Algebra I All-in-One For Dummies. Mary Jane Sterling

This method is a bit nicer than looking at all the multiples of 96.

Applying Fractional Operations

      Now that you have the tools necessary, you can investigate ways to perform binary operations on fractions. Addition and subtraction go together, because they both require common denominators. Multiplication and division are paired, because they can be performed without having to create the same denominator. And division is just “multiplication adjusted”!

      Adding and subtracting fractions

      You can add fractions together or subtract one from another if they have a common denominator. After you find the common denominator and change the fractions to their equivalents, you can add the numerators together or subtract them (keeping the denominators the same).

      Adding and subtracting fractions takes a little special care. You can add quarts and gallons if you change them to the same unit. It’s the same with fractions. You can add thirds and sixths if you find the common denominator first.

      To add or subtract fractions:

      1 Convert the fractions so that they have the same value in the denominators.Find out how to do this in the section, “Finding common denominators.”

      2 Add or subtract the numerators.Leave the denominators alone.

      3 Reduce the answer, if needed.

      

Q. In her will, Jane gave of her money to the Humane Society and of her money to other charities. How much was left for her children’s inheritance?

A. The fractions and aren’t compatible because the denominators don’t have any factors in common. The fraction has the larger denominator and can be written as or or , and so on. You can stop at because 3 divides 21 evenly: and . Add the numerators to get the total designation to charity in Jane’s will: . Subtract that total from the whole of Jane’s proceeds to find what portion is allotted to her children: . Jane’s children will be awarded of her estate.

      Q.

      A. First find the common denominator, 24, and then complete the addition:

      Q.

      A. You need a common denominator of 30:

      The whole number parts are separated from the fractional parts to keep the numbers in the computations smaller. Be sure to apply the subtraction to both the whole number and fraction when needed.

      Q.

      A. In this problem, you see another option: you can change both mixed numbers to improper fractions. The common denominator is 56:

      27

28

      29

      30

      31

      Multiplying and dividing fractions

      Multiplying fractions is really a much easier process than adding or subtracting fractions, because you don’t have to find a common denominator. Furthermore, you can take some creative steps and reduce the fractions before you even multiply them.

      When multiplying fractions, you can pair up the numerator of any fraction in the problem with the denominator of any other fraction; then divide each by the same number (reduce). Doing so saves you from having large numbers to multiply and then to reduce later.

      Yes, multiplying fractions is a tad easier than adding or subtracting them. Multiplying is easier because you don’t need to find a common denominator first. The only catch is that you have to change any mixed numbers to improper fractions. Then, at the end, you may have to change the fraction back again to a mixed number. Small price to pay.

      When multiplying fractions, follow these steps:

      1 Change all mixed numbers to improper fractions.

      2 Reduce any numerator-denominator combinations, if possible.

      3 Multiply the numerators together and the denominators together.

      4 Reduce the answer if necessary.

      Here’s an example: Suppose Sadie worked hours at time-and-a-half. How many hours will she get paid for?

      Write the problem as and then rewrite the mixed numbers as improper fractions. . Reducing the fractions before multiplying can make multiplying the fractions easier. Smaller numbers are more manageable, and if you reduce the fractions before you multiply, you don’t have to reduce them afterward.

      The product has a 32 in the first numerator and a 2 in the second denominator. Even though the 32 and 2 aren’t in the same fraction, you can reduce them because this is a multiplication