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Guided Practice

Write the reciprocal of 2/3.

The reciprocal of a number is the number you multiply it by to equal 1. To make 1 whole using 2/3, you need a total of 1 two-thirds plus 1/2 of a two-thirds.

So, 2/3× 11/2 = 1. Or, 2/3×3/2= 1.

So, the reciprocal of 2/3 is 11/2, or 3/2.

Determine 2/3÷3/4.

Consider that 1 divided by 3/4 is 4/3, because
4/3×3/4= 1.

If we multiply the quantity 1 ÷3/4 by 2/3, this will be equal to 2/3÷3/4. And this will also be equal to 2/3×4/3.

To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.

Jeryl needs 2/3 cup of oil for a recipe, but she only has 1/4-cup containers. How many 1/4-cup containers of oil must she use for the recipe?

How many 1/4's can fit into 2/3?

2/3÷1/4=2/3×4/1
            =8/3, which is 22/3.

Determine 7/8÷1/2. Write your answer as a fraction (e.g., 1/3).

7/8÷1/2=

Any number (except for 0) multiplied by its is equal to 1.

There is two-thirds plus two-thirds in 1 whole.

Write the reciprocal of 1/3 as a fraction (e.g., 1/3):

What is the reciprocal of 1/2?

The reciprocal of 1/2 is , because
1/2× = 1.

What is the reciprocal of 2?

2 × = 1.

So, the reciprocal of 2 is .

What is the reciprocal of 3/4?

3/4× ( + ) = 1

3/4× ( = 1

The reciprocal of 3/4 is .

What is the reciprocal of 1?

The reciprocal of 1 is .

1 divided by 3/4 is 4/3.

So, × 1 ÷3/4=2/3× .

To divide two fractions, the first fraction by the of the second fraction.

Determine 1/2÷2/6.

1/2÷2/6=1/2×

1/2÷2/6=        

Determine 4/5÷ 5.

4/5÷ 5 =4/5×1/5

4/5÷ 5 =

Determine3/8÷1/2.

3/8÷1/2=3/8×

3/8÷1/2=        

What is 1/2÷1/6?

1/2÷1/6=

There are one-fourths plus one-fourth in two thirds.

Sal makes 6 and 3/4 cups of punch. He pours the punch into 1/2-cup containers. How many containers does Sal use? Write your answer as a fraction.

Sal uses containers.

Suppose the area of a rectangle is 35/4 square meters. Its length is 7/2 meters. What is the width of the rectangle? Write your answer as a fraction in simplest form.

The width is meters.

The net of a rectangular prism is shown. The net shows all the faces of the prism. Think of a net as the figure formed when you unfold the sides of a solid figure.

The surface area of a solid figure is the sum of the areas of all the faces.

Determine the volume of the aquarium.
Write your answers as fractions (e.g., 1/2).

7/8×3/4×1/2=  

The volume is cubic feet.

Determine the exact volume of the rectangular prism. Write your answer as a decimal.

The volume is cubic inches.

The cube has all edge lengths the same:
5.2 cm. What is the exact volume of the cube? Write your answer as a decimal.

The volume is cubic centimeters.

What is the volume of the stage?

The volume is cubic feet.

Label the net with the dimensions of the aquarium from the video. What is the exact surface area of the aquarium as a fraction in simplest form?

The surface area is square feet.

Label the net with the dimensions of the rectangular prism from the first exercise. What is the exact surface area of that rectangular prism as a decimal?

The surface area is square inches.

Label the net with the dimensions of the stage. What is the exact surface area of the stage?

The surface area is square feet.

The block with the letter "D" is a special kind of rectangular prism called a cube. All of its side lengths are equal to 5.2 cm. What is the exact surface area of the cube as a decimal?

The surface area is square cm.

These data show the results of a survey. Students were asked how tall they were in inches. What is the typical height of a student in the survey?

Heights of Students (in.)

The mean or median of a data set can be used to describe a typical, or average, value of the data. The median is the middle value when the data are arranged in order from least to greatest or greatest to least. The mean is the sum of all the values divided by the number of values.

What is the median student height? What is the mean height? Give the exact answers.

The median height is in.

The mean height is     in.

The range of a data set is the difference between the maximum and minimum of the data. What is the range of the student height data?

The range is in.

The mode of a data set is the value that occurs most frequently. What is the mode of the student height data?

There are two modes:
in. and in.

Determine the mean, median, mode, and range of the data. Give exact answers.

12, 99, 20, 25, 32, 31, 31, 7

Mean:    

Median:

Mode:    

Range:   

Determine the mean, median, mode, and range of the data. Give exact answers.

0, 50, 1, 49, 2, 48, 3, 47, 4, 46, 25, 25

Mean:    

Median:

Mode:    

Range:   

Determine the mean, median, and range of the data. Give exact answers.

9.6, 6.9, 2.5, 12.1, 3.0, 18.0, 10.9

Mean:    

Median:

Range:   

÷

When you multiply two numbers and their product is 1, then the two numbers are reciprocals of each other.

Examples:

In each example, the two factors are reciprocals of each other. The number 1 is a reciprocal of itself.

One way to divide two fractions is to use reciprocals. Dividing one fraction by another is the same as multiplying the first fraction by the reciprocal of the second fraction.

Examples:

Complete each number sentence by writing the reciprocal of the number shown. Write each number as a fraction with a slash (/) or as an integer.

4/5× = 1

×1/10= 1

Determine each quotient. Write each answer as a fraction with a slash (/) or as an integer.

3/5÷2/4=

7 ÷7/5=    

Determine the quotient. Write the answer in simplest form as a fraction with a slash (/) or as an integer.

1/3÷1/3=

Determine the quotient. Write the answer in simplest form as a fraction with a slash (/) or as an integer.

3/4÷9/5=

Determine the quotient. Write the answer in simplest form as a fraction with a slash (/) or as an integer.

6/1÷7/1=