6.1.4 Multiplying Mixed Numbers

• I can multiply proper fractions, improper fractions and mixed numbers using a variety of strategies

• I can estimate the product of a fraction or decimal multiplication problem.

​Without calculating, estimate approximately how far you think Jules has run. Explain your estimation strategy to your teammates.

Math Response

On your whiteboard, draw a generic rectangle and help Jules calculate.   $$2\frac{2}{3}\cdot4\frac{3}{5}$$

Type your final answer in the box.

Type answer here

Correct Answer: 12\frac{4}{15}

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​Mrs. McElveen plans to plant a section of the school garden with tomatoes.  The section measures 2.5 meters by 7.75 meters.  She is wondering how much area the tomato plants will cover.  Owen made the sketch below to help determine the area. 

Open Ended

How does Owen’s sketch shows an area of 2.5 meters by 7.75 meters?

Math Response

On your whiteboard, copy and complete the generic rectangle by filling in the area of each part.  Use decimals or fractions. How much area in the school garden is Mrs. McElveen using for tomato plants?

Type answer here

Correct Answer: 19\frac{3}{8}

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Dropdown

Each batch of Anita’s famous bran muffins calls for $$3\frac{1}{3}$$  cups of bran.  Anita wants to make  $$2\frac{3}{4}$$  batches of muffins so that she has enough for everyone in her class. Which type of problem is this? ​ ​ ​

Select answer

Math Response

Wait! Instead of drawing the entire generic rectangle, maybe we can change the mixed numbers to improper fractions and then multiply!

Change $$3\frac{1}{3}$$ to an improper fraction.

Type answer here

Correct Answer: \frac{10}{3}

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Math Response

Now change $$2\frac{3}{4}$$ to an improper fraction.

Type answer here

Correct Answer: \frac{11}{4}

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Math Response

Nice!

$$3\frac{1}{3}=\frac{10}{3}$$ and $$2\frac{3}{4}=\frac{11}{4}$$

Now we can multiply $$\frac{10}{3}\times\frac{11}{4}$$ .

Try it!

Type answer here

Correct Answer: \frac{110}{12}

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Math Response

Try a new one!

$$2\frac{2}{3}\cdot\frac{3}{11}$$

Change the mixed numbers to improper fractions using MAD.

Then multiply the improper fractions using the Train Track strategy.

Type answer here

Correct Answer: \frac{24}{33}

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Math Response

Try a new one!

$$\frac{4}{7}\cdot2\frac{1}{2}$$

Change the mixed numbers to improper fractions using MAD.

Then multiply the improper fractions using the Train Track strategy.

Type answer here

Correct Answer: \frac{20}{14}

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