Multiplying and Dividing Fractions Lesson

​Dividing Fractions and Mixed Numbers

​School Year 2022-2023

​Essential Question: How do you fluently divide fractions and mixed numbers?

Students will:

• Compute quotients of fractions divided by fractions (including mixed numbers).

  Interpret quotients of fractions.

  Solve word problems involving division of fractions by fractions.​

​As always, let's start with some review...

Open Ended

In the expression:

124.6 ÷ 0.23

How do you determine how many times you must move the decimal point?

Time to head to the world of dividing fractions...​

Multiple Choice

3.) Find the reciprocal of $$\frac{3}{4}$$  

• 34

• $$\frac{4}{3}$$  

• $$-\frac{3}{4}$$  

• $$-\frac{4}{3}$$  

Multiple Choice

4.)  Find the reciprocal of $$\frac{6}{7}$$  

• 67

• $$-\frac{6}{7}$$  

• $$-\frac{7}{6}$$  

• $$\frac{7}{6}$$  

Multiple Choice

5.) Find the reciprocal of 4.

• $$\frac{1}{4}$$  

• $$-\frac{1}{4}$$  

• $$-\frac{7}{6}$$  

• $$\frac{7}{6}$$  

Multiple Choice

6.)  Find the reciprocal of  $$2\frac{2}{3}$$  

• $$\frac{8}{3}$$  

• $$-\frac{8}{3}$$  

• $$\frac{3}{8}$$  

• $$-\frac{3}{8}$$  

Multiple Choice

7.) How many $$\frac{1}{2}$$  foot pieces can you cut out of a 7 foot piece of wood?

• 3.5 pieces

• 7 pieces

• 14 pieces

• 18 pieces

Multiple Choice

8.)  Papa Millstein wants to divide a  $$\frac{5}{8}$$   pound bag of trail mix into 10 equal bags.  How much trail mix will each bag contain? 

• $$\frac{15}{8}$$  pounds

• $$\frac{1}{5}$$  pound

• 16 pounds

• $$\frac{1}{16}$$  pound

Fill in the Blanks

Multiplying and Dividing Fractions

I can multiply and divide fractions.

​I can multiply and divide negative fractions.

​Vocabulary

​Reciprocal - a reciprocal of a number is another number than, when multiplied together, their product is 1. To find the reciprocal of a fraction, flip the fraction.

Multiple Choice

I can multiply fractions.

$$\frac{1}{4}\cdot\frac{3}{5}=$$  

• $$\frac{3}{9}$$  

• $$\frac{1}{3}$$  

• $$\frac{5}{12}$$  

• $$\frac{3}{20}$$  

Multiple Choice

I can multiply fractions.

$$\frac{1}{8}\cdot\frac{8}{11}=$$  

Make sure to simplify!

• $$\frac{11}{64}$$  

• $$\frac{8}{11}$$  

• $$\frac{1}{11}$$  

• $$\frac{8}{88}$$  

Multiple Choice

I can divide fractions.

$$\frac{1}{3}\div\frac{2}{7}=$$  

• $$\frac{7}{6}$$  

• $$\frac{6}{7}$$  

• $$\frac{2}{21}$$  

• $$\frac{21}{2}$$  

Multiple Choice

I can divide fractions.

$$\frac{3}{5}\div\frac{4}{5}$$  

Make sure to simplify!

• $$\frac{3}{4}$$  

• $$\frac{12}{25}$$  

• $$\frac{15}{20}$$  

• $$\frac{25}{12}$$  

Multiple Choice

I can multiply fractions.

$$\frac{1}{4}\cdot\left(-\frac{3}{5}\right)=$$  

• $$\frac{3}{9}$$  

• $$\frac{3}{20}$$  

• $$\frac{5}{12}$$  

• $$-\frac{3}{20}$$  

Multiple Choice

I can multiply fractions.

$$-\frac{1}{8}\cdot\left(-\frac{8}{11}\right)=$$  

Make sure to simplify!

• $$\frac{11}{64}$$  

• $$-\frac{8}{11}$$  

• $$\frac{1}{11}$$  

• $$-\frac{8}{88}$$  

Multiple Choice

I can divide fractions.

$$-\frac{1}{3}\div\left(-\frac{2}{7}\right)=$$  

• $$\frac{7}{6}$$  

• $$\frac{6}{7}$$  

• $$\frac{2}{21}$$  

• $$\frac{21}{2}$$  

Multiple Choice

I can multiply and divide negative fractions.

$$-\frac{3}{5}\div\frac{4}{5}$$  

Make sure to simplify!

• $$-\frac{3}{4}$$  

• $$\frac{12}{25}$$  

• $$\frac{3}{4}$$  

• $$\frac{15}{20}$$