A focused Grade 5 learning session for Multiplying Fractions by Fractions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can multiply fractions by fractions.
Multiplying Fractions by Fractions is the Grade 5 skill of students multiply a fraction by a fraction, understanding the product (a/b) × (c/d) = ac/bd. They use area models to visualize the multiplication and understand why the product is smaller than either factor when both are less than 1.
Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.
The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.
Question: The area model below shows \(\frac{1}{2} \times \frac{3}{4}\). What fraction is shaded (overlap region)?
How the model helps: The rectangle is divided into 8 equal parts (4 columns \(\times\) 2 rows). The overlap covers 3 of those 8 parts, so \(\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}\).
Question: The rectangle model shows the overlapping shaded region for \(\frac{3}{5} \times \frac{2}{3}\). What fraction of the whole rectangle is overlapped?
Answer: \(\frac{6}{15}=\frac{2}{5}\)
Question: Area model for \(\frac{3}{4} \times \frac{1}{2}\). The shaded (overlap) region represents what fraction?
Answer: \(\frac{3}{8}\)
Question: A recipe calls for \(\frac{2}{3}\) cup of flour. You want to make \(\frac{1}{2}\) of the recipe. How much flour do you need?
Answer: \(\frac{1}{3}\) cup
Why it works: \(\frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3}\) cup.
Multiplying Fractions by Fractions gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
Keep the whole consistent, show equal parts clearly, and explain what the fraction means.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is \(\frac{2}{3} \times \frac{1}{4}\)?
Answer C: \(\frac{2}{12}\) or \(\frac{1}{6}\)
Multiply the numerators and denominators: \(\frac{2}{3}\times\frac{1}{4}=\frac{2}{12}\). Since both 2 and 12 can be divided by 2, the product simplifies to \(\frac{1}{6}\).
Multiply: \(\frac{1}{2} \times \frac{1}{3}\)
Answer B: \(\frac{1}{6}\)
Multiply numerators and denominators: \(\frac{1 \times 1}{2 \times 3} = \frac{1}{6}\).
The area model below shows \(\frac{1}{2} \times \frac{3}{4}\). What fraction is shaded (overlap region)?
Answer A: \(\frac{3}{8}\)
The rectangle is divided into 8 equal parts (4 columns \(\times\) 2 rows). The overlap covers 3 of those 8 parts, so \(\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}\).
Multiply: \(\frac{2}{3} \times \frac{3}{4}\)
Answer B: \(\frac{1}{2}\)
\(\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}\), which simplifies to \(\frac{1}{2}\).
What is \(\frac{3}{4} \times \frac{2}{5}\) in simplest form?
Answer B: \(\frac{3}{10}\)
\(\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}\) (divide by 2).
The shaded overlap represents \(\frac{2}{3} \times \frac{2}{5}\). What fraction of the whole rectangle is shaded?
Answer C: \(\frac{4}{15}\)
The rectangle has 15 cells (5 columns \(\times\) 3 rows). The shaded overlap region is 4 cells out of 15, so \(\frac{4}{15}\).
Multiply \(\frac{2}{3} \times \frac{3}{4}\). Which choice shows the product in simplest form?
Answer D: \(\frac{1}{2}\)
Multiply the numerators and denominators: \(\frac{2}{3}\times\frac{3}{4}=\frac{6}{12}\). Since 6 is half of 12, \(\frac{6}{12}=\frac{1}{2}\).
Sarah has \(\frac{3}{4}\) of a pound of chocolate. She uses \(\frac{1}{3}\) of it to make brownies. How much chocolate does she use?
Answer A: \(\frac{3}{12}\) pounds or \(\frac{1}{4}\) pounds
\(\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}\) pound.
Multiply: \(\frac{1}{4} \times \frac{1}{5}\)
Answer C: \(\frac{1}{20}\)
\(\frac{1}{4} \times \frac{1}{5} = \frac{1}{20}\) (multiply numerators and denominators).
The rectangle model shows the overlapping shaded region for \(\frac{3}{5} \times \frac{2}{3}\). What fraction of the whole rectangle is overlapped?
Answer A: \(\frac{6}{15}=\frac{2}{5}\)
The rectangle has 15 equal cells. The overlap covers 6 cells, so the product is \(\frac{6}{15}=\frac{2}{5}\).
Multiply: \(\frac{2}{5} \times \frac{2}{3}\)
Answer C: \(\frac{4}{15}\)
\(\frac{2}{5} \times \frac{2}{3} = \frac{2 \times 2}{5 \times 3} = \frac{4}{15}\).
