Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 4, Problem 13A
To determine

(a)

Multiply the mixed fractions and reduce to lowest term.

Expert Solution
Check Mark

Answer to Problem 13A

The multiplication of fractions is 1012.

Explanation of Solution

Given:

The number is 123×6310.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number 123 is 53.

The improper fraction of 6310 is 6310.

Multiply 53×6310 as follows:

Multiply the numerators 5 and 63.

  =5×63=315

Multiply the denominators 3 and 10.

  =3×10=30

Therefore, the multiplication of fractions is as follows:

  =31530

The greatest common factor of 315 and 30 is 15.

Divide numerator and denominator of fraction by 15.

  =315÷1530÷15=212

The mixed conversion of 212 is as follows:

  210 21 2 _ 01

The mixed conversion of 212 is 1012.

Thus, the multiplication of fractions is 1012.

Conclusion:

The multiplication of fractions is 1012.

To determine

(b)

Multiply the mixed fractions and reduce to lowest term.

Expert Solution
Check Mark

Answer to Problem 13A

The multiplication of fractions is 254364.

Explanation of Solution

Given:

The number is 3516×734.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number 3516 is 5316.

The improper fraction of 734 is 314.

Multiply 5316×314 as follows:

Multiply the numerators 53 and 31.

  =53×31=1643

Multiply the denominators 16 and 4.

  =16×4=64

Therefore, the multiplication of fractions is as follows:

  =164364

The mixed conversion of 164364 is as follows:

  64 25 1643 128 _

0363 0320 _

43

The mixed conversion of 164364 is 254364.

Thus, the multiplication of fractions is 254364.

Conclusion:

The multiplication of fractions is 254364.

To determine

(c)

Multiply the mixed fractions and reduce to lowest term.

Expert Solution
Check Mark

Answer to Problem 13A

The multiplication of fractions is 11916.

Explanation of Solution

Given:

The number is 458×212.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number 458 is 378.

The improper fraction of 212 is 52.

Multiply 378×52 as follows:

Multiply the numerators 37 and 5.

  =37×5=185

Multiply the denominators 8 and 2.

  =8×2=16

Therefore, the multiplication of fractions is as follows:

  =18516

The mixed conversion of 18516 is as follows:

  1611 185 16 _ 025 16 _ 9

The mixed conversion of 18516 is 11916.

Thus, the multiplication of fractions is 11916.

Conclusion:

The multiplication of fractions is 11916.

To determine

(d)

Multiply the mixed fractions and reduce to lowest term.

Expert Solution
Check Mark

Answer to Problem 13A

The multiplication of fractions is 61332.

Explanation of Solution

Given:

The number is 123×1014×38.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number 123 is 53.

The improper fraction of 1014 is 414.

The third is already in improper fraction that is 38.

Multiply 53×414×38 as follows:

Multiply the numerators 5, 41 and 3.

  =5×41×3=615

Multiply the denominators 3, 4 and 8.

  =3×4×8=96

Therefore, the multiplication of fractions is as follows:

  =61596

The greatest common factor of 615 and 96 is 3.

Divide numerator and denominator of fraction by 3.

  =615÷396÷3=20532

The mixed conversion of 20532 is as follows:

  326 205 192 _ 013

The mixed conversion of 20532 is 61332.

Thus, the multiplication of fractions is 61332.

Conclusion:

The multiplication of fractions is 61332.

To determine

(e)

Multiply the mixed fractions and reduce to lowest term.

Expert Solution
Check Mark

Answer to Problem 13A

The multiplication of fractions is 201256.

Explanation of Solution

Given:

The number is 2332×3×18.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number 2332 is 6732.

The second number is 3.

The third is already in improper fraction that is 18.

Multiply 6732×3×18 as follows:

Multiply the numerators 67, 3 and 1.

  =67×3×1=201

Multiply the denominators 32 and 8.

  =32×8=256

Therefore, the multiplication of fractions is as follows:

  =201256

Thus, the multiplication of fractions is 201256.

Conclusion:

The multiplication of fractions is 201256.

To determine

(f)

Multiply the mixed fractions and reduce to lowest term.

Expert Solution
Check Mark

Answer to Problem 13A

The multiplication of fractions is 3713.

Explanation of Solution

Given:

The number is 223×223×514.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of first mixed number 223 is 83.

The improper fraction of second mixed number 223 is 83.

The improper fraction of third mixed number 514 is 214.

Multiply 83×83×214 as follows:

Multiply the numerators 8, 8 and 21.

  =8×8×21=1344

Multiply the denominators 3, 3 and 4.

  =3×3×4=36

Therefore, the multiplication of fractions is as follows:

  =134436

The greatest common factor of 1344 and 36 is 12.

Divide numerator and denominator of fraction by 12.

  =1344÷1236÷12=1123

The mixed conversion of 1123 is as follows:

  337 112 09 _ 022 21 _ 01

The mixed conversion of 1123 is 3713.

Thus, the multiplication of fractions is 3713.

Conclusion:

The multiplication of fractions is 3713.

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