Page 1 -- CCM6 Unit 9 –Measurement Conversions, Percents, Percent Applications

UNIT 9

2016-17

Percents and Measurement Conversions

CCM6 Name: ________________ Math Teacher:___________ Projected Test Date:_____ Topic

Page #

Unit 9 Vocabulary Use Equivalent Ratios to Convert Between Metric Measurements Use Equivalent Ratios to Convert Between Customary Measurements Use Equivalent Rates to Convert Between Customary and Metric Measurements Understand Percent Convert between Percents, Fractions and Decimals Find Percent of a Number Percent Applications (including Taxes, Tips, and Discounts) Unit 9 Study Guide

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5-8 9-10 11-12 13-14 15-17 18-23 24-25

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Unit 9 Vocabulary cent

a cent is equivalent to 1/100 of a dollar in US circulation

cross product

the product of numbers on the diagonal when comparing two ratios

Customary System

a system of measurement used in the U.S. The system includes units for measuring length, capacity, and weight

discount

the amount of decrease in price

Metric System

a system of measurement based on tens. The basic unit of capacity is the liter. The basic unit of length is meter. The basic unit of mass is the gram.

percent

ratio that compares a number to 100

Tax

a percent of the cost of an item added to the initial bill

Tip

the amount of money added to a bill for service; usually a percent of the bill

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Use Equivalent Ratios to Convert within the Metric System

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HW:

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Converting between Customary Measures using Equivalent Ratios WARMUP:

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Warmup Cont’d

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MEASURES Within the CUSTOMARY SYSTEM

Customary Units of Length

Customary Units of Weight

1 foot (ft) = ________ inches (in)

1 pound (lb) = ________ ounces (oz)

1 yard (yd) = ________ ft = _______ yd

1 ton = ______ lbs = __________ oz

1 mile (mi) = ________ ft = _______ yd

Customary Units of Capacity

What tricks have you learned in the past to help you remember these?

1 cup (c) = _____ fluid ounces (fl oz) 1 pint (pt) = _____c = _____fl oz 1 quart (qt) = _____ pt = ____ c = _____ fl oz 1 gallon (gal) = _____ qt = ____ pt = ____ c =_______fl oz

12 in = 1 ft 3 ft = 1 yd

16 oz = 1 lb 2000 lb = 1 t

You can use equal ratios to convert between customary problems…. Example #1: 72 in = ________yd ÷2 Set up 2 equal ratios:

72 𝑖𝑛

= 𝑦𝑑

Work it out!

36 𝑖𝑛 1 𝑦𝑑

•2

Example #2: 12 qt = ________ gal

Set up 2 equal ratios:

12 𝑞𝑡 𝑔𝑎𝑙

4 𝑞𝑡

= 1 𝑔𝑎𝑙 7

2 c = 1 pt 2 pt = 1 qt 4 qt = 1 gal

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Day 7: Practice with Converting Customary Measures….Set up two equal ratios! 1a.

10 T = __________ lb 1T = 10 T 2000lb ?

2a.

32 oz = _____ qt

3a.

14 C = _____ pt

4a.

2,000 lb = _____ T

5a.

56 oz = _____ C

6a.

4 gal = ______ oz

7a.

132 in = ______ ft

8a.

7 T = __________ lb

9a.

2 mi = ___________ ft

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1b.

4 mi = ___________ ft

2b.

128 oz = _____ qt

3b.

112 oz = _____ lb

4b.

1 lb = ________ oz

5b.

1 mi = ___________ ft

6b.

4 gal = ______ qt

7b.

144 in = ______ ft

8b.

3 mi = ___________ ft

9b.

