Percents - Find the Part!

Percents - Find the Part!

By the end of this lesson you should be able to say...

• I can figure out the part of an equation if I have the percent and the whole.

State and National Standards

• 6.NS.8 Interpret, model, and use ratios to show the relative sizes of two quantities. Describe how a ratio shows the relationship between two quantities. Use the following notations: a/b, a to b, a:b.

• CCSS.MATH.CONTENT.6.RP.A.3.C

  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Multiple Choice

Review Question
Simplify this expression:

 $\frac{3}{7}+\frac{17}{21}$  

•  $\frac{20}{28}$  

•  $\frac{5}{7}$  

•  $\frac{26}{21}$  

•  $1\frac{5}{21}$  

Challenge Question

• You have a pile of pennies that you want to count.  When the pennies are put in groups of 2 there is one penny left over. When they are put in groups of three, five and six there is also one penny left over. But when they are put in groups of seven there are no pennies left over. How many pennies could there be?

• How will you start solving this problem?

• How can you be sure you are right?

• Is there only one answer, or are there many?

Percents

Remember a percent is a number that stands for part of 100.

We use them when shopping, when checking our grades and when looking at sports statistics.

Writing Percents - 3 Ways

• Words - 60 percent

• Percent symbol (%) 60%

• Fraction  $\frac{75}{100}$  

• (Also, it can be a decimal .75)

Percentage and Fractions

• 75% can also be shown in Fraction Form

•  $\frac{75}{100}$  this can be simplified  by dividiing by the GCF

•  $\frac{75\div25}{100\div25}=\frac{1}{4}$  so  $\frac{75}{100}$ and  $\frac{1}{4}$  are equivalent.

Multiple Select

What are two other ways to write 75 percent?

• $\frac{7.5}{10}$

• $\frac{75}{100}$

• 75

• 75%

Percents as decimals

• Any percent can be written as a fraction and a decimal

• 30% =  $\frac{30}{100}$   

•  $\frac{30}{100}\ written\ as\ a\ decimal\ is\ .30$  

• So, to write a percent as a decimal move the decimal two places to the left and drop the percen symbol.  30% = .30

Multiple Choice

What is the simplest fraction form of 60%

• $\frac{60}{100}$

• $\frac{30}{50}$

• $\frac{6}{10}$

• $\frac{3}{5}$

Open Ended

Why would you want to simplify a percentage as a fraction? Why does that matter?

Multiple Choice

What is 75% as a decimal

• 75.0

• 7.5

• .75

• .075

Multiple Choice

What is 4% as a decimal?

• 4

• 0.4

• 0.04

• 40.0

Multiple Choice

What about 125%? How would you write that as a decimal?

• 125.0

• 12.5

• 1.25

• .125

Multiple Select

Choose all correct ways to write 62 percent.

• 62

• $\frac{62}{100}$

• .62

• 62%

Percentages in 3 Parts

• There are three parts in any percent statement: the whole, the part, and the percent.

• For example: 16 is 20% of 80. 80 is the whole amount, 16 is the part, and 20% is the percent.

You try...

• There are 20 people in the library. Twelve of them are children. 60% of the people in the library are children.

• What number is the part? What number is the whole? What is the percent?

• Part = 12, Whole = 20, Percent = 60%

• Part = Percent x Whole or 12 = 60% x 20

The Percent Equation (Here's where it becomes Algebra!)

• Part = Percent x Whole

• 25 = .25 x 100

• (Remember your fact families!)

Multiple Select

What is 40% of 300? First, what do we know?

• Part

• Whole

• Percent

Multiple Choice

What is 40% of 300? Next, what is 40% as a decimal?

• 40

• 4

• .40

• .04

Multiple Choice

What is 40% of 300? Remember the equation -

part = percent x whole. Which represents our information correctly

• $x=0.40\cdot300$

• $0.40\ =\ x\cdot300$

• $300=x\cdot0.40$

28% of 125 is what number?

• Write the percent as a decimal

• Determine what you know and what you need to find (part, whole percent).

• Make a variable the unknown

• Set up the equation

• Simplify (solve)

28% of 125 is what number?

Review

• Percentages can be shown in different ways

• Written: 35 percent

• Percent sign: 35%

• Fraction  $\frac{35}{100}or\ \frac{7}{20}$  

• Decimal   0.35

There is a process to solving percent questions!

• Write the percent as a decimal

• Determine what you know and what you need to find (part, whole percent).

• Make a variable the unknown

• Set up the equation: part = percent x whole

• Simplify (solve)

Poll

How do you feel about finding the missing part of a percentage?

Poll

What's confusing?

• Simplifying fractions

• Making percentages into decimals?

• Figuring what is the part, percent and whole

• Solving the problem

Open Ended

Any questions?