**common denominators**). Remember that 1 deserve to be stood for by a fraction when the numerator and also denominator space the exact 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 the it together a division problem. 2÷2=1. 9÷9=1. 52÷52=1. Also, remember the in multiplication anything multiplied by 1 is the same value. 2*1=2. 9*1=9. 52*1=52. That math fact is referred to as the

**identity property**that multiplication. We\"re walking to use this trick come make choose fractions. We recognize that 1/3 * 1 = 1/3. Let\"s to speak our fraction problem required the equipment to have the denominator 18 (bottom number). Usage the principle that 1 is

**equivalent**come 6/6. The means...• Start: 1/3 * 1 = 1/3• Swap: 1/3 * 6/6 = 1/3• multiply the Fractions: (1*6)/(3*6) = 6/18• simplify to check Answer: 6/18 = 1/3We supplied the identity property to develop equivalent fractions. We created the exact same denominator for every one of our terms. Comparing FractionsYou will obtain a lot of difficulties where you are asked to to compare fractions. Is 1/2 larger or smaller than 1/3? you should currently know around \"

**greater than**\" and \"

**less than**\" symbols. It\"s less complicated with totality numbers...• compare 2 and also 1. You understand that 2 is higher than one.• to compare 13 and 27. You know that thirteen is much less than twenty-seven.• compare -40 and -2. We have operated with negative integers before. -40 is less than -2.So what around fractions? One some levels it\"s simply as easy. Fountain with larger denominators (bottom number) have much more pieces that space possible. As soon as you have much more pieces that are possible in the very same space, the pieces need to be smaller. If the number of pieces (numerator) in each fraction is the same, the one v the bigger denominator will always be less than the other. This only works as soon as you can compare the same number of pieces.

**Examples:**Compare 1/2 and 1/5. Think around a pie. One pie is cut into two pieces and one is cut into five pieces. Which piece is bigger? fifty percent of a pie is bigger than one 5th of a pie. For this reason 1/2 is higher than 1/5.Compare 5/8 and also 5/10. Start by noticing the you have five pieces of each. Due to the fact that they space the very same number, we have the right to ignore them. Then look at the denominators and also think around pieces that a pie. One eighth the a pie is bigger than a tenth the a pie. Basically, friend have five bigger pieces contrasted to 5 smaller pieces. Therefore 5/8 is higher than 5/10.When the numerators are the same, us don\"t have to worry around converting any numbers. Let\"s look at prefer fractions (same denominators). They space easy. You only need to focus on the values of the numerators there is no converting anything.

**Examples:**Compare 2/9 and also 6/9.You have the same denominators, so the size of the piece is the same. Now look as much as the numerators. 2 pieces compared to six pieces. You have actually this one. If 2 2/9 to compare 8/17 to 3/17Once again, you have the same denominators. The pieces space the same size. To compare eight come three. Since eight is higher than three...8/17 > 3/17The easy ones space out the the means now. However what happens as soon as you have unlike fountain (different denominators) with different numerators? You room going to should make them \"like fractions\" to really compare them. That means you will need the same bottom number (common denominators) for each fraction. You\"re walk to need a small multiplication to perform this one.

**Examples:**Compare 5/6 and also 17/18We have sixths and also eighteenths for denominators. We should make them prefer fractions. They have actually the typical factor of 6 (6x3=18). That\"s good, us only have actually to deal with the 5/6 term. The 17/18 can stay the means it is. Due to the fact that we understand that 6x3=18, let\"s main point the numerator and also the denominator by 3. Usage the start-swap-multiply process from above.5/6 = 5/6 * 1 = 5/6 * 3/3 = (5*3)/(6*3) = 15/18Now you can compare 15/18 and 17/18. No problem.15/18 to compare 6/9 and 3/4.Notice that we have ninths and fourths for denominators. There are no common factors ~ above this problem. The fast means is to create equivalent fractions for each term and also compare them. How? main point the an initial term by 4/4 and also the 2nd by 9/9. In other words, we will certainly be multiply both the top and bottom number of one ax by the denominator that the other. Use the start-swap-multiply process 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 view that? once you main point by the denominator that the other term, you wind increase with favor fractions. Currently we have the right to compare 24/36 and 27/36. Simple as pie.24/36

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