8,000 lb = _____ T

Page 9 -- CCM6 Unit 9 –Measurement Conversions, Percents, Percent Applications

Converting between Metric and Customary Set up two equal ratios and find the missing piece. Use the conversion charts below. METRIC to CUSTOMARY:

CUSTOMARY to METRIC:

Now, let’s try some: a) 5 inches = _________cm *We are converting from inches to cm so use the chart on the _____. 1 𝑖𝑛𝑐ℎ 2.54 𝑐𝑚

b) 8 km = ________mi

=

𝑥

*We are converting from km to mi so use the chart on the _________. 1 𝑘𝑚 0.621 𝑚𝑖

c) 18 g = ________ oz

5 𝑖𝑛𝑐ℎ𝑒𝑠

=

8 𝑘𝑚 𝑥

*Use the chart to the ______________. _______ = _______

d) 3.5 qt = ______L

*Use the chart to the ______________. _______=_______

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Page 10 -- CCM6 Unit 9 –Measurement Conversions, Percents, Percent Applications

HW METRIC to CUSTOMARY:

CUSTOMARY to METRIC:

1) 16 in = ____________cm

2) 345 lb = __________kg

3) 56 g = ___________oz

4) 450 km = ____________mi

5) 1200 mL =__________fl oz

6) 40 m = ____________ft

7) Penny has a pencil that is 19 cm long. How long is this pencil in inches?

8) A cookie recipe (1 batch) calls for 1 lb of butter. How many grams of butter would be in 3 batches?

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Converting between percents, fractions and decimals Percent to Decimal

Examples

To convert a percent to a decimal, just divide by 100…or move the decimal place two to the left.

1) 50% = ________

2) 82% = ________

*In a decimal, the point is after the __________place.

3) 12.5% = ________

**In a percent, the point is after the _______________place.

4) 101% = ________

5) Why is it okay to have a percent over 100%?

Decimal to Percent To move the decimal from the ones place to the hundredths place, either: 1) move the decimal 2 places right (so it is after the ______________ place). 2) multiply by 100 to move the decimal two places right.

Examples

Percent to Fraction Since a percent is a value out of 100, type it in as a fraction over 100 and hit enter. Or put it over 100 and simplify like normal.

Examples

1) 0.22 = _______% 2) 0.2 = _______% 3) 2.0 = _______%

1) 32% = _______

2) 8% = ________

3) 125% = _______ Fraction to Percent To turn a fraction into a percent, simply multiply by 100. Or make an equal ratio that has a denominator of 100.

Examples 3 1) 5 = ________% 2)

3 4

= ________% 7

3) 1 10 = ________% 13

If your answer is a percent, you must put the percent symbol!

Page 14 -- CCM6 Unit 9 –Measurement Conversions, Percents, Percent Applications

𝟕 𝟏𝟎𝟎

𝟐𝟑 𝟏𝟎𝟎

𝟎. 𝟏𝟔

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Understand Percents WARMUP: Use your calculator to find the percents.

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Percent Applications with Tips/Discounts/Taxes COMMON APPLICATIONS WITH PERCENTS…USE a CALCULATOR! Big Idea What is it? Problem TAX $ is You go to the store and a) _______________ to buy a pair of jeans that cost $32.59. Sales tax in the final price. Raleigh, NC is 6.75%. TAX a) How much extra will you pay in tax?

TIP $ is ______________ to TIP the final bill.

b) What is your final price to pay? You go out to Buffalo Brothers for dinner with a few friends. Your bill (including tax) is $28.73. You want to leave a 20% tip.

b)

a)

b) a) What is your tip $?

DISCOUNT

mixed

DISCOUNT means there is a _________ so you ___________ the $ from the price.

In reality, sometimes there are DISCOUNTS and you still have to pay TAX— this stuff combines in real life!

b) What is your total cost? Hooray! American Eagle a) is having a sale on jeans! All pairs are 25% off! If jeans regularly cost $39.95, what will you pay for a pair of jeans? b) a) How much $ is taken off due to the discount? b) What will you pay? Bath and Body works is having a 35% off sale on Tervis cups. Normally they cost $18.95. a) What is the discount?

a)

b)

b) What is the sale price? c) c) If sales tax is 6.75%, what will you pay in taxes? d) d) What is your final cost? 18

Solution

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Page 20 -- CCM6 Unit 9 –Measurement Conversions, Percents, Percent Applications PERCENT APPLICATIONS WORKSHEET –work it out and check it! HINT: What is the PART and What is the WHOLE? Make 2 equal ratios!

