A focused Grade 6 learning session for Dividing Fractions by Fractions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving dividing fractions by fractions.
Dividing Fractions by Fractions means using equal parts, number lines, and clear fraction language to describe parts of a whole.
For Dividing Fractions by Fractions, a useful visual model is a quick drawing, array, table, number line, graph, or labeled diagram that shows what each number means.
Question: What is \(\frac{3}{4}\div\frac{1}{2}\)?
Answer: \(1\frac{1}{2}\)
Question: Evaluate: \(\frac{5}{6}\div\frac{1}{3}\)
Answer: \(\frac{5}{2}\) or \(2\frac{1}{2}\)
Question: A recipe calls for \(\frac{3}{4}\) cup of sugar. If you want to make exactly half of the recipe (so that every ingredient is halved), how much sugar do you need? Which expression represents this situation?
Why it works: "Half the recipe" means multiply each ingredient by \(\frac{1}{2}\), not divide by \(\frac{1}{2}\). So you want \(\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}\) cup of sugar.
Answer: \(\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}\) cup
Dividing Fractions by Fractions becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Equal parts first, fraction name second.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is \(\frac{3}{4}\div\frac{1}{2}\)?
Answer C: \(1\frac{1}{2}\)
Friendly reminder: when you divide by a fraction, you can multiply by its reciprocal (“flip” the divisor and multiply). \(\frac{3}{4}\div\frac{1}{2}=\frac{3}{4}\times\frac{2}{1}=\frac{6}{4}\), which simplifies to \(\frac{3}{2}\), or \(1\frac{1}{2}\).
Evaluate: \(\frac{5}{6}\div\frac{1}{3}\)
Answer C: \(\frac{5}{2}\)
Rewrite the division as multiplication by flipping \(\frac{1}{3}\): \(\frac{5}{6}\times\frac{3}{1}=\frac{15}{6}\). Simplify \(\frac{15}{6}\) to \(\frac{5}{2}\) (or mixed form \(2\frac{1}{2}\)).
What is \(\frac{2}{3}\div\frac{4}{5}\)?
Answer B: \(\frac{5}{6}\)
Invert \(\frac{4}{5}\) to \(\frac{5}{4}\), then multiply: \(\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}\). That reduces nicely to \(\frac{5}{6}\).
Compute: \(\frac{7}{8}\div\frac{1}{4}\)
Answer C: \(3\frac{1}{2}\)
\(\frac{7}{8}\times\frac{4}{1}=\frac{28}{8}=\frac{7}{2}=3\frac{1}{2}\).
A recipe calls for \(\frac{3}{4}\) cup of sugar. If you want to make exactly half of the recipe (so that every ingredient is halved), how much sugar do you need? Which expression represents this situation?
Answer B: \(\frac{3}{4}\times\frac{1}{2}\)
"Half the recipe" means multiply each ingredient by \(\frac{1}{2}\), not divide by \(\frac{1}{2}\). So you want \(\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}\) cup of sugar.
What is \(\frac{4}{5}\div\frac{2}{3}\)?
Answer D: \(\frac{6}{5}\)
\(\frac{4}{5}\times\frac{3}{2}=\frac{12}{10}=\frac{6}{5}\).
How many \(\frac{1}{4}\)-cup servings are in \(2\) cups?
Answer B: \(8\)
You are counting how many \(\frac{1}{4}\)-cup servings fit inside \(2\) cups---that’s a division problem: \(2\div\frac{1}{4}\). Rewrite as \(2\times 4\), which equals \(8\) servings.
Evaluate: \(\frac{1}{2}\div\frac{1}{8}\)
Answer B: \(4\)
Dividing by \(\frac{1}{8}\) is the same as multiplying by \(8\). So \(\frac{1}{2}\div\frac{1}{8}=\frac{1}{2}\times 8\), which simplifies to \(4\).
A trail is \(3\frac{1}{2}\) miles long. How many \(\frac{3}{4}\)-mile lengths fit along the trail?
Answer C: \(4\frac{2}{3}\)
Change \(3\frac{1}{2}\) to \(\frac{7}{2}\), then divide by multiplying by \(\frac{4}{3}\): \(\frac{7}{2}\times\frac{4}{3}=\frac{28}{6}\), which simplifies to \(\frac{14}{3}\) or \(4\frac{2}{3}\) lengths along the trail.
What is \(\frac{9}{10}\div\frac{3}{5}\)?
Answer D: \(\frac{3}{2}\)
\(\frac{9}{10}\times\frac{5}{3}=\frac{45}{30}=\frac{3}{2}\).
Compute: \(\frac{6}{7}\div\frac{2}{3}\)
Answer B: \(\frac{9}{7}\)
\(\frac{6}{7}\times\frac{3}{2}=\frac{18}{14}=\frac{9}{7}\).
