We"ll be making a many "like fractions" in this section (fractions through common denominators). Remember that 1 deserve to be represented by a fraction when the numerator and denominator room the very same value. 2/2 is the very same as 1. 9/9 is the exact same as 1. 52/52 is the same as one. If that is confusing, think of it together a department problem. 2÷2=1. 9÷9=1. 52÷52=1. Also, remember that in multiplication anything multiply by 1 is the same value. 2*1=2. 9*1=9. 52*1=52. The math reality is dubbed the identity property of multiplication. We"re walk to usage this trick to make favor fractions. We understand that 1/3 * 1 = 1/3. Let"s speak our portion problem needed the systems to have the denominator 18 (bottom number). Use the ide that 1 is equivalent to 6/6. That 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 provided the identification property to develop equivalent fractions. We produced the exact same denominator for all of our terms. Compare FractionsYou will get a lot of difficulties where you room asked to to compare fractions. Is 1/2 bigger or smaller than 1/3? girlfriend should already know about "greater than" and "less than" symbols. It"s simpler with entirety numbers...• to compare 2 and 1. You understand that 2 is better than one.• to compare 13 and 27. You understand that thirteen is less than twenty-seven.• to compare -40 and also -2. We have worked with an adverse integers before. -40 is much less than -2.So what around fractions? One part levels it"s simply as easy. Fountain with bigger denominators (bottom number) have much more pieces that are possible. As soon as you have much more pieces the are feasible in the very same space, the pieces need to be smaller. If the number of pieces (numerator) in each portion is the same, the one through the larger denominator will always be less than the other. This just works as soon as you have the right to compare the same variety of pieces.Examples:Compare 1/2 and also 1/5. Think about a pie. One pie is cut into 2 pieces and one is reduced into five pieces. Which piece is bigger? fifty percent of a pie is bigger 보다 one 5th of a pie. For this reason 1/2 is greater than 1/5.Compare 5/8 and 5/10. Begin by noticing the you have 5 pieces that each. Due to the fact that they space the very same number, we have the right to ignore them. Climate look at the denominators and also think around pieces of a pie. One eighth of a pie is bigger than a tenth that a pie. Basically, you have 5 bigger pieces contrasted to 5 smaller pieces. Therefore 5/8 is greater than 5/10.When the numerators room the same, us don"t have to worry around converting any numbers. Let"s look at like fractions (same denominators). They room easy. Friend only need to focus on the worths of the numerators there is no converting anything.Examples:Compare 2/9 and also 6/9.You have actually the very same denominators, for this reason the dimension of the pieces is the same. Now look as much as the numerators. Two pieces contrasted to 6 pieces. You have actually this one. If 2 2/9 compare 8/17 to 3/17Once again, you have actually the same denominators. The pieces space the exact same size. To compare eight come three. Since eight is higher than three...8/17 > 3/17The simple ones are out that the means now. Yet what happens as soon as you have unlike fountain (different denominators) with various numerators? You space going to must make them "like fractions" to really compare them. That method you will require the exact same bottom numbers (common denominators) because that each fraction. You"re walking to require a small multiplication to do this one.Examples:Compare 5/6 and 17/18We have actually sixths and eighteenths because that denominators. We must make them favor fractions. They have the typical factor that 6 (6x3=18). That"s good, we only have actually to address the 5/6 term. The 17/18 have the right to stay the way it is. Because we know that 6x3=18, let"s multiply the numerator and also the denominator through 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 have the right to 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 room no usual factors on this problem. The fast method is to create equivalent fractions for each term and 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 multiplying both the top and also bottom number of one hatchet by the denominator the the other. Usage 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 view that? once you multiply by the denominator that the other term, girlfriend wind up with choose fractions. Currently we deserve to compare 24/36 and also 27/36. Simple as pie.24/36


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Useful reference MaterialsWikipedia:https://en.wikipedia.org/wiki/Fraction_%28mathematics%29Encyclopædia Britannica:http://www.britannica.com/topic/fractionUniversity of Delaware:https://sites.google.com/a/udel.edu/fractions/


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