AI Study GuruUnderstand the idea
Multiply or divide the top and bottom of a fraction by the same number and the value stays the same. That is because you cut the whole into more pieces but take proportionally more of them. So 1 out of 2 equals 2 out of 4 and 3 out of 6. To simplify, divide top and bottom by their common factor until no common factor except 1 remains. To check equivalence, cross multiply: for a over b and c over d, compare a times d with b times c. Equal products mean equal fractions.
See a worked example
Half a chocolate bar equals two quarters. 1 over 2 becomes 2 over 4 when top and bottom are doubled. Divide 6 over 8 by 2 and 2 to get 3 over 4. Cross check: 2 times 6 equals 12 and 3 times 4 equals 12, so 2 over 3 equals 4 over 6.
A useful check
A common error is adding the same number to top and bottom instead of multiplying. Adding changes the value. Only multiplying or dividing both by the same number keeps the fraction equivalent.
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