Transcript Applications of Rational Numbers

PRE-ALGEBRA
Lesson 6-9 Warm-Up
PRE-ALGEBRA
Applications of Rational
Numbers (6-9)
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 5 of the trip on the first day, 0.2 of the trip the second day,
16
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.
50
5
• 800 mi. = 5 • 800
= 250 mi.
First Day
16
16
1
1
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
PRE-ALGEBRA
Applications of Rational
Numbers (6-9)
Method 2: Compare the four parts of the trip in the same form, like
decimals.
5
= 5  16
= 0.3125
First Day
16
30% = 0.30
150
800 = 150  800
= 0.2
Second Day
= 0.3.
Third Day
= 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.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Additional Examples
Janice spent $75.00 at the store. She spent 0.25 of the
2
money on a sweater, 22% on shoes, 5 of the money on a
jacket, and the rest on a shirt. Which item cost the most?
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.
2
5
• $75.00 = $30.00
Janice spent 2 of $75.00 on a jacket.
5
$75.00 – $18.75 – $16.50 – $30.00 = $9.75 Janice spent the remaining amount
on a shirt.
Janice spent the most, $30.00, on the jacket.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Additional Examples
(continued)
Method 2: Write the portions spent on the four items in the same form.
Compare.
0.25
22% = 0.22
2
5 = 0.4
9.75
= 0.13
75
The portion spent on the sweater is a decimal.
Write the percent spent on the shoes as a decimal.
Write the fraction spent on the jacket as a decimal.
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.
PRE-ALGEBRA
Applications of Rational
Numbers (6-9)
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 = 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
10
300 pages + 120 pages = 420 pages
Number of pages 2nd
printer prints in 12 min.
420 pages
= 420  12 = 35 pages / min.
12 min.
The second printer prints 5 pages more per minute, so it’s faster.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Additional Examples
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.
40
= 1.25
32
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
=8
Write 20% as a decimal.
Multiply.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Additional Examples
(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.
48
= 1.2
40
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's
rate is faster.
PRE-ALGEBRA
Applications of Rational
Numbers (6-9)
To estimate a percent, change it to a fraction or decimal that’s close to its
How can you use
estimation percent value. You can use the table below for common percent, fraction, and decimal
problems that don’t equivalents.
require an exact
answer.?
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%  1  0.4
Round percent up to the closest
3
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.
PRE-ALGEBRA
Applications of Rational
Numbers (6-9)
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
1
7.75% 
 0.1
10
7.75% of 30  0.1 • 30  3
The sale’s tax is about $3.
Round percent up to the closest
fraction or decimal equivalent
Estimate 35% of $49.95
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.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Additional Examples
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
25% of 18
1
4
=5
Round up to a compatible number close to 18.
• 20 Estimate.
Multiply.
There are about 5 milligrams of iron in one serving of cereal.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Additional Examples
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
29.95 ≈ 30
25% of 29.95 ≈ 0.25 • 30
= 7.5
Use the decimal equivalent of 25%.
Round the regular price.
Estimate.
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.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Additional Examples
(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.
PRE-ALGEBRA
Applications of Rational Numbers
LESSON 6-9
Lesson Quiz
1. Marissa spent exactly 2 hours studying. She spent 0.35 of the time
on math, 3 of the time on history, and the rest of the time on
8
literature. Which subject did she spend the most time studying?
history
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?
the Baker family
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?
about 400 grams
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?
no
PRE-ALGEBRA