Look over the example on the following page. 2-15363=1213=?361&123&12=123613=x363x=36x=363=121&94&9=9361&49&4=43613+14+19=12+9+436=2536

Example:Denominators Prime factorsAll fractions convertedTry the following challenge to make equivalent fractions with the lowest common denominators.This challenge will reinforce your knowledge in this area.Check your work to ensure your answers are correct. If they are correct, you may continue. Ifnot, review paragraph 2106 before continuing.2-16xyLCM=x&x&y&y=x2y2x2xy2x&yx&xx&y&yaxy=a&x&yx&x&y&y=axyx2y2bx2=b&y&yx&x&y&y=by2x2y2cxy2=c&xx&x&y&y=cxx2y2(Solve)Make equivalent fractions using the LCD.(a)(b)34,45,39=1824,78,69=axy,bx2,cxy2

2107. Mixed Numbers and Improper FractionsYou will also find when dealing with electronic equations that you must convert mixed numbersto equivalent improper fractions. If you treat the mixed number as two fractions and convert tolike fractions over a common denominator, all you have to do is add them. Look at the exampleprovided showing a mixed number converted to an equivalent improper fraction.Example: 2-17(Solutions)(a)(b)34,45,39=1824,78,69==34,45,13=34,78,234560,4860,20601824,2124,1624523=51&33+=153+23=173523=15+23=173

Try the following challenge converting mixed numbers to improper fractions. This challenge willreinforce your knowledge in this area.Check your answers to make sure they are correct. If they match the responses below, you arecorrect, and may continue. If not, review paragraph 2107 before continuing.2108.Improper Fractions to Mixed NumbersNow that you have mastered changing mixed numbers to improper fractions, we will cover theinverse operation. You will learn to perform long division using whole numbers. If youremember back in Study Unit 1, lesson 4, solving polynomial equations can be more difficult. Thesteps you must take will be to divide the numerator by the denominator. The even number oftimes the denominator goes into the numerator becomes the whole number.2-18(Solve)Convert into improper fractions.(a)(b)(c)1113=78=56=(Solutions)(a)(b)(c)11137856=486+56=32+78+78=130+1113=14313=13013+1113=32+78=398=48+56=5361113=101&1313+111378=41&88+7856=81&66+56104101088448

The remainder becomes the fractional part of the mixed number. Look at the examples on how toconvert mixed numbers.Example:(a)(b)Try out the following challenge converting improper fractions to mixed numbers. This challengewill reinforce your knowledge in this area.2-191733 17 = 5 with a remainder of 2=523a+2a2+1a-2a-2°a2+0a+1a2-2a2a+12a-45=a+2+5a-2(Solve)Convert into mixed fractions.(a)(b)(c)12353942x2-5x-2

Check your work to ensure your answers are correct and if they match the following responses.

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- Addition, Subtraction, Negative and non-negative numbers