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Answer :
Final answer:
To find the largest fraction among 10/13, 11/14, 14/15, or 17/18, subtract each from 1. The smallest difference from 1 indicates that 17/18 is the largest fraction among the given options.
Explanation:
To determine which fraction is larger among 10/13, 11/14, 14/15, or 17/18, we can compare each fraction to 1 by subtracting each one from 1 to see which is closer to 1, since the closer a fraction is to 1, the larger it is. Here is the step-by-step comparison:
- 1 - 10/13 = 3/13
- 1 - 11/14 = 3/14
- 1 - 14/15 = 1/15
- 1 - 17/18 = 1/18
Now, we can see that 1/18 is the smallest difference, so 17/18 is the closest to 1, which makes it the largest fraction.
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Rewritten by : Barada
To solve these type of problem you have to make the denominator the same or use the claculator.
let us do this problem by making the denominator the same.
[tex]\frac{10}{13} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{11}{14} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{14}{15} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{17}{18} \\\\ \frac{10}{13}\times \frac{3780}{3780} \ \ \ \ \ \ \ \ \ \frac{11}{14} \times \frac{3510}{3510} \ \ \ \ \ \ \ \ \ \frac{14}{15} \times \frac{3276}{3276} \ \ \ \ \ \ \ \ \ \frac{17}{18} \times \frac{2730}{2730}[/tex]
[tex]\frac{37800}{49140} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{38610}{49140} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{45864}{49140} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{46410}{49140} [/tex]
So, now. the one with the largest numerator is the largest fraction
In this case, [tex] \frac{46410}{49140}[/tex] is the largest which is equal to [tex] \frac{17}{18} [/tex].
So, the largest fraction is [tex] \frac{17}{18} [/tex].
let us do this problem by making the denominator the same.
[tex]\frac{10}{13} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{11}{14} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{14}{15} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{17}{18} \\\\ \frac{10}{13}\times \frac{3780}{3780} \ \ \ \ \ \ \ \ \ \frac{11}{14} \times \frac{3510}{3510} \ \ \ \ \ \ \ \ \ \frac{14}{15} \times \frac{3276}{3276} \ \ \ \ \ \ \ \ \ \frac{17}{18} \times \frac{2730}{2730}[/tex]
[tex]\frac{37800}{49140} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{38610}{49140} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{45864}{49140} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{46410}{49140} [/tex]
So, now. the one with the largest numerator is the largest fraction
In this case, [tex] \frac{46410}{49140}[/tex] is the largest which is equal to [tex] \frac{17}{18} [/tex].
So, the largest fraction is [tex] \frac{17}{18} [/tex].
