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fractions

by Tina
(Sedalia)











































Sarah spends 1/4 of her income for transportation,1/6 of her income for food,and 1/3 of her income for rent and utilities. What fractional part of Sarah's income is left for all of her other expenses?

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Jun 21, 2010
Fractional Income
by: Staff

The question:

Sarah spends 1/4 of her income for transportation,1/6 of her income for food, and 1/3 of her income for rent and utilities.

What fractional part of Sarah's income is left for all of her other expenses?


The answer:



Note: “1” represents 100% of all income. This can also be written as the fraction 1/1.


Leftover Income = 1 (total income) – 1/4 (transportation) – 1/6 (food) – 1/3 (rent)

Leftover Income = 1/1 – 1/4 – 1/6 – 1/3


To complete the subtraction, all denominators must be the same.

This can be accomplished by multiplying each of the existing fractions by another fraction. Any numbers can be used to create the second fraction. However, the value of the second fraction (which will be used as a multiplier) must always be equal to the number “1”. For example, 12/12 =1, 3/3 = 1, 2/2 = 1, 4/4 = 1.

Why must the value of the fractions used as a multiplier be equal to the number 1? The reason: multiplying anything by “one” does not change its original value. 1/4 multiplied by 1 is still 1/4, 1/6 multiplied by 1 is still 1/6, and 1/3 multiplied by 1 is still 1/3.

The numbers chosen for each fraction used as a multiplier will be those numbers which cause the final denominator of every fraction to be the same (after multiplication is complete). In this case, every denominator will be equal to the number 12 after multiplication is complete.



Leftover Income = (1/1)(12/12) – (1/4)(3/3) – (1/6)(2/2) – (1/3)(4/4)

Leftover Income = 12/12 – 3/12 – 2/12 – 4/12

Leftover Income = (12 – 3 – 2 – 4)/12

Leftover Income = 3/12


Finally, reduce the fraction 3/12 to its lowest terms

Leftover Income = 1/4


Final answer: 1/4 of Sarah’s income is left for all her other expenses.



Thanks for writing.


Staff
www.solving-math-problems.com



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