Keeping the whole consistent when comparing fractions
Before comparing fractions, check that their wholes are the same size. Comparing only shaded areas of differently sized shapes can obscure the meaning of numerator and denominator.
Try it yourself first.
Draw two strips of equal length. Divide one into four equal parts and the other into eight. Shade three parts of the first and six of the second. Compare the shaded lengths.
View the solution or example answer
3/4 and 6/8 represent equal lengths. Halving each quarter increases the number of pieces without changing the shaded proportion. This shows why the fractions are equivalent.
Your next step.
Before simplifying fractions, use a drawing to explain why dividing the numerator and denominator by the same number preserves the value. Keep the meaning clear as the calculation becomes shorter.
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