What is tofraction 42.875 ?

The solution to tofraction 42.875 is 42 7/8

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Popular Pre Algebra >

Convert to a Simplified Fraction 42.875

Solution

tofraction

Solution

42 \frac{7}{8}

Decimal

42.875

Solution steps

42.875

Rewrite as

= 42 + 0.875

Convert

0.875

to a fraction:

\frac{7}{8}

0.875

Multiply and divide by 10 for every number after the decimal point.

There are

3

digits to the right of the decimal point, therefore multiply and divide by

1000

= \frac{0.875 \cdot 1000}{1000}

= \frac{875}{1000}

Reduce the fraction

\frac{875}{1000} : \frac{7}{8}

\frac{875}{1000}

Find a common factor of

875

and

1000

in order to cancel it out

Greatest Common Divisor of

875, 1000 : 125

875, 1000

Greatest Common Divisor (GCD)

Prime factorization of

875 : 5 \cdot 5 \cdot 5 \cdot 7

875

875

divides by

5875 = 175 \cdot 5

= 5 \cdot 175

175

divides by

5175 = 35 \cdot 5

= 5 \cdot 5 \cdot 35

35

divides by

535 = 7 \cdot 5

= 5 \cdot 5 \cdot 5 \cdot 7

5, 7

are all prime numbers, therefore no further factorization is possible

= 5 \cdot 5 \cdot 5 \cdot 7

Prime factorization of

1000 : 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

1000

1000

divides by

21000 = 500 \cdot 2

= 2 \cdot 500

500

divides by

2500 = 250 \cdot 2

= 2 \cdot 2 \cdot 250

250

divides by

2250 = 125 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

The prime factors common to

875, 1000

are

= 5 \cdot 5 \cdot 5

Multiply the numbers:

5 \cdot 5 \cdot 5 = 125

= 125

Factor out

125

from the numerator and the denominator

875 = 125 \cdot 7, 1000 = 125 \cdot 8

= \frac{125 \cdot 7}{125 \cdot 8}

Cancel the common factor:

125

= \frac{7}{8}

= \frac{7}{8}

= 42 + \frac{7}{8}

= 42 \frac{7}{8}

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Frequently Asked Questions (FAQ)

What is tofraction 42.875 ?
The solution to tofraction 42.875 is 42 7/8

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