Dividing Fractions - Keep, Change, Flip

Pre-Algebra · Axiom Academy

LESSON Dividing Fractions: Keep, Change, Flip See why dividing by a fraction is the same as multiplying by its reciprocal — then run the Keep-Change-Flip shortcut on real problems. 1. Division Asks "How Many Fit?" Before any rule, remember what division means . is not scary — it just asks: how many halves fit inside 3? How many -pieces fit into 3 whole bars? 2. Why Flipping the Fraction Works Here is the heart of it. Ask "how many 's make a whole?" A quarter is one of 4 equal pieces — so it takes 4 of them to rebuild the whole. Counting how many 's fit is the same as scaling up by 4 . 3. The Shortcut: Keep, Change, Flip Now we can name the three moves that turn any fraction division into a multiplication. Watch what happens to : KEEP the first fraction exactly as it is. FLIP the second fraction (swap top and bottom — its reciprocal). Keep-Change-Flip turned the problem into . To multiply fractions, multiply straight across — tops together, bottoms together — then simplify. 5. Your Turn: A Recipe Problem A recipe needs cup of flour. You have 4 cups. How many batches can you make? That is "how many 's fit in 4?" — a division, . Write 4 as , then Keep, Change, Flip. You didn't just memorize "flip and multiply" — you saw why dividing by a fraction counts how many pieces fit, which is the same as scaling by the reciprocal.

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