# Algebra: Fraction Problems

In these lessons, we will learn how to solve fraction word problems that deal with fractions and algebra. Remember to read the question carefully to determine the numerator and denominator of the fraction.

We will also learn how to solve word problems that involve comparing fractions, adding mixed numbers, subtracting mixed numbers, multiplying fractions and dividing fractions.

Related Topics: More Algebra Word Problems

### Fraction Word Problems using Algebra

Example:

2/3 of a number is 14. What is the number?

Solution:

Step 1: Assign variables :

Let x = number

Step 2: Solve the equation

Isolate variable x

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 $$\frac{4}{7}$$

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.

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. 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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