Worked Example 1
Show that 0.75, 3/4 and 15/20 are the same rational number.
Reduce each to lowest terms75/100 ÷ 25 = 3/4, and 15/20 ÷ 5 = 3/4
All three reduce to the same thingOne point on the number line written three ways.
Why reducing worksDividing top and bottom by the same number is dividing by 1, which changes nothing.
Worked Example 2
Arrange 2/3, 5/8 and 7/12 in order, smallest first.
Find a common bottomLCM of 3, 8 and 12 is 24
Rewrite2/3 = 16/24, 5/8 = 15/24, 7/12 = 14/24
Now the tops decide it7/12 < 5/8 < 2/3
Check with decimals0.583, 0.625, 0.667. Two independent methods agreeing is worth the extra thirty seconds.
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