ALGEBRA PLACEMENT TEST WITH COMPLETE
SOLUTIONS 100% 2023/2024
John's car insurance premium is $1515.00. He has the option of making four equal payments but will
be charged an additional $25 processing fee. If he chooses the four-payment option, what is the
amount of each payment?
1515 + 25 = 1540
1540/4 = 385.00 per payment
A shipment of 1344 CD's is to be packed into cartons containing 24 CD's each. How many cartons are
necessary to ship these CD's?
1344/24 = 56 cartons
A loan of $10,020.00 is to be paid off in 60 equal monthly payments. How much is each payment
(excluding interest)
10, = 167 payments
Susan's Cell phone provider charges her $35.00 per month for the first 300 minutes of calls and $0.70
for each minute over 300. If she uses 340 minutes of calls in a given month, how much will she be
charged?
340 - 300 = 40 minutes
40 * 0.70 = 28
35 + 28 = $63
mixed number and improper form fractions
1.) 1 and 2/3 = mixed number
2.) 5/3 = improper fraction
How to find the product of two fractions
(a/b) * (c/b) = ac/bd
ex: 2/11 * 4/9 = 8/99
how to find the quotient of two fractions
a/b / c/d =
a/b X d/c or ad/cb
49 ounces of a solution is to be poured into test tubes with capacity 3 1/2 ounces. How many test
tubes will be filled
49 / (3 1/2) = 49 / (7/2) = 49 * 2/7 = 14 test tubes will be filled
how to find the sum(+/-)of two fractions with a common denominator `
a/c + b/c = (a+b)/c
, how to find the sum(+/-) of two fractions with DIFFERENT denominators
4/3 + 5/8 = 4/3 8/8 + (5/8 3/3) = 32/24 + 15/24 = 47/24 or 1 and 23/24
decimal notation
7 and 13/100 = 7.13
.125 = 125/1000 or 1/8
when adding or subtracting numbers in decimal notation make sure to align the decimal point
ex: 23.1 + 3.78
When multiplying two numbers in decimal notation, first multiply the numbers disregarding the
decimal point(s).
The number of places to the right of the decimal point in the product should be the SUM of the places
to the right of the decimal point in each of the factors.
6.35 * 2.1
635 *21 = 13335
move decimal 3 places to right = 13.335
percents
- indicates fraction 1/100 or ratio 1 to 100
23% = 23/100 0r .23
100% = 100/100 or 1.00
change the decimal to a percent
a. .25 = 25%
b. .085 = 8.5%
c. 1.52 = 152%
change the percent to a decimal
a 2% = .02
b. 5.5% = .055
c. 0.3% = .003
A class contains 12 female and 8 male students. What percent of the class is female?
12 + 8 = 20
12/20 * (5/5) = 60/100
= 60%
SOLUTIONS 100% 2023/2024
John's car insurance premium is $1515.00. He has the option of making four equal payments but will
be charged an additional $25 processing fee. If he chooses the four-payment option, what is the
amount of each payment?
1515 + 25 = 1540
1540/4 = 385.00 per payment
A shipment of 1344 CD's is to be packed into cartons containing 24 CD's each. How many cartons are
necessary to ship these CD's?
1344/24 = 56 cartons
A loan of $10,020.00 is to be paid off in 60 equal monthly payments. How much is each payment
(excluding interest)
10, = 167 payments
Susan's Cell phone provider charges her $35.00 per month for the first 300 minutes of calls and $0.70
for each minute over 300. If she uses 340 minutes of calls in a given month, how much will she be
charged?
340 - 300 = 40 minutes
40 * 0.70 = 28
35 + 28 = $63
mixed number and improper form fractions
1.) 1 and 2/3 = mixed number
2.) 5/3 = improper fraction
How to find the product of two fractions
(a/b) * (c/b) = ac/bd
ex: 2/11 * 4/9 = 8/99
how to find the quotient of two fractions
a/b / c/d =
a/b X d/c or ad/cb
49 ounces of a solution is to be poured into test tubes with capacity 3 1/2 ounces. How many test
tubes will be filled
49 / (3 1/2) = 49 / (7/2) = 49 * 2/7 = 14 test tubes will be filled
how to find the sum(+/-)of two fractions with a common denominator `
a/c + b/c = (a+b)/c
, how to find the sum(+/-) of two fractions with DIFFERENT denominators
4/3 + 5/8 = 4/3 8/8 + (5/8 3/3) = 32/24 + 15/24 = 47/24 or 1 and 23/24
decimal notation
7 and 13/100 = 7.13
.125 = 125/1000 or 1/8
when adding or subtracting numbers in decimal notation make sure to align the decimal point
ex: 23.1 + 3.78
When multiplying two numbers in decimal notation, first multiply the numbers disregarding the
decimal point(s).
The number of places to the right of the decimal point in the product should be the SUM of the places
to the right of the decimal point in each of the factors.
6.35 * 2.1
635 *21 = 13335
move decimal 3 places to right = 13.335
percents
- indicates fraction 1/100 or ratio 1 to 100
23% = 23/100 0r .23
100% = 100/100 or 1.00
change the decimal to a percent
a. .25 = 25%
b. .085 = 8.5%
c. 1.52 = 152%
change the percent to a decimal
a 2% = .02
b. 5.5% = .055
c. 0.3% = .003
A class contains 12 female and 8 male students. What percent of the class is female?
12 + 8 = 20
12/20 * (5/5) = 60/100
= 60%
