Rule 15: DIVISION

To divide a fraction by a whole number, or a whole number by a fraction, convert the division process to a multiplication process, and complete the following steps.

1.
Convert the whole number to a fraction
2.
Change the tex2html_wrap_inline50 sign to tex2html_wrap_inline52 and invert the fraction to the right of the sign.
3.
Multiply the numerators.
4.
Multiply the denominators.
5.
Reduce the results. (See Rule 10)
a.
Factor the product of the numerators.
b.
Factor the product of the denominators.
c.
Look for the fractions that have a value of 1.

Example : Multiply tex2html_wrap_inline54 .

Answer: The answer is tex2html_wrap_inline56 .

Solution: Convert the 7 to the fraction tex2html_wrap_inline58 . The problem tex2html_wrap_inline54 can now be written as tex2html_wrap_inline62

Change the division sign to multiplication and invert the fraction to the right of the sign. tex2html_wrap_inline64

Multiply the numerators and the denominators, but leave them in factored form. tex2html_wrap_inline66

The numerator and denominator do not share a common factor, therefore the answer is tex2html_wrap_inline68
.

Check: You can check the answer with your calculator. Calculate 3 divided by 4 and divide that result by 7. Now calculate 3 divided by 28. If the answers are the same, you have correctly worked this problem.

If you are interested in reviewing another example, click on the word Example.

Work the following problems and click on Answer to check your results.

Problem 1: Calculate tex2html_wrap_inline70 and reduce your answer.

Answer


Problem 2: Calculate tex2html_wrap_inline72 and reduce your answer.

Answer


Problem 3: Calculate tex2html_wrap_inline74 and reduce your answer.

Answer


Problem 4: Calculate tex2html_wrap_inline76 and reduce your answer.

Answer


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