pre-algebra. lesson 6-9 warm-up pre-algebra how do you solve a word problem involving rational...

$: PRE-ALGEBRA. Lesson 6-9 Warm-Up PRE-ALGEBRA How do you solve a word problem involving rational numbers in more than one form (i.e. a mixture of fractions,$
PRE-ALGEBRA

PRE-ALGEBRA

Lesson 6-9 Warm-Up

PRE-ALGEBRA

How do you solve a word problem involving rational numbers in more than one form (i.e. a mixture of fractions, decimals, and percents)

To solve a problem involving a combination of decimals, fractions, and / or percents, write all of the numbers in the same form before doing anything else. This way, the numbers can be accurately compared to one another.

Example: A family drove 800 mi. from Oakland, Ca. to Seattle, Wash. They drove of the trip on the first day, 0.2 of the trip the second day, 30% of the trip the third day, and 150 mi. on the last day. On which day did they drive the farthest?

Method 1: Compare the distance traveled each day.

• 800 mi. = • = 250 mi. First Day

0.2 • 800 mi. = 1600 = 160 mi. Second Day

0.30 • 800 mi. = 2400 = 240 mi. Third Day (30% = 0.30)

= 240 mi. Fourth Day

They drove the furthest, 250 mi., on the first day

5 16

5 16

5 16

800 11

50

Applications of Rational Numbers (6-9)

PRE-ALGEBRA

Method 2: Compare the four parts of the trip in the same form, like decimals.

= 5 16 = 0.3125 First Day

= 0.2 Second Day

30% = 0.30 = 0.3. Third Day

= 150 800 = 0.1875 Fourth Day

0.3125 0.30 0.20 0.1875 or First Third Second Fourth

They drove the furthest on the first day.

5 16

150 800


PRE-ALGEBRA

Janice spent $75.00 at the store. She spent 0.25 of the money on a sweater, 22% on shoes, of the money on a jacket, and the rest on a shirt. Which item cost the most?

25

Method 1: Find the cost of each item. Compare.

0.25 • $75.00 = $18.75 Janice spent 0.25 of $75.00 on a sweater.

0.22 • $75.00 = $16.50 Janice spent 22%, or 0.22, of $75.00 on shoes.

25

25

• $75.00 = $30.00 Janice spent of $75.00 on a jacket.

$75.00 – $18.75 – $16.50 – $30.00 = $9.75 Janice spent the remaining amounton a shirt.

Janice spent the most, $30.00, on the jacket.

Applications of Rational NumbersLESSON 6-9

Additional Examples

PRE-ALGEBRA

(continued)

Method 2: Write the portions spent on the four items in the same form. Compare.

0.25 The portion spent on the sweater is a decimal.

22% = 0.22 Write the percent spent on the shoes as a decimal.

25 = 0.4 Write the fraction spent on the jacket as a decimal.

9.75 75

= 0.13 Divide 9.75, the amount spent on the shirt, by 75 to find the portion spent on the shirt.

Compare the decimals: 0.4 > 0.25 > 0.22 > 0.13. Janice spent the most on the jacket.


Additional Examples

PRE-ALGEBRA

How do you compare rates in different forms?

To compare two or more rates written in different forms, write the rates in the same form (same units) so they can be compared.

Example: One printer print 300 pages in 10 min. A second printer prints 40% more pages in 12 min. Which printer prints faster?

Step 1: Find the unit rate of the first printer.

= 300 10 = 30 pages / min. Unit rate of 1st printer

Step 2: Find the unit rate of the second printer.

40% of 300 = 0.40 x 300 = 12000 = 120 pages Find 40% of 300

300 pages + 120 pages = 420 pages Number of pages 2nd

printer prints in 12 min.

= 420 12 = 35 pages / min.

The second printer prints 5 pages more per minute, so it’s faster.

300 10

420 pages 12 min.


PRE-ALGEBRA

Gavin read 40 pages of a book in 32 minutes. Brian read 20%

more pages of the same book in 40 minutes. Who read faster?

