LESSON 6
FRACTIONS
Understanding Parts of a Whole
What is a Fraction?
A fraction represents a part of a whole. When we divide something into equal parts and take some of those parts, we use a fraction to describe how many parts we have out of the total.
A fraction has two parts: the numerator (top number) tells how many parts we have, and the denominator (bottom number) tells how many equal parts the whole is divided into. For example, in 3/4, we have 3 parts out of 4 equal parts.
Types of Fractions
A proper fraction has a numerator smaller than its denominator (like 3/4) and represents less than one whole. An improper fraction has a numerator equal to or greater than its denominator (like 7/4). A mixed number combines a whole number and a proper fraction (like 1 and 3/4).
Equivalent Fractions
Equivalent fractions are different fractions that represent the same value. You can create equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. Simplifying a fraction means dividing both parts by their greatest common factor.
Adding and Subtracting Fractions
To add or subtract fractions, they must have the same denominator (called a common denominator). If they do not, find the least common denominator first, convert each fraction, then add or subtract the numerators and keep the denominator.
Multiplying and Dividing Fractions
To multiply fractions, multiply the numerators together and the denominators together, then simplify. To divide fractions, flip the second fraction (find its reciprocal) and then multiply. This is sometimes remembered as 'keep, change, flip'.
Key Facts
The word 'fraction' comes from the Latin 'fractio', meaning to break. Fractions literally represent broken or divided wholes.
Every whole number can be written as a fraction — just use 1 as the denominator. For example, 5 = 5/1.
The ancient Egyptians used fractions as far back as 1800 BC, but they only used unit fractions (fractions with 1 in the numerator).
A fraction with the same numerator and denominator always equals 1. For example, 7/7 = 1.