lesson
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Imagine two identical pizza boxes: one has 43 of a pizza left, and the other has 65. Both are missing exactly one slice, so are they equal, or is one box holding more food?
To solve this without guessing, we need clear visual and numerical justifications to prove which fraction is larger.
Missing Piece Strategy
When two fractions are both one unit slice away from 1 whole, compare the size of the missing piece.
Cutting a whole into 6 equal pieces makes each piece smaller than cutting it into 4 equal pieces, which means 61<41.
📊Create an interactive visual comparison between 3/4 and 5/6 using two horizontal bar models of identical length. Top bar: divided into 4 equal segments, 3 shaded in blue, 1 unshaded segment labeled 'Missing 1/4'. Bottom bar: divided into 6 equal segments, 5 shaded in green, 1 unshaded segment labeled 'Missing 1/6'. A dotted vertical guide shows that 1/6 is smaller than 1/4, making the 5/6 bar longer. Include a bold callout: 'Smaller missing piece = Larger fraction remaining'. Card background #ffffff, text #1e2945, border #e6e6e6.
Since 65 is missing a smaller piece, it leaves more pizza behind, proving that 65>43.
What happens when fractions aren't close to 1 whole and have completely different missing pieces?
Common Denominators
A common denominator splits two different wholes into identical, same-sized parts so we can compare the numerators directly.
Let's compare 83 and 125 by finding a shared multiple of their denominators, 8 and 12.
Multiplying 83 by 33 gives the equivalent fraction 249, while multiplying 125 by 22 gives 2410.
📊Show two side-by-side transformation cards for equivalent fractions. Left card: 3/8 with arrows showing multiplication of top and bottom by 3 to reach 9/24. Right card: 5/12 with arrows showing multiplication of top and bottom by 2 to reach 10/24. Below both cards, show two fraction bars divided into 24 tiny equal sections: one bar has 9 sections filled in blue (labeled 9/24), the second has 10 sections filled in purple (labeled 10/24). Highlight that 10/24 > 9/24.