**How to Perform Basic Mathematical Operations on
Fractions**

By Alex McAlpine www.BrainLubeOnline.com

__Introduction__

In this manual, it is assumed that the user has a firm understanding of basic addition, subtraction, multiplication, division, and fractions. This manual is broken into two parts, ÔBasic OperationsÕ and ÔShort CutsÕ. Upon completion of this manual, you should possess all the knowledge needed to quickly and accurately perform basic math functions on fractions.

Basic Operations

Addition

I. Find the lowest common denominator. This is the lowest number both denominators can evenly go into.

¹Ú₂+¹Ú₃= 6 (lowest common
denominator)

II. Multiply the number of times the original denominator will go into the common denominator by the numerator for each fraction. This replaces the original numerator.

¹Ú₂+¹Ú₃= ³Ú₆+²Ú₆

III. Add the numerator and carry the common denominator.

³Ú₆+²Ú₆= ⁵Ú₆

**Subtraction**

I. Find the lowest common denominator.

⁹Ú₁₀-¹Ú₅= 10

II. Multiply the number of times the original denominator will go into the common denominator by the numerator for each fraction. This is the same process as in addition.

⁹Ú₁₀-¹Ú₅=
⁹Ú₁₀-²Ú₁₀

III. Subtract the numerators.

⁹Ú₁₀-²Ú₁₀= ⁷Ú₁₀

**Multiplication**

To multiply fractions simply multiply the denominators, then multiply the numerators.

²Ú₃*⁵Ú₁₂= ¹⁰Ú₃₆

NOTE: Next you may need to reduce the fraction to the lowest terms. To reduce, you need to find the greatest common factor of the numerator and the denominator.

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**Reduction**

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I. The greatest common factor is the largest number that can evenly go into both the numerator and the denominator. Divide the numerator by the greatest common factor.

¹⁰Ú₃₆= 2 (greatest common factor)

II. Divide both the denominator and the numerator by the greatest common factor.

¹⁰Ú₃₆= ⁵Ú₁₈ (reduced to lowest terms)

**Division**

I. Flip the places of the numerator and denominator in the second fraction.

¹Ú₆/¹Ú₅=
¹Ú₆/⁵Ú₁

II. Multiply both numerators and denominators just as you would a standard multiplication problem.

¹Ú₆/⁵Ú₁= ¹Ú₆*⁵Ú₁= ⁵Ú₆

NOTE: As in standard multiplication you may need to reduce the result to lowest terms.

__Short Cuts__

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Canceling

To eliminate the need to reduce a result of multiplication and division problems, you can use a method called canceling.

I. Find the greatest common factor of the first fractions numerator and the second fractions denominator (if any).

²Ú₃*⁵Ú₁₂= 2 (greatest
common factor)

II. Divide the numerator and denominator by this number and replace with result respectively.

²Ú₃*⁵Ú₁₂=
¹Ú₃*⁵Ú₆

III. Do the same with the first fractions denominator and the second fractions numerator if possible.

¹Ú₃*⁵Ú₆= ¹Ú₃*⁵Ú₆ (not possible)

IV. Multiply as a standard fraction, and the result will have already been reduced.

¹Ú₃*⁵Ú₆= ⁵Ú₁₈

**Multiplying mixed numbers using improper fractions**

Instead of multiplying the whole numbers and then the fractions respectively, you can make improper fractions and then multiply conventionally.

I. To make an improper fraction, multiply the whole number by the denominator.

3¹Ú₃*2¹Ú₄ 3¹Ú₃= 9 2¹Ú₄= 8

II. Add the result to the numerator and replace in the numerators spot. Leave the denominator unchanged.

3¹Ú₃*2¹Ú₄= ¹⁰Ú₃*⁹Ú₄

III. Multiply in the conventional way.

¹⁰Ú₃*⁹Ú₄ = ⁹⁰Ú₁₂

NOTE: Reduction to simplest form is optional.

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