**common denominators**). Remember the 1 have the right to be represented by a fraction when the numerator and also denominator room the very same value. 2/2 is the exact same as 1. 9/9 is the same as 1. 52/52 is the very same as one. If the is confusing, think that it as a department problem. 2÷2=1. 9÷9=1. 52÷52=1. Also, remember the in multiplication anything multiply by 1 is the very same value. 2*1=2. 9*1=9. 52*1=52. That math fact is called the

**identity property**of multiplication. We"re walking to usage this trick come make favor fractions. We understand that 1/3 * 1 = 1/3. Let"s say our fraction problem required the systems to have actually the denominator 18 (bottom number). Usage the ide that 1 is

**equivalent**to 6/6. That means...• Start: 1/3 * 1 = 1/3• Swap: 1/3 * 6/6 = 1/3• main point the Fractions: (1*6)/(3*6) = 6/18• simplify to inspect Answer: 6/18 = 1/3We used the identification property to develop equivalent fractions. We created the same denominator for every one of our terms. To compare FractionsYou will obtain a lot of difficulties where you room asked to compare fractions. Is 1/2 bigger or smaller than 1/3? friend should currently know around "

**greater than**" and also "

**less than**" symbols. It"s much easier with entirety numbers...• compare 2 and 1. You understand that two is higher than one.• to compare 13 and also 27. You recognize that thirteen is less than twenty-seven.• compare -40 and also -2. Us have worked with an unfavorable integers before. -40 is less than -2.So what around fractions? One part levels it"s just as easy. Fractions with bigger denominators (bottom number) have much more pieces that are possible. Once you have an ext pieces that are possible in the exact same space, the pieces have to be smaller. If the number of pieces (numerator) in each portion is the same, the one with the bigger denominator will constantly be much less than the other. This only works once you have the right to compare the same number of pieces.

**Examples:**Compare 1/2 and also 1/5. Think around a pie. One pie is cut into 2 pieces and one is reduced into five pieces. Which item is bigger? fifty percent of a pie is bigger than one fifth of a pie. So 1/2 is better than 1/5.Compare 5/8 and also 5/10. Start by noticing the you have five pieces that each. Because they space the same number, we deserve to ignore them. Climate look in ~ the denominators and also think about pieces the a pie. An eighth the a pie is bigger 보다 a tenth of a pie. Basically, friend have five bigger pieces compared to 5 smaller pieces. So 5/8 is higher than 5/10.When the numerators are the same, we don"t need to worry about converting any type of numbers. Let"s watch at favor fractions (same denominators). They are easy. Girlfriend only require to emphasis on the values of the numerators there is no converting anything.

**Examples:**Compare 2/9 and also 6/9.You have actually the very same denominators, therefore the dimension of the pieces is the same. Currently look as much as the numerators. Two pieces contrasted to six pieces. You have actually this one. If 2 2/9 to compare 8/17 come 3/17Once again, you have the very same denominators. The pieces room the same size. To compare eight come three. Since eight is better than three...8/17 > 3/17The straightforward ones space out that the means now. Yet what happens when you have unlike fractions (different denominators) with various numerators? You are going to need to make them "like fractions" to yes, really compare them. That method you will require the exact same bottom numbers (common denominators) because that each fraction. You"re going to need a little multiplication to perform this one.

**Examples:**Compare 5/6 and 17/18We have actually sixths and also eighteenths for denominators. We should make them favor fractions. They have the common factor of 6 (6x3=18). That"s good, us only have to resolve the 5/6 term. The 17/18 deserve to stay the method it is. Due to the fact that we recognize that 6x3=18, let"s main point the numerator and the denominator by 3. Usage the start-swap-multiply procedure from above.5/6 = 5/6 * 1 = 5/6 * 3/3 = (5*3)/(6*3) = 15/18Now you deserve to compare 15/18 and 17/18. No problem.15/18 to compare 6/9 and 3/4.Notice that we have actually ninths and also fourths for denominators. There space no common factors on this problem. The fast means is to develop equivalent fractions for each term and also compare them. How? multiply the very first term through 4/4 and also the 2nd by 9/9. In various other words, we will be multiply both the top and also bottom numbers of one term by the denominator that the other. Use the start-swap-multiply procedure from above for both terms.6/9 = 6/9 * 1 = 6/9 * 4/4 = (6*4)/(9*4) = 24/363/4 = 3/4 * 1 = 3/4 * 9/9 = (3*9)/(4*9) = 27/36Did you watch that? once you main point by the denominator that the various other term, girlfriend wind up with like fractions. Now we deserve to compare 24/36 and also 27/36. Easy as pie.24/36

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Useful reference Materials

**Wikipedia:**

*https://en.wikipedia.org/wiki/Fraction_%28mathematics%29*

**Encyclopædia Britannica:**

*http://www.britannica.com/topic/fraction*

**University of Delaware:**

*https://sites.google.com/a/udel.edu/fractions/*

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