Cross-multiply and divide by the leftover guy! 1. Sue answers 42 out of 60 questions correctly. What percent of her answers are correct?

2. On a 20-item practice test, how many questions must you answer correctly for a score of 80% correct?

3. A teacher earns $38,500 per year. If 18% of her income is withheld for taxes, how much money is withheld for taxes? How much of her income is left after taxes?

4. At $450 per month, a student pays $5400 a year in rent. If his annual income is $15,000, what percent of his income is spent on rent?

5. In one state, sales tax is 6%. If sales tax on a car is $564.00, find the price of the car before tax.

6. Of the 540 seniors at Lake City High School, 35% are going on a school trip. If the buses ordered for the trip seat 42 students, how many buses will be needed so that each student will have a seat?

7. If the sales tax rate is 6%, find the tax on a $429.95 television to the nearest cent.

8. A car salesperson advertises 18% off the price of a $12,900.00 Yugo. What would the sale price be? 20

Page 21 -- CCM6 Unit 9 –Measurement Conversions, Percents, Percent Applications 9. Barb earns a 26% commission on each lab manual she sells. If she sells 1200 manuals at $9.95 each, find her commission.

10. A carpet salesperson claims that a carpet on sale for $12.95 per square yard is 30% off its original price. What was its original price to the nearest cent?

A stereo costs $149.95 and is 20% off. The tax is 6%. 11. Discount = $___________ 12. Sale Price = $__________ 13. Sales Tax = $__________ 14. Final Cost = $___________

15. In an election, one candidate claimed 52% of the votes, while the other candidate claimed 2681 votes. If 5000 people voted, how do you know the election results are invalid? Hint: What percent is the “other” candidate? What must be the sum of the percents in an election?

16. If you answered 37 items correctly on a test, and received a score of 74%, how many items were on the test?

ANSWERS 1. 70% 2. 16 3. $6,930 $31,570 4. 36% 5. $ 9,400 6. 189 and 5 7. $25.80 8. $10,578 9. $3,140.40 10. $43.17 11. $29.99 12. $119.96 13. $7.20 14. $127.16 15. 52% + 53% ≠ 100% 16. 50 21

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ANSWERS: 1) $91 2)238 3)$896

4)189 5)$93.60 6)360 7)45 8)360 mg 22

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ANSWERS: 9) a=$9.90 b=$$35.10 10)637g and 588 b 11)~$4 12)a=100 b=40 c=125 13)a=$8.70 b=$66.70 14)a=$24 b=$96 23

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CCM6 – Unit 9 (Measurement Conversions/%/% Applications) STUDY GUIDE Measurement—metric/customary 1. In the space to the right, draw gallon guy/gallon land.

2.

Use gallon guy to answer these questions: a) 8 qt = _________ pts b) 4 gal = _________ qts c) 8 cups = _________pts

3.

1 yard = _________ feet, and 1 foot = _____________ inches, so 1 yard = ____________ inches

4.

1 pound = _____________ ounces, so in 80 ounces there are ___________ pounds.

5. In the space below draw the memory tool to order the metric prefixes (Hint: King Henry….)

6.

Convert these metric measures using the tool above: a) 7 mm = ___________cm b) 8 kg = ____________g

For the problems below, use the charts to the right. It doesn’t matter which chart you use! 7.

18 in = ___________cm

8.

20 mL = __________fl oz

9.

25 kg = ___________lbs 24

c) 4.5 cm = _______m

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Percent 10. On the line segment below, mark and label 0%, 25%, 50%, 75%, and 100%.

11. Write the percent shaded for the picture below.

12. Find 22% of 80.

13. Find 40% of 75.

14. A jacket costs $49.95. It is on sale for 30% off. a) Discount = $___________ b) Sale Price= $___________ 15. At the store, you buy items that total $38.34. Sales tax is 8%. a)

Sales Tax = $___________

b)

Total Cost = $__________

16. A bag contains 88 jelly beans. You ate 25% of them. How many were left in the bag?

17. There were 150 students on the Sharks team. 46% of the students were boys. How many boys on the Sharks team? _______________ boys How many girls on the Sharks team? _______________ girls

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