Step 1: Find Gavin’s rate.

4032

= 1.25 Divide the number of pages by the number of minutes reading.

Gavin read 1.25 pages/min.

Step 2: To find Brian’s rate, first find the number of pages read in 40 minutes.

20% of 40 = 0.20 • 40 Write 20% as a decimal.

= 8 Multiply.


Additional Examples

PRE-ALGEBRA

(continued)

Step 3: Brian read 20% more pages. Add.

40 + 8 = 48

Brian read 48 pages in 40 minutes.

Step 4: Find Brian’s rate.

4840

= 1.2 Divide the number of pages by the number of minutes reading.

Brian read 1.2 pages/min.

Gavin read more pages per minute than Brian, so Gavin'srate is faster.


Additional Examples

PRE-ALGEBRA

How can you use estimation percent problems that don’t require an exact answer.?

To estimate a percent, change it to a fraction or decimal that’s close to its value. You can use the table below for common percent, fraction, and decimal equivalents.

Example: A jacket is on sale for 35% off of $49.95. After the discount, 7.75% sales tax is added. Is $30.00 enough money to buy the jacket?

Step 1: Estimate the discount on the jacket.

35% 0.4 Round percent up to the closest fraction or decimal equivalent

49.95 50 Round the price of the jacket.

35% of 49.95 0.4 • 50 20 Estimate 35% of $49.95

The discount is about $20.

13


PRE-ALGEBRA

Step 2: Estimate the sale price of the jacket.

50 – 20 30 Estimate the sale price

The sale price of the jacket is about $30.

Step 3: Estimate the sales tax

7.75% 0.1 Round percent up to the closest fraction or decimal equivalent

7.75% of 30 0.1 • 30 3 Estimate 35% of $49.95

The sale’s tax is about $3.

Step 4: Add the tax to the sales price.

$30 + $3 = $33.

The total cost is about $33.

$30 is not enough to buy the jacket.

1 10


PRE-ALGEBRA

The RDI for iron is 18 mg. If a serving of cereal has 25% of the

RDI for iron, about how many milligrams of iron are in one serving?

18 20 Round up to a compatible number close to 18.

14

25% of 18 • 20 Estimate.

= 5 Multiply.

There are about 5 milligrams of iron in one serving of cereal.


Additional Examples

PRE-ALGEBRA

A pair of shoes is 25% off of $29.95. After the

discount, 6.5% sales tax is added. Is $20 enough money to buy

the shoes?

Step 1: Estimate the discount on the shoes.

25% = 0.25 Use the decimal equivalent of 25%.

29.95 ≈ 30 Round the regular price.

25% of 29.95 ≈ 0.25 • 30 Estimate.

= 7.5 Multiply.

The discount is about $7.50.

Step 2: Subtract to find the sale price of the shoes.

$30 – $7.50 = $22.50

The sale price of the shoes is about $22.50.


Additional Examples

PRE-ALGEBRA

(continued)

Step 3: Estimate the amount of tax.

6.5% ≈ 0.1 Use a decimal close to 6.5%.

6.5% of 22.50 ≈ 0.1 • 22.50 Estimate

= 2.25

The amount of tax is about $2.25.

Step 4: Add the tax to the sale price: $22.50 + $2.25 = $24.75.

The total cost is about $24.75, so $20 is not enough.


Additional Examples

PRE-ALGEBRA

1. Marissa spent exactly 2 hours studying. She spent 0.35 of the time on math, of the time on history, and the rest of the time on literature. Which subject did she spend the most time studying?

2. Two families are traveling in cars. The Baker family travels 60 miles

in 70 minutes. The Doyan family travels 25% farther in 100 minutes. Which family travels at the faster rate?

3. Cole mixes different types of soil. The total mass of the mixture is 2,050 grams. Sand makes up 18% of the mixture’s mass. About what is the mass of the sand?

4. A shirt normally sells for $14.95. It is on sale for 25% off plus 8.00% sales tax. Is $12.00 enough to buy the shirt?

history

about 400 grams

the Baker family

38

no

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