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

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Change the mixed number to an improper fraction.

      3 Change the mixed number to an improper fraction.

      4 Change the mixed number to an improper fraction.

      5 Change the improper fraction to a mixed number.

      6 Change the improper fraction to a mixed number.

Finding Fraction Equivalences

      In algebra, all sorts of computations and manipulations use fractions. In many problems, you have to change the fractions so that they have the same denominator or so that their form is compatible with what you need to solve the problem. Two fractions are equivalent if they have the same value, such as and . To create an equivalent fraction from a given fraction, you multiply or divide both the numerator and denominator by the same number. This technique is basically the same one you use to reduce a fraction.

      Rewriting fractions

      When you multiply or divide the numerator and denominator of a fraction by the same number, you don’t change the value of the fraction. In fact, you’re basically multiplying or dividing by 1 because any time the numerator and denominator of a fraction are the same number, it equals 1.

      For example, how much of a 32-ounce package are you using if your recipe calls for 12 ounces? You’re using of the package. If you divide both the 12 and the 32 by 4, you’re basically dividing by , which equals 1. The same goes for multiplying the numerator and denominator by the same number. So, you’re using of the package.

      Here’s another example: Create two new versions of the fraction — one with smaller numbers and one with larger numbers.

      To come up with smaller numbers, you need to find something that divides both the 16 and the 20 evenly. There are two possibilities: 2 and 4.

      The fraction is said to be in “lowest possible terms” because there are no common factors available. No whole numbers can divide the two numbers evenly except for 1.

      There is no end to the possibilities when creating multiples of a particular fraction:

       and and , and so on. You choose the numbers that work best for you in the situation.

      However, not all fractions with large numbers can be changed to smaller numbers. Certain rules have to be followed so that the fraction maintains its integrity; the fraction has to have the same value as it did originally.

      

Q. Find a fraction equivalent to with a denominator of 40.

      A. Because 5 times 8 is 40, you multiply both the numerator and denominator by 5. In reality, you’re just multiplying by 1, which doesn’t change the real value of anything.

      Q. Reduce by multiplying the numerator and denominator by . The same thing is accomplished if you divide both the numerator and denominator by 3.

      A. or

      7 Find an equivalent fraction with a denominator of 28 for .

      8 Find an equivalent fraction with a denominator of 30 for .

      9 Reduce this fraction: .

10 Reduce this fraction: .

      Determining lowest terms

      A fraction is in its lowest common terms when there is no common factor of the numerator and denominator except the number 1. Nothing will divide both of them evenly.

      

To reduce fractions to their lowest terms, follow these steps:

      1 Look for numbers that evenly divide both the numerator and the denominator.If you find more than one number that divides both evenly, choose the largest.

      2 Divide both the numerator and the denominator by the number you chose, and put the results in their corresponding positions.

      When reducing fractions, your fraction isn’t wrong if you don’t choose the largest-possible divisor. It just means that you have to divide again to get to the lowest terms. When reducing the fraction , you might have chosen to divide by 6 instead of 12. In that case, you’d get the fraction , which can be reduced again by dividing the numerator and denominator by 2. Choosing the largest number possible just reduces the number of steps you have to take.

      Q.

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