12. A class consists 2/5 of freshmen,1/4 sophomores, and 1/10 juniors; the rest are seniors. What fraction of the class is seniors?
Fraction of seniors =
10. Explain an error pattern in each of the following: a. 13/35=1/5, 27/73=2/3,16/64=1/4
The numerator of right side fraction is the digit in the 10’s place of the numerator of the left side fraction.
The denominator of the right side fraction is the digit in the unit’s place of the denominator of the left side fraction. b. 4/5+2/3=6/8, 2/5+3/4=5/9, 7/8+1/3=8/11
The numerator of the sum is the sum of the numerators of the summands.
The denominator of the sum is the sum of the denominators. c.8 3/8-6 ¼=2 2/4, 5 3/8-2 2/3=3 1/5, 2 2/7-1 1/3=1 ¼
The integer part is subtracted from the integer part.
The numerator is subtracted from the numerator.
The denominator is subtracted from the denominator. d. 2/3*3=6/9,1/4*6=6/24,4/5*2=8/10
Instead of multiplying the numerator, the denominator is multiplied.
16. John took all his money out of his savings account. He spent $50 on a radio and of what remained on presents. Half of what was left he put back in his checking account, and the remaining $35 he donated to charity. How much money did John originally have in his savings account?
Amount he donated to charity = $35.
Amount put back in checking account = $35.
Amount spent on radio = $50
Original amount = $50 + $35 + $35 = $120.
7. How would you respond to each of the following students? a. Iris claims that if we have two positive rational numbers, the one with the greater numerator is the greater.
Consider the rational numbers and
The one with greater numerator is
But and is greater than So the claim of Iris is not correct.
b. Shirley claims that if we have two positive rational numbers, the one with the greater denominator is the lesser.
Consider rational numbers and
The one with greater denominator is
But and is less than
So the claim of Shirley is not correct.
11. In each of the following, order the decimals from greatest to least: 13.4919, 13.492, 13.49183, 13.49199 -1.453,-1.45,-1.4053,-1.493
13.492, 13.49199, 13.4919, 13.49183, -1.4053, -1.45, -1.453, -1.493
19. Jane’s car travels 224 mi on 12 gal of gas. Rounded to the nearest mile per gallon, how many miles to the gallon does her car get?
Distance travelled on 12 gallons = 224 miles
Distance travelled on 1 gallon = miles = miles = miles (approximately)
Her car gets 13 miles to the gallon.
2. Convert each of the following repeating decimals to a/b form, where a, b are integers and b?0. a.0.4
c.1.396
e.-2.34 1.
a. If a grocery store advertised three lemons for $2.00, what is the cost of one lemon?
Cost of 1 lemon =$ =
The cost of 1 lemon is 66.67 cents b. If you choose to buy exactly one lemon at the cost given in part (a), what are you charged? How is the store treating the repeating decimal cost of one lemon?
One lemon is charged 67 cents.
The repeating decimal is approximated to the nearest cent. d. Explain whether or not a grocery store would ever use a repeating decimal as a cost for an item.
The grocery never uses the repeating decimal as such. The price can be quoted only to nearest cent. e. Explain whether you think cash registers ever work with repeating decimals.
Cash registers never work with repeating decimals.
18. Write each of the following square roots in the form a÷b where a and b are integers and b has the least value possible: a. v180
b. v363
c. v252
20. In a photograph of a father and his daughter, the daughter’s height is 2.3 cm and the father’s height is 5.8 cm. If the father is actually 188 cm tall, how tall is the daughter?
5.8 cm in the photo corresponds to 188 cm
1 cm in the photo corresponds to cm
2.3 cm in the photo corresponds to cm
The daughter’s height is 74.55 cm.
8. Write a paragraph in which you use the terms ratio and proportion correctly.
9. List three real-word situations that involve ratio and Proportion
Length measured inches is proportional to length measured in cms.
They are in the ratio 1:2.54 = 100:254
Money measured in dollars is proportional to that measured in cents.
They are in the ratio 1:100 = 2:200
Suppose the price of pen is $2
The amount spent is proportional to the number of pen bought. They are in the ratio 2:1 = 20:10
22. John paid $330 for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a 10% discount and still make 20% of the price he paid for it. At what price should the bike be marked?
Profit = 20%
Selling Price = 120% of cost price = 120% of $330 =
Discount = 10%
Selling Price = 90% of marked price = marked price
Marked Price = Selling Price = Selling Price
The bike must be marked at $440
6. To save for their retirement, a couple deposits $4000 in an account that pays 5.9% annual interest compounded quarterly. What will be the value of their investment after 20 yr?
Amount after 20 years =
4. The effect of depreciation can be computed using a formula similar to the formula for compound interest. a. Assume depreciation is the same each month. Write a problem involving depreciation and solve it.
Suppose the vale of an asset in the beginning be $10,000. The rate of depreciation is 1% per month.
Let us compute the value of the asset after 3 months.
Value in the beginning = $10,000.00
Depreciation for month 1 = 1% of $10,000 = $10,000
Value after 1 month = $10,000.00 - $100.00 = $9,900.00
Depreciation for month 2 = $9,900
Value after 2 months = $9,900.00 - $ 99.00 = $9,801.00
Depreciation for month 3 = $ 9,801
Value after 3 months = $9,801.00 - $98.01 = $9,702.99 b. Develop a general formula for depreciation defining what each variable in the formula stands for.
Let be the monthly rate of depreciation. The value of an asset of value after n months is
Value = . Value in the beginning = A
Depreciation for month 1 =
Value after month 1 =
Depreciation for month 2 =
Value after 2 months =
Proceeding like this , the value after n months is
Suppose and Then,