ACT Math : Algebra
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Example Question #104 : Expressions
The expression
can be rewritten as:
To simplify this problem, let’s look at each term individually. 
Example Question #105 : Expressions
The product of two consecutive odd negative integers is 
The problem gives us the product of two consecutive odd negative integers, so we know that one number is 
At this point, the more algebraically inclined student might recognize that if 
But this is the ACT, and the faster method by far is to simply recognize that if the product of our two integers is 
Example Question #102 : Expressions
Suzanne is at the grocery store. She has $5.00 to spend on produce. Oranges are $2.50 per pound, apples cost $1.50 per pound and bananas are $0.50 per pound. Which combination of fruit will fit her budget?
1.5 pounds of oranges and 4 pounds of bananas
3 pounds of apples and 2 pounds of bananas
2 pounds of oranges and 1 pound of apples
1 pound of oranges, 1 pound of apples and 2 pounds of bananas
1 pound of oranges, 1.5 pounds of apples and 1.5 pounds of bananas
1 pound of oranges, 1 pound of apples and 2 pounds of bananas
Make a simple algebra equation and test it against each combination:
Total Cost = $2.50 * (# Oranges) + $1.50 * (# Apples) + $0.50 * (# Bananas)
Example Question #1011 : Algebra
Change to a mixed number
To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction.
Example Question #4 : Algebraic Fractions
What is the average of 
To average, we have to add the values and divide by two. To do this we need to find a common denomenator of 6. We then add and divide by 2, yielding 4.5/6. This reduces to 3/4.
Example Question #5 : Algebraic Fractions
Which of the following is equivalent to 
None of the answers are correct
This problem is solved the same way ½ + 1/3 is solved. For example, ½ + 1/3 = 3/6 + 2/6 = 5/6. Find a common denominator then convert each fraction into an equivalent fraction using that common denominator. The final step is to add the two new fractions and simplify.
Example Question #1012 : Algebra
A train travels at a constant rate of 
Set up the conversions as fractions and solve:
Example Question #1013 : Algebra
Simplify.
Can't be simplified
To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified
Example Question #1014 : Algebra
Simplify:
x2 – y2 can be also expressed as (x + y)(x – y).
Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).
This simplifies to (x – y).
Example Question #1015 : Algebra
Simplify:
Notice that the 
Now multiply both the numerator and denominator by the conjugate of the denominator:
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