Common Denominator Case Study

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Abbey Jacobson
Math 212
Reflection 2
Reflect 4.4
⅖ths is larger than 2/7ths because when changing the fraction to a common denominator, in this case 35, we get 14/35ths and 10/35ths respectively.
4/10ths is larger than 3/8ths, I found this by finding the common denominator of 80 and changing the fractions accordingly to get 32/80 and 30/80 respectively.
When comparing 6/11 and ⅗ we find the ⅗ is larger when we find the common denominator. The common denominator is 55, we get 30/55 and 33/55 respectively, showing that ⅗ is larger than 6/11.
I multiplied ¾ by 2 to get 6/8, to make it visually easy to find the larger fraction between ¾ and ⅝. We see that ¾ is larger.
I found the common denominator of 6/5 and 8/7, changing them to 42/35 and
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By multiplying 4 by 2 we get 8, which makes it a common numerator with 8/15, we get 4/7 as 8/14 and can now compare it to 8/15. Since we know that 1 unit cut into 14 equal sizes pieces will produce larger pieces than 1 unit cut into 15 equal size pieces, 4/7 has to be the larger fraction.
Common Denominator
To find the common denominator of ⅘ and 9/10 we need to multiply ⅘ by 2, making it 8/10. Now that the two fractions have the same denominator we can now compare the two fractions. We can think of each fraction as 1 unit cut into ten equal size pieces. In one unit we would shade 8 of the 10 pieces to represent 8/10 and we would shade 9 out of the 10 pieces on the other unit, because we can see that the second unit has 9 out of the 10 pieces shaded we know that 9/10 is the larger fraction.
Benchmark
7/13 and 11/23 are best compared through the benchmarking strategy. We are going to use ½ as our benchmark for these two fractions. First we need to divide each of the denominators by 2 to get 6.5 and 11.5 respectively. As we can see 7 is greater than 6.5, this means that 7/13 will be to the right of ½ on a number line. 11 is less than 11.5 meaning 11/23 will be to the left of ½ on a number line. We know that the number furthest to the right on a number line is the larger number, so 7/13 is the greater

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