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.

### Fraction Word Problems using Algebra

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)

77x^{2} + 539x + 924 – 77x^{2} – 539x = 12x^{2} + 120x + 252

12x^{2} + 120x – 672 = 0

x^{2} + 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?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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 **Example:**

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

Solution:

Step 1: Assign variables :

Letx= number

Step 2: Solve the equation

Isolate variablex

* Answer:* The number is 21.

**Example:**

**Solution:**

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)

77x

12x

x

(x – 4)(x + 14) = 0

x = 4 (negative answer not applicable in this case)

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.

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.

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?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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