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 Question from staci, a student: order from least to greatest on a number line, 7/10 3/5 5/10

Staci,

If you're using a number line, just draw them on and they will sort themselves.

Some other strategies if you aren't actually using a number line:

• find a common denominator and sort in ascending order of numerators: so 2/17 < 5/17 < 11/17 < 23/17

• find a common numerator and sort in descending order of denominators: so 2/17 < 2/9 < 2/5

• with a common difference between the numerator and denominator the larger the numbers the closer to 1 the magnitude is: so 2/3 < 4/5 < 10/11, but 25/23 < 17/15 < 5/3

• use benchmarks such as 1/2 and 1:
1/17 [< 1/2] < 3/5 [< 1] < 7/4

• (a+b)/(c+d) is between a/c and b/d: so if you can sort the outer ones you're done:
1/5 = 2/10 < 2/9, so 1/5 < 3/14 < 2/9

• if permitted, you can use a calculator: one of the reasons for using decimals or decimal approximations is that they are easy to sort. (With decimals however it's often harder to see patterns!)

-RD

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