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Questions and Answers
Explain how you would model $5 \times \frac{2}{3}$.
Explain how you would model $5 \times \frac{2}{3}$.
I would draw five circles and shade each circle to show $\frac{2}{3}$.
When you multiply $\frac{2}{3}$ by a fraction less than one, how does the product compare to the factors?
When you multiply $\frac{2}{3}$ by a fraction less than one, how does the product compare to the factors?
The product will be less than both factors since I am finding part of a part.
What is $\frac{2}{3} \times 6$?
What is $\frac{2}{3} \times 6$?
4
What is $\frac{4}{5} \times 7$?
What is $\frac{4}{5} \times 7$?
What is $8 \times \frac{5}{7}$?
What is $8 \times \frac{5}{7}$?
What is $\frac{7}{8} \times \frac{3}{8}$?
What is $\frac{7}{8} \times \frac{3}{8}$?
What is $\frac{1}{2} \times \frac{3}{4}$?
What is $\frac{1}{2} \times \frac{3}{4}$?
What is $\frac{7}{8} \times \frac{4}{7}$?
What is $\frac{7}{8} \times \frac{4}{7}$?
What is $2 \times \frac{3}{11}$?
What is $2 \times \frac{3}{11}$?
What is $\frac{5}{8} \times \frac{2}{3}$?
What is $\frac{5}{8} \times \frac{2}{3}$?
What is $\frac{7}{12} \times 8$?
What is $\frac{7}{12} \times 8$?
$3 \times \frac{2}{3}$ will be ____________ 3.
$3 \times \frac{2}{3}$ will be ____________ 3.
$\frac{5}{7} \times 3$ will be ____________ 5/7.
$\frac{5}{7} \times 3$ will be ____________ 5/7.
There is $\frac{5}{6}$ of an apple pie left from dinner. Tomorrow, Ms. McKay plans to eat $\frac{1}{6}$ of the pie that was left. How much of the whole pie will be left after she eats tomorrow?
There is $\frac{5}{6}$ of an apple pie left from dinner. Tomorrow, Ms. McKay plans to eat $\frac{1}{6}$ of the pie that was left. How much of the whole pie will be left after she eats tomorrow?
If the recipe calls for $\frac{2}{3}$ cup of oil, how much oil will they need if they want to make 4 times the amount?
If the recipe calls for $\frac{2}{3}$ cup of oil, how much oil will they need if they want to make 4 times the amount?
Write an expression that matches Matt's model.
Write an expression that matches Matt's model.
$\frac{3}{3} \times \frac{4}{7}$ is __________________ 4/7.
$\frac{3}{3} \times \frac{4}{7}$ is __________________ 4/7.
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Study Notes
Multiplication of Fractions
- Modeling multiplication of fractions can be visualized by using circles; for example, modeling 5 x 2/3 involves drawing five circles and shading 2/3 of each.
- When multiplying a fraction (like 2/3) by another fraction less than one, the product is smaller than both factors, representing "part of a part."
Specific Fraction Multiplications
- Multiplying 2/3 by 6 results in 4.
- For 4/5 multiplied by 7, the product is 5 3/5.
- 8 times 5/7 equals 5 5/7.
- The multiplication of 7/8 by 3/8 results in 21/64.
- Half (1/2) multiplied by 3/4 equals 3/8.
- 7/8 multiplied by 4/7 simplifies to 1/2.
- The product of 2 and 3/11 yields 6/11.
- 5/8 multiplied by 2/3 gives 5/12.
- Multiplying 7/12 by 8 results in 4 2/3.
Relationships in Multiplication
- 3 x 2/3 is less than 3.
- Multiplying 5/7 by 3 results in a value greater than 5/7.
Real-Life Applications
- If there is 5/6 of an apple pie left and Ms. McKay plans to eat 1/6 of it, 25/36 of the whole pie remains after her consumption.
- If a recipe calls for 2/3 cup of oil and the desired amount is quadrupled, a total of 2 2/3 cups of oil is needed.
Mathematical Expressions
- An expression corresponding to a model could be represented as 1/3 x 3/4.
- The equation 3/3 x 4/7 equates to 4/7, demonstrating equal values.
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