Multiplication of Fractions

​Fractions

• Multiplication

• Division

Multiple Choice

Change this mixed number to an improper fraction

$$3\ \frac{5}{7}$$  

• $$\frac{26}{7}$$  

• $$\frac{15}{7}$$  

• $$\frac{21}{7}$$  

Multiple Choice

Change this mixed number to an improper fraction

$$8\ \frac{1}{2}$$  

• $$\frac{16}{2}$$  

• $$\frac{17}{2}$$  

• $$\frac{8}{2}$$  

​Multiplying Fractions

​Steps:

1. Multiply the two numerators

2. Multiply the two denominators

3. Simplify the fraction by dividing both the numerator and denominator by their largest common factor, if needed.

​Multiplying Fractions

​Steps:

1. Multiply the numerators

2. Multiply the denominators

3. Simplify the fraction by dividing both the numerator and denominator by their largest common factor, if needed.

Multiple Choice

What must be done in multiplying mixed numbers?

• Change mixed numbers to improper fractions before multiplying them.

• Multiply first the whole numbers.

• Multiply separately the fractions from the whole numbers.

• Multiply the product of the whole numbers to the product of the fractions.

Multiple Choice

$$Multiply\ and\ simplify\ if\ needed\ \frac{2}{3}\ \times\frac{6}{12}=$$  

• $$\frac{1}{3}$$  

• $$\frac{12}{36}$$  

• $$\frac{18}{24}$$  

• $$\frac{4}{12}$$  

Multiple Choice

Multiply and simplify if needed

• 5 / 9

• 3 / 10

• 1 / 4

• 23 / 20

Multiple Choice

$$What\ is\ the\ product\ of\ \frac{3}{5}\times\frac{8}{9}?$$  

• $$\frac{24}{41}$$  

• $$\frac{8}{15}$$  

• $$\frac{9}{45}$$  

Multiple Choice

$$Give\ the\ product\ of\ \frac{9}{13}\ and\ \frac{26}{12}.$$  

• $$\frac{3}{2}$$  

• $$\frac{5}{3}$$  

• $$\frac{2}{3}$$  

Multiple Choice

$$\frac{2}{3}\times\frac{3}{5}=$$  

• $$\frac{6}{15}$$  

• $$\frac{1}{5}$$  

• $$\frac{2}{5}$$  

• $$\frac{3}{5}$$  

Multiple Choice

$$\frac{5}{8}\times\frac{4}{10}=$$  

• $$\frac{1}{8}$$  

• $$\frac{4}{8}$$  

• $$\frac{1}{4}$$  

• $$\frac{2}{8}$$  

Multiple Choice

$$1\times\frac{2}{3}=$$  

• $$\frac{1}{10}$$  

• $$\frac{3}{10}$$  

• $$\frac{2}{3}$$  

• $$\frac{2}{7}$$  

Multiple Choice

$$1\frac{1}{3}$$  X  $$1\frac{1}{8}$$  =

• $$1\frac{1}{2}$$  

• $$1\frac{2}{3}$$  

• $$\frac{3}{4}$$  

• $$\frac{3}{8}$$  

Multiple Choice

$$2\frac{1}{2}$$  X  $$1\frac{3}{5}$$  =

• $$\frac{1}{4}$$  

• $$\frac{1}{2}$$  

• 2

• 4

Multiple Choice

$$1\frac{7}{8}\times2\frac{2}{9}=$$  

• $$3\frac{1}{6}$$  

• $$3\frac{19}{27}$$  

• $$4\frac{1}{6}$$  

• $$4\frac{4}{9}$$  

Multiple Choice

Will the product of the following multiplication problem get larger than 8, smaller than 8 or equal 8?

$$\frac{8}{1}$$ x $$\frac{9}{8}$$

• product will get smaller than 8

• product will get larger than 8

• product will stay the 8

Multiple Choice

Will the product of the following multiplication problem get larger than 4, smaller than 4, or equal 4?

4 x $$\frac{5}{6}$$

• product will get smaller than 4

• product will get larger than 4

• product will stay the 4

Math Response

$$\frac{3}{4\ }of\ 6$$  

Type answer here

Correct Answer: 4\frac{1}{2}

Deg^°

Rad

Math Response

$$\frac{1}{2}of\ 16$$  

Type answer here

Correct Answer: 8

Deg^°

Rad

​Vocabulary Words

​Improper Fraction - Fraction whose numerator is larger than the denominator.

​

​Whole Number - A fraction where the denominator is always 1.

​

Simplifying Fractions - ​dividing the numerator and denominator by the same number. Placing the fraction in lowest terms.

Denominator - The bottom number of a fraction that tells how many equal parts are in the whole.

​

​Numerator - The top number of a fraction that tells how many parts of a whole are being considered.

