Multiplying and Dividing Rational Numbers

Multiplying Rational Numbers

8/31 Lesson

Vocabulary

● Product
● Both
● And
● But
● However

Multiple Choice

Convert into an improper fraction.

• $$\frac{37}{2}$$

• $$\frac{52}{7}$$

• $$\frac{7}{37}$$

• $$\frac{37}{7}$$

Multiple Choice

Convert into an improper fraction.

• $$\frac{15}{2}$$

• $$\frac{10}{5}$$

• $$\frac{17}{5}$$

• $$\frac{11}{2}$$

Match

Match the following

• $$3\frac{1}{2}$$  

• $$2\frac{5}{7}$$  

• $$6\frac{4}{5}$$  

• $$2\frac{4}{5}$$  

7/2

19/7

34/5

14/5

• 7/2

• 19/7

• 34/5

• 14/5

Learn: Multiply Numbers Rules

Same Sign = +ve

Different Sign = -ve

With an odd # of negatives, you will get a negative product.

Ex:
(-2)(-3)(-1)(-5)(-6)=Negative 180
There are 5 negatives

Odd # of Negatives

With an even # of negatives, you will get a positive product.

Ex:
(-2)(-3)(-5)(-6)= Positive 180
There are 4 negatives.

​Even # of Negatives

Multiplying with Multiple Negatives

Multiple Select

The product of six negative numbers would result in the answer being....

• positive

• negative

• zero

Multiple Select

The product of nine negative numbers would result in the answer being....

• positive

• negative

• zero

Multiple Choice

If I have a negative multiplied with a positive, what will the answer be?

• Positive 

• Negative 

Multiple Choice

If I have a positive multiplied with a positive, what will the answer be?

• Positive 

• Negative 

Multiple Choice

If I have two negatives what will the product be?

• Negative 

• Positive 

Learn: Multiply Rational Numbers

Multiple Choice

When you multiply two negatives, your answer is ____

• positive

• negative

Multiple Choice

$$\left(-\frac{3}{4}\right)\times\frac{1}{8}=$$  

• $$-\frac{3}{32}$$  

• $$\frac{3}{32}$$  

• $$\frac{4}{18}$$  

• $$-\frac{4}{18}$$  

Multiple Choice

$$\frac{1}{6}\left(\frac{3}{5}\right)$$  

• $$-\frac{1}{10}$$  

• $$\frac{1}{10}$$  

• $$\frac{5}{18}$$  

• $$-\frac{5}{18}$$  

Multiple Choice

$$-\frac{2}{7}\left(\frac{3}{5}\right)$$  

• $$-\frac{10}{21}$$  

• $$\frac{10}{21}$$  

• $$\frac{6}{35}$$  

• $$-\frac{6}{35}$$  

Multiple Choice

$$-\frac{6}{7}\left(-\frac{8}{9}\right)$$  

• $$\frac{16}{21}$$  

• $$-\frac{16}{21}$$  

• $$\frac{48}{7}$$  

• $$-\frac{48}{7}$$  

Learn: Multiply Rational Numbers: Different Forms

Multiple Choice

$$3\ \frac{1}{3}\times5$$  =

• $$\frac{35}{3}$$  

• $$\frac{11}{3}$$  

• $$\frac{50}{3}$$  

• $$\frac{65}{3}$$  

Multiple Choice

$$2\ \frac{3}{4}\times3$$  =

• $$\frac{65}{4}$$  

• $$\frac{55}{4}$$  

• $$\frac{33}{4}$$  

• $$\frac{44}{3}$$  

Multiple Choice

$$3\ \frac{1}{2}\times10$$  =

• 36

• 20

• 35

• 12

Multiple Choice

$$2\ \frac{1}{3}\ \left(-4\ \frac{1}{5}\right)$$  

• $$\frac{147}{15}$$  

• $$-\frac{147}{15}$$  

• $$-8\ \frac{1}{5}$$  

• $$8\ \frac{1}{5}$$  

Multiple Choice

4 x 0.03

• 12

• 0.12

• 120

• 0.012

Multiple Choice

11.3 × 2.5

• 79.1

• 13.8

• 22.597

• 28.25

Fill in the Blanks

Solve -6.5(-0.3)

Multiple Choice

11.3 × 2.5

• 79.1

• 13.8

• 22.597

• 28.25

Multiple Choice

Multiply and simplify if possible.

