Algebra: Fraction Problems

Fraction Word Problems using Algebra

Algebra fraction word problems involve using algebraic equations to solve problems that include fractions. These word problems combine the concepts of fractions with algebraic techniques to solve for unknown quantities.

The following diagram gives the steps to solve a fraction word problem using Algebra.

 

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Example:
\(\frac{2}{3}\) of a number is 14. What is the number?

Solution:
Step 1: Assign variables :
Let x = number
Step 2: Solve the equation
\(14 = \frac{2}{3}x\)
Isolate variable x
\(x=14\times\frac{3}{2} = 21\)

Answer: The number is 21.

Example:
The numerator of a fraction is 3 less than the denominator. When both the numerator and denominator are increased by 4, the fraction is increased by fraction.

Solution:
Let the numerator be x,
then the denominator is x + 3,
and the fraction is \(\frac{x}{{x + 3}}\)
When the numerator and denominator are increased by 4, the fraction is \(\frac{{x + 4}}{{x + 7}}\)
\(\frac{{x + 4}}{{x + 7}} - \frac{x}{{x + 3}} = \frac{{12}}{{77}}\)
77(x + 4)(x + 3) – 77x(x+7) = 12(x + 7)(x + 3)
77x² + 539x + 924 – 77x² – 539x = 12x² + 120x + 252
12x² + 120x – 672 = 0
x² + 10x – 56 = 0
(x – 4)(x + 14) = 0
x = 4 (negative answer not applicable in this case)

Answer: The original fraction is \(\frac{4}{7}\)

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How to solve Fraction Word Problems using Algebra?
Examples:
(1) The denominator of a fraction is 5 more than the numerator. If 1 is subtracted from the numerator, the resulting fraction is 1/3. Find the original fraction.
(2) If 3 is subtracted from the numerator of a fraction, the value of the resulting fraction is 1/2. If 13 is added to the denominator of the original fraction, the value of the new fraction is 1/3. Find the original fraction.
(3) A fraction has a value of 3/4. When 14 is added to the numerator, the resulting fraction has a value equal to the reciprocal of the original fraction, Find the original fraction.

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Algebra Word Problems with Fractional Equations
Solving a fraction equation that appears in a word problem
Example:
One third of a number is 6 more than one fourth of the number. Find the number.

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Fraction and Decimal Word Problems
How to solve algebra word problems with fractions and decimals?
Examples:
(1) If 1/2 of the cards had been sold and there were 172 cards left, how many cards were printed?
(2) Only 1/3 of the university students wanted to become teachers. If 3,360 did not wan to become teachers, how many university were there?
(3) Rodney guessed the total was 34.71, but this was 8.9 times the total. What was the total?

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