​

​KCF - Keep, Change Flip

​

Reciprocal - ​any two numbers whose product is one when multiplied (flipped fraction)

​

Mixed Number - ​a number including a whole number and a fraction.

​

​

​

Steps to follow for dividing fractions

Step 1 - Only have fractions in the division sentence

Make sure you do not have any mixed numbers in the division sentence.

​

Step 2 - Keep, Change, Flip

Keep the first fraction the same, change the division sign to multiplication, and flip the second fraction.

​

Step 3 - ​Multiply

You will multiply straight across. Simplify if needed and convert to a mixed number. ​

Dividing Fractions

​Dividing Fractions

Multiple Choice

22/5 is the reciprocal of ____________?

• 4.4

• 4  4/10

• 22/5

• 5/22

Multiple Choice

What is the reciprocal of 2?

• 4

• 1/2

• 2/1

• 2/2

Multiple Choice

What is the reciprocal of  $$\frac{5}{8}$$  

• $$\frac{8}{5}$$  

• $$\frac{5}{8}$$

• $$-\ \frac{5}{8}$$  

• $$-\ \frac{8}{5}$$  

Multiple Choice

What is the reciprocal of 12/7?

• 7/12

• 1  5/7

• 3/6

• 12/7

Multiple Choice

What is the reciprocal of 2/3?

• 2/3

• 1/4

• 3/2

• 4/6

Match

Match the following fraction with the reciprocal

• 1/6

• 3/4

• 2/7

• 9/10

• 3/8

6

4/3

7/2

10/9

8/3

• 6

• 4/3

• 7/2

• 10/9

• 8/3

Multiple Choice

$$\frac{5}{6}\div\frac{3}{4}$$  

Divide the fractions. Simplify the answer if needed.

• 15/24

• 20/18

• 10/9

• 18/24

Multiple Choice

$$\frac{6}{7}\div\frac{1}{4}$$  

Divide the fractions. Simplify the answer if needed.

• 24/7

• 6/28

• 3/14

• 7/24

Multiple Choice

$$\frac{2}{3}\div\frac{5}{4}$$  

Divide the fractions. Simplify the answer if needed.

• $$\frac{15}{8}$$

• $$\frac{8}{15}$$

• $$\frac{10}{12}$$

• $$\frac{5}{6}$$

Drag and Drop

Steps in dividing a whole number and a fraction:

1. ​ ​​

Placeholder

2. ​

Placeholder

3. ​

Placeholder

4. ​

Placeholder

Drag these tiles and drop them in the correct blank above

Convert the whole number into a fraction

KCF

Multiply the numerators and denominators

Simplify if needed

Multiple Choice

When dividing fractions, we use KCF:

• Keep, Circle, Flip

• Keep, Change, Fraction

• Keep, Change, Flip

Multiple Choice

What is the reciprocal of $$3\frac{7}{8}$$  

• $$\frac{31}{8}$$  

• $$\frac{8}{31}$$  

• $$3\frac{8}{7}$$  

Math Response

$$6\div\frac{1}{2}$$

Divide and simplify if needed.

Type answer here

Correct Answer: 12

Deg^°

Rad

Math Response

$$3\div\frac{2}{3}$$

Divide and simplify if needed.

Type answer here

Correct Answer: \frac{9}{2}

Deg^°

Rad

Math Response

$$4\div\frac{3}{5}$$

Divide and simplify if needed.

Type answer here

Correct Answer: \frac{20}{3}

Deg^°

Rad

Open Ended

Divide the following fractions.

$$6\frac{3}{4}\div\frac{4}{5}$$  

Multiple Choice

When dividing with mixed numbers, you have to _______ before you start.

• Change mixed numbers to improper fractions

• Change improper fractions to mixed numbers

• Divide the whole numbers first

Open Ended

Divide the following fractions.

$$\frac{7}{8}\div2\frac{1}{5}$$  

Multiple Choice

$$\frac{6}{7}\div5$$

• $$\frac{2}{7}$$  

• $$\frac{6}{35}$$  

• $$\frac{35}{6}$$  

Multiple Choice

Ashley's mom made $$6\frac{1}{2}$$  pounds of homemade sweet potato chips for a potato chip party. If there are a total of 8 people at the party, how many pounds of sweet potato chips does each person get to enjoy?

• $$\frac{13}{16}$$  of a pound

• $$8\frac{1}{4}$$  of a pound

Multiple Choice

Ashley has $$5\frac{1}{2}$$  kg of sugar. She wants to make cookies for her friends. The cookie recipe calls for $$\frac{2}{3}$$  kg of sugar per dozen cookies.

How many dozen cookies can she make?

• $$6\frac{1}{3}$$  dozen

• $$7\frac{1}{5}$$  dozen

• $$8\frac{1}{4}$$  dozen

Multiple Choice

Which of the following is NOT a rule in dividing fractions?

