2Rational NumbersThe term Rational Numbers refers to any number that can be written as a fraction.This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers.An integer, like 4, can be written as a fraction by putting the number 1 under it.
3Multiplying Fractions When multiplying fractions, they do NOT need to have a common denominator.To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator.If the answer can be simplified, then simplify it.Example:
4Simplifying Diagonally When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end.From the last slide:An alternative:1You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.
5Mixed NumbersTo multiply mixed numbers, convert them to improper fractions first.1
6Sign Rules Remember, when multiplying signed numbers... Positive * Positive =Positive.Negative * Negative =Positive.Positive * Negative =Negative.
7Try These: MultiplyMultiply the following fractions and mixed numbers:
9Solutions (alternative): Multiply Note: Problems 1, 2 and 4 could have been simplified before multiplying.1221121313
10Dividing FractionsWhen dividing fractions, they do NOT need to have a common denominator.To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep it-Change it-Flip it(multiply by the reciprocal)Change Operation.Flip 2nd Fraction.
11Dividing FractionsFinish the problem by following the rules for multiplying fractions.
12Try These: DivideDivide the following fractions & mixed numbers: