7.4D Review

7.4D Review

7.4D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

Find the Percentage of a Whole

To find a percentage of a whole, multiply the percent (written as a decimal) by the whole. Remember, to convert a percent to a decimal, divide the percent by 100.

percent (as decimal) × whole = part (of whole)

 $\frac{percent}{100}\ =\ decimal\ value$  

Calculating the Percentage of a Whole

Example: Summer bought $55.60 of clothes before sales tax. If sales tax is 7.5%, how much did she pay in taxes? How much did she spend overall?

Step 1: Convert your percent to a decimal

7.5% written as a decimal is 0.075.

Step 2: Calculate the percentage of a whole (find the amount of sales tax)

0.075 × $55.60 = $4.17

Now, to solve the second part of the question, add the sales tax to the cost of the clothes.

$55.60 + $4.17 = $59.77

So, Summer spent $59.77 with tax included.

Percent of Change

To find percent increase or decrease, divide the change in amount by the original amount. Then convert your answer to a percent.

Change in amount = Greater value - Lesser value

percent (as decimal) = change in amount ÷ original amount

Calculating Percent of Change

Example: A company had 125 employees on February 1. Three months later, the company had 105 employees. What was the percent decrease in the number of employees at the company?

Step 1: Calculate change in amount (greater value - lesser value)

125 − 105 = 20

Step 2: Calculate percent of change by dividing the change in amount by the original number of employees.

20 ÷ 125 = 0.16

Step 3: Convert your decimal to a percent

0.16 written as a percent is 16%.

So, the number of employees at the company decreased by 16%.

Solving Problems involving Ratios, Rates, Etc..

Often times you will be asked questions like the following: "A fish makes 480 dives in 10 hours. At this rate, how many dives did the fish do in 4 hours?"

When asked questions like the one above you can either:

1. Calculate Unit Rate

2. Use one of the three proportional relationship methods to solve (horizontal, vertical, cross multiplication).

Using Unit Rate to solve problems involving Ratios, Rates, etc...

Using Unit Rate to solve the following problem...
"A fish makes 480 dives in 10 hours. At this rate, how many dives did the fish do in 4 hours?"

Step 1: Set up your ratios (y/x)

 $\frac{480\ dives}{10\ hrs}$  
Step 2: Calculate Unit Rate (divide the numerator by the denominator)
 $\frac{480\ dives}{10\ hrs}\ =\ 48\ dives\ per\ hour$  
Step 3: Solve the problem (multiply your unit rate by the given number of hours)
48 (unit rate) x 4 = 192 dives

Using Proportional Relationship method to solve problems involving rates, ratios, etc...

Use one of the three proportional relationship methods to solve the following problem...
"A fish makes 480 dives in 10 hours. At this rate, how many dives did the fish do in 4 hours?"

Step 1: Write the rates you are comparing (make sure your units are on the same side dives in numerator ; hrs in denominator)

 $\frac{480\ dives}{10\ hrs}\ =\ \frac{x\ dives}{4\ hrs}$  
Step 2: Solve for x using one of the three proportional relationship methods (I used the vertical method (10 x 48 = 480, therefore 4 x 48 =x)
 $\frac{480\ dives}{10\ hrs}\ =\ \frac{x\ dives}{4\ hrs}\ x\ =\ 192\ dives$  

YOUR TURN!

Work through the practice problems on the following slides!

Multiple Choice

Xochitl purchase a pair of shoes that were on sale for $52.50. There is an 8% sales tax rate. What is the sales tax for the pair of shoes in dollars and cents?

• $4.16

• $56.70

• $0.41

• $4.20

Multiple Choice

At Emily's summer camp, there were 80 girls and 12 counselors. At this rate, how many counselors should they have for 100 girls?

• 10

• 14

• 15

• 16

Multiple Choice

The price of an iPhone 11 Pro was reduced from $1600 to $1200. By what percentage was the price of the iPhone reduced?

• 15%

• 40%

• 25%

• 100%

Multiple Choice

The physician knows that 1 inch is equal to 2.54 centimeters. He will need a needle 7.5 cm long to take a bone marrow sample. This is equal to how many inches? Round to the nearest hundreth of an inch.

• 1.91 inches

• 2.52 inches

• 2.96 inches

• 3.0 inches

Multiple Choice

Panchita is buying an Apple computer that normally sells for $890.00 and a printer for $49.00. The state sales tax rate is 6%. What is the total cost of her purchases including sales tax?

• $939.00

• $56.34

• $882.66

• $995.34

Multiple Choice

One fluid ounce is approximately 30 milliliters. A water bottle holding 20 fluid ounces would hold how many milliliters (mL)?

• 1.5 mL

• 66.7 mL

• 260 mL

• 600 mL

Multiple Choice

There were 75 people waiting in line for concert tickets. Only 40% actually got tickets. How many got tickets?

• 30

• 35

• 45

• 50

Multiple Choice

A boat traveled at 27 miles in 2 hours. At this rate, how many miles will the boat travel in 1/2 of an hour?

•  $13\ \frac{1}{2}$  

•  $6\ \frac{3}{4}$  

•  $3\ \frac{3}{8}$  

•  $24\ \frac{1}{2}$  

Multiple Choice

Russell has a collection of 1,200 pennies. Of these pennies, 25% are dated before 1980, 35% are dated from 1980 to 2000, and the rest are dated after 2000. How many pennies in Russell’s collection are dated from 1980 to 2000?

• 300

• 420

• 480

• 350

Multiple Choice

A donut shop makes a total of 300 donuts on Tuesday morning to sell. Of the 300, 80 of them are plain and the rest are chocolate. If the donut shop plans to sell a total 750 donuts on Saturday morning, how many of them will be chocolate?

• 200 donuts

• 250 donuts

• 440 donuts

• 550 donuts