Fractions: A Mathematical Guide

Want a refresher on the exciting world of fractions? Maybe you need a handy reference guide to stick in your math notebook to study before test time. This guide shows you how to write fractions as decimals, how to find common multiples, factors, and denominators, and how to add, subtract, multiply and divide fractions.

Fractions are numbers that name parts of something. Fractions and decimals are two similar ways of writing numbers. Any fraction can be rewritten as a decimal. To rewrite a fraction as a decimal, divide the denominator into the numerator. For example, 8/100 = 0.08 and 9/20 = 0.45.

To change a mixed number to a decimal, change the fraction part to a decimal and add it to the whole number. For example, 1 7/8 = 1 +(7/8) - 1 + 0.875 = 1.875.

A fraction has a numerator (the top number) and a denominator (the bottom number). A mixed number is the combination of a whole number and a fraction, such as 1 1/2. An improper fraction has numerator larger than the denominator such as 9/4.

To write a decimal as a fraction, write the decimal as a fraction with a denominator of 10, 100, 1000, or another multiple of 10. 0.7 = seven tenths or 7/10.

A factor is a number that can be multiplied by another number to give a certain product. The factors of 12 are 1, 2, 3, 4, 6, and 12 because 1 x 12 = 12, 2 x 6 = 12, 3 x 4 = 12. Any composite number can be written as the product of prime number factors. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. No matter how a factor tree is made for a given number, the prime factors in bottom row are always the same. To find all the factors of a number, list all the numbers that can divide into it evenly. A number will always have 1 and itself as factors.

Common factors are factors that are the same. Two or more numbers can have common factors. The greatest common factor (GCF) is the largest factor shared by both numbers.

A multiple is the product of any given number and a factor such as 1,2,3, etc. Common multiples are multiples that two or more numbers that share or have in common.

The least common multiple (LCM) is the least multiple that a group of numbers has common. To find the LCM, find the common multiples and choose the least one.

The least common denominator (LCD) is the least multiple that two or more denominators have in common. First find the least common multiple of the denominators. Rewrite each fraction as an equivalent fraction using the LCD as the denominator.

A fraction in simplest form occurs when the numerator and denominator have no common factors. To write a fraction in simplest form, find the GCF of the numerator and denominator. Divide the numerator by the denominator.

To add fractions with common denominators, first add the numerators. Put the sum over the common denominator, and simplify.

To add mixed numbers, follow the same steps as above. For example, 1 5/6 + 1 3/6 = 2 8/6 = 2 + 1 +2/6 = 3 1/3.

To subtract fractions and improper fractions with common denominators, subtract the denominators, put the difference over the common denominator, and simplify.

To subtract mixed numbers, subtract the fractions, subtract the whole numbers, and simplify.

With different denominators, to add fractions, you must find a common denominator and rewrite each number using the common denominator and then simplify.

To multiply fractions, change the mixed numbers to improper fractions. Multiply the numerators and then multiply the denominators.

To divide fractions, write the fraction's reciprocal by switching the numerator and the denominator. For example: ¾ / 3/2 = ¾ x 2/3 + ½.

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