• Division turns to multiplication while the divisor is changed into its multiplicative inverse.

• Divide the numerator by numerator and denominator by denominator.

• Retain the dividend.

• Proceed to multiplication of fractions after changing the operation and divisor by their inverses.

Multiple Choice

Which of the following is the quotient of $$3\frac{5}{9}\div\frac{2}{3}$$ in simplest form?

• $$3\frac{5}{6}$$  .

• $$3\ \frac{10}{27}$$  

• $$\frac{96}{18}$$  

• $$5\ \frac{1}{3}$$  

Multiple Choice

Follow all steps to divide

$$3\ \frac{3}{4}\div2\ \frac{7}{8}$$  

• $$6\ \frac{21}{32}$$  

• $$\frac{30}{23}$$  

• $$1\ \frac{7}{23}$$  

Multiple Choice

A baker has 24 cupcakes. $$\frac{1}{4}$$  of them are chocolate.The rest are strawberry.How many are strawberry?

• 6

• 8

• 12

• 18

Multiple Choice

A team of runners is needed to run a ¹/₄ mile relay race . If each runner must run ¹/₁₆ mile.  How many runners do they need to run the race?

• 4

• 5

• 1/64

• 2

Multiple Choice

Teacher Sab conducts piano lessons 5 days every week. Each lesson lasts for $$1\frac{4}{5}$$  hour. How many hours in a week does Sab teach piano?

• 7

• 8

• 9

• 10

Multiple Choice

Tasha eats half her snack and gives the other half to her 2 best friends for them to share equally. What portion of the whole snack does each friend get?

• 4

• $$\frac{1}{2}$$

• $$\frac{1}{4}$$

• 2

Multiple Choice

Mrs. Silverstein bought 3 cakes for a birthday party. She cuts each cake into quarters (1/4) and plans to serve each guest one quarter of a cake. How many guests can she serve with all of her cakes?

• $$\frac{1}{12}$$

• 12

• 20

• 36

Multiple Choice

Damien has a bucket of popcorn. He puts $$\frac{1}{2}$$   of it away for later.  The rest of the popcorn is shared with himself and 3 friends. What fraction of the bucket of popcorn does each person get?

• $$\frac{1}{6}$$  

• $$\frac{3}{2}$$  

• $$\frac{1}{8}$$  

• 1

Multiple Choice

Kamari completed his math homework in 1/3 of an hour.

He had to complete 4 math problems.

He spent an equal amount of time on each problem.

How much of an hour did Kamari spend on each problem?

• 1/12

• 1/7

• 3/4

• 12

Multiple Choice

Andrea has 80 coins in her collection. She shared 3/4 of her collection with friends. How many coins did she share?

• 20

• 50

• 60

• 70

Multiple Choice

A stack of boards is 21″ high. Each board is 1¾″ thick. How can you find the number of boards?

• 21 × 1¾

• 1¾ ÷ 21

• 21 ÷ 1¾

Multiple Choice

There are 12 yards of fabric. Each pillow uses 2/3 yard. How many pillows can be made?

• 8 pillows

• 12 pillows

• 18 pillows

Multiple Choice

Twelve whole pizzas are eaten. Each person eats ¼ pizza. How many people eat pizza?

• 48 people 

• 16 people

• 8 people

• 3 people

Multiple Choice

A 21-foot long rope is cut into 3/8-foot pieces. Which expression finds the number of pieces?

• 21 ÷ 3/8

• 21 × 3/8

• 3/8 ÷ 21

• 21 − 3/8

Multiple Choice

A recipe calls for 2/5 of a pound of chicken for each person. If there are 8 people to be fed, how many pounds of chicken are required?

• 1/5 pound

• 3 1/5 pounds

• 2 2/5 pounds

• 20 pounds

Multiple Choice

Kai spent 24 days at Grandma's house last summer.

His sister spent ⅜ of that time at Grandma's.

How many days did Kai's sister spend at Grandma's house last summer?

• 6 days

• 9 days

• 14 days

• 64 days

Multiple Choice

Jaz read for 4/8 of an hour every day of the week. How many hours does she read each week?

• 3 1/2 hours

• 3 hours

• 2 4/8 hours

• 4 hours

Multiple Choice

To stay healthy, we should drink 6 1/2 glasses of water a day. If we follow this guideline, how much water would we drink in a full week?

• 32 1/2 cups

• 45 cups

• 33 cups

• 45 1/2 cups

Multiple Choice

There are 2 cups of chocolate chips in a bag. If the serving is $$\frac{1}{3}$$   of a cup, how many servings are there in a bag?

• $$\frac{1}{6}$$ serving

• 6 servings

Multiple Choice

Corey had $$\frac{1}{4}$$   of a yard of fabric. He cuts the fabric into 5 equal pieces. How long is each piece of fabric?

• 20 yd.

• $$\frac{1}{20}$$   yd.