A Comprehensive Cheat Sheet for Fractions

A Comprehensive Cheat Sheet for Fractions Fractions Cheat Sheet This cheat sheet provides a basic outline of what you need to know about fractions when you are required to perform computations that involve fractions. Computations refer to addition, subtraction, multiplication and division. You should have an understanding of simplifying fractions and calculating common denominators prior to adding, subtracting, multiplying and dividing fractions. Multiplying Fractions Once you remember that the numerator refers to the top number and the denominator refers to the bottom number of a fraction, you are on your way to being able to multiply fractions. You will multiply the numerators, then multiply the denominators and will be left with an answer that may require one additional step: simplifying. Lets try one: 1/2 x 3/41 x 3 32 x 4 8Therefore the answer is 3/8 Dividing Fractions Again, you need to know that the numerator refers to the top number and the denominator refers to the bottom number. In the case of division of fractions, you will invert the divisor and then multiply. Put simply, turn the second fraction upside down (this is called the reciprocal) and then multiply. Lets try one: 1/2 x 1/31/2 x 3/1 (we just flipped 1/3 to 3/1)3/3 which we can simplify to 1 Notice that I began with Multiplication and Division? If you remember the above, you wont have much difficulty with those two operations as they dont involve calculating the like denominators. However, when subtracting and adding fractions, were are often required to calculate the like or common denominators. Adding Fractions When  adding fractions with the same denominator, you leave the denominator as it is and add the numerators. Lets try one:3/4 9/413/4 Of course, now the numerator is larger than the denominator so you would simplify and have a mixed number:3 1/4 However, when adding fractions with unlike denominators, a common denominator needs to be found prior to adding the fraction. Lets try one:2/3 1/4 (the lowest common denominator is 12)8/12 3/12 11/12 Subtracting Fractions When subtracting fractions with the same denominator, leave the denominator as it is and subtract the numerators. Lets try one:9/4 - 8/4 1/4However, when subtracting fractions without the same denominator, a common denominator needs to be found prior to subtracting the fraction. Lets try one:1/2 - 1/6 (the lowest common denominator is 6) 3/6 - 1/6 2/6 which can be reduced to 1/3 There are times when youll simplify the fractions when it makes sense.