is reasonable.

(b) 632 times normal x times 29

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Answer

(b) multiline equation line 1 623 line 2 separator multiplication 29 low line line 3 5688 line 4 plus plus plus 12640 low line line 5 18328

Estimate:600 times normal x times 30 equals 18000; this is close to the answer you calculated.

Carry out these calculations and then use an estimate to check whether your answer is reasonable.

(c) 584 times normal x times 72

Solution symbol

Answer

(c) multiline equation line 1 584 line 2 separator multiplication 72 low line line 3 1168 line 4 plus plus plus 40880 low line line 5 42048

Estimate:600 times normal x times 70 equals 42000; this is close to the answer you calculated.

Exercise symbolExercise 4: Dividing

Carry out these calculations and then use an estimate to check whether your answer is reasonable.

(a) 267 division 12

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Answer

(a) equation sequence 267 equals 20 times normal x times 12 plus 27 equals 22 times normal x times 12 plus three

Thus, equation left hand side 267 division 12 equals right hand side 22 times cap r times 13.

Estimate: 250 division 10 equals 25; this is close to our answer you calculated.

(b) 265 division 25

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Answer

(b) 265 equals 25 times normal x times 10 plus 15

Thus, equation left hand side 265 division 25 equals right hand side 10 times cap r times 15.

Estimate:250 division 25 equals 10; this is close to the answer you calculated.

(c) 299 division 13

Solution symbol

Answer

(c) equation sequence 299 equals 13 times normal x times 20 plus 39 equals left parenthesis 13 x 20 right parenthesis plus left parenthesis three x 13 right parenthesis equals left parenthesis 13 x 20 right parenthesis equals 13 x 23 right parenthesis

Thus, 299 division 13 equals 23.

Estimate:300 division 15 equals 20; this is close to the answer you calculated.

3.3.12 Multiplication and Division Puzzle

3.5 Quiz Time