• - ¹ / ₁ ₈

• ¹ / ₁ ₈

• - ⁴ / ₉

• 3 ⁵ / ₇

Multiple Choice

Multiply and simplify if possible.

• - ¹ / ₉

• ¹ / ₉

• - 9

• 9

Multiplying Mixed Numbers

Step 1 Convert the mixed number into improper fraction

Step 2 Multiply the numerator by the numerator and the denominator by the denominator

Step 3 Simplify if possible

Multiple Choice

What is the product of 2 1/2 x 3/4 in simplest form?

• 1 5/8

• 2 5/8

• 1 7/8

• 7/8

Multiple Choice

What is the product of 24 and 1/8?

• 24/192

• 24/8

• 24 1/8

• 3

Multiple Choice

Sharon is making cookies. Her recipe calls for 2 1/4 cups of flour. She wants to make 3 1/2 times the recipe. How much flour will she need?

• 6 1/8 cups

• 6 3/4

• 63/8

• 7 7/8 cups

Multiple Choice

Tony's recipe for soup calls for 1 1/4 teaspoons of salt. He wants to use 1/2 that amount. How much salt will he use?

• 3/8 teaspoon

• 5/8 teaspoon

• 3/4 teaspoon

• 1 teaspooon

Fill in the Blanks

$-\frac{3}{2}\times\left(-\frac{4}{5}\right)$  

Fill in the Blanks

$-\frac{3}{2}\times\frac{4}{5}$  

Fill in the Blanks

$\frac{2}{5}\times\frac{4}{5}$  

Multiple Choice

Find the product.

• 9/24

• 9/28

• 6/32

• 1/28

Multiple Choice

Find the product. Then Simplify!

• 3/50

• 30/5

• 6

• 1 1/5

Multiple Choice

Find the product. 

• 2/14

• 1/49

• 2/7

• 1/14

Multiple Choice

Multiply. HINT: Change the mixed numbers to improper fractions (Texas 2 step).

• 3 1/10

• 85/20

• 4 5/20

• 4 1/4

Multiple Choice

Convert the mixed number into an improper fraction.

• 26/7

• 44/7

• 15/7

• 84/7

Applications of Rational Numbers

Directions: Answer the following questions related to operations of adding, subtracting, multiplying and dividing rational numbers (integers, decimals and fractions).

Multiple Choice

Jim biked 2 1/4 miles on Monday and 3 5/8 miles on Tuesday. To determine how much further he traveled on Tuesday than on Monday, you would...

• Add

• Subtract

• Multiply

• Divide

Open Ended

Jim biked 2 1/4 miles on Monday and 3 5/8 miles on Tuesday. How much further had he traveled on Tuesday than on Monday?

Multiple Choice

After a back to school party, 7 friends had 3 1/2 watermelons left over. If they each decided to take equal parts home, they would need to...

• Add

• Subtract

• Multiply

• Divide

Open Ended

After a back to school party, 7 friends had 3 1/2 watermelons left over. The each decided to take equal parts home. How much should each person take home?

Multiple Choice

Sherry needs 3 2/3 cups of sugar to bake a cake. She is baking 4 cakes for a church gathering. Sherry would need to _ to determine how many cups of sugar she needs for these cakes.

• Add

• Subtract

• Multiply

• Divide

Open Ended

Sherry needs 3 2/3 cups of sugar to bake a cake. She is baking 4 cakes for a church gathering. How many cups of sugar does she need for these cakes?

Multiple Choice

Richard had 3 pieces of rope. One piece was 3/8 yard long, another was 1 1/4 yards long, and the third was 2 1/2 yards long. To find the total amount of rope Richard had, you would need to...

• Add

• Subtract

• Multiply

• Divide

Open Ended

Richard had 3 pieces of rope. One piece was 3/8 yard long, another was 1 1/4 yards long, and the third was 2 1/2 yards long. What is the total amount of rope Richard had?