We"ll be making a many "like fractions" in this section (fractions through common denominators). Remember the 1 have the right to be represented by a fraction when the numerator and denominator space the same value. 2/2 is the exact same as 1. 9/9 is the exact same as 1. 52/52 is the very same as one. If the is confusing, think of it together a division problem. 2÷2=1. 9÷9=1. 52÷52=1. Also, remember the in multiplication anything multiply by 1 is the exact same value. 2*1=2. 9*1=9. 52*1=52. The math reality is called the identity property of multiplication. We"re walk to use this trick come make prefer fractions. We understand that 1/3 * 1 = 1/3. Let"s to speak our fraction problem essential the equipment to have the denominator 18 (bottom number). Use the principle 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 inspect Answer: 6/18 = 1/3We provided the identification property to produce equivalent fractions. We created the same denominator for every one of our terms. Comparing FractionsYou will gain a lot of of problems where you are asked to to compare fractions. Is 1/2 larger or smaller than 1/3? you should already know around "greater than" and also "less than" symbols. It"s easier with entirety numbers...• compare 2 and also 1. You know that two is better than one.• compare 13 and also 27. You understand that thirteen is less than twenty-seven.• to compare -40 and also -2. Us have operated with an unfavorable integers before. -40 is less than -2.So what about fractions? One some levels it"s just 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 possible in the same space, the pieces need to be smaller. If the variety of pieces (numerator) in each fraction is the same, the one with the bigger denominator will constantly be much less than the other. This only works as soon as 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 reduced into 2 pieces and one is cut into 5 pieces. Which piece is bigger? half of a pie is bigger 보다 one fifth of a pie. So 1/2 is better than 1/5.Compare 5/8 and also 5/10. Begin by noticing the you have five pieces the each. Since they room the exact same number, we can ignore them. Then look at the denominators and also think about pieces the a pie. One eighth of a pie is bigger 보다 a tenth the a pie. Basically, girlfriend have five bigger pieces compared to five smaller pieces. For this reason 5/8 is greater than 5/10.When the numerators space the same, us don"t have to worry around converting any numbers. Let"s look at favor fractions (same denominators). They are easy. Girlfriend only require to focus on the worths of the numerators there is no converting anything.Examples:Compare 2/9 and 6/9.You have actually the exact same denominators, for this reason the size of the piece is the same. Now look as much as the numerators. 2 pieces compared to six pieces. You have this one. If 2 2/9 compare 8/17 come 3/17Once again, you have the very same denominators. The pieces are the same size. Compare eight to three. Since eight is better than three...8/17 > 3/17The simple ones are out that the method now. Yet what happens as soon as you have unlike fractions (different denominators) with different numerators? You are going to must make lock "like fractions" to really compare them. That means you will require the very same bottom number (common denominators) for each fraction. You"re going to need a tiny multiplication to execute this one.Examples:Compare 5/6 and also 17/18We have actually sixths and eighteenths because that denominators. We must make them choose fractions. They have the common factor that 6 (6x3=18). That"s good, us only have to address the 5/6 term. The 17/18 deserve to stay the means it is. Due to the fact that we know that 6x3=18, let"s main point the numerator and 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 have the right to compare 15/18 and 17/18. No problem.15/18 to compare 6/9 and 3/4.Notice the we have actually ninths and fourths because that denominators. There room no typical factors top top this problem. The fast way is to create equivalent fractions because that each term and also compare them. How? multiply the very first term by 4/4 and the second by 9/9. In various other words, we will certainly be multiply both the top and also bottom number of one hatchet by the denominator that the other. Use the start-swap-multiply procedure from over 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 check out that? as soon as you multiply by the denominator the the various other term, girlfriend wind up with like fractions. Now we have the right to compare 24/36 and 27/36. Simple as pie.24/36

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