ACT Math : Algebra
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Example Questions
Example Question #21 : Algebraic Fractions
If 
If 10 pizzas cost x dollars, then each pizza costs x/10. Similarly, each soda costs y/6. We can add the pizzas and sodas together by finding a common denominator:
Example Question #22 : Algebraic Fractions
According the pie chart, the degree measure of the sector representing the number of workers spending 5 to 9 years in the same role is how much greater in the construction industry chart than in the financial industry chart?
Since the values in the pie charts are currently in terms of percentages (/100), we must convert them to degrees (/360, since within a circle) to solve the question. The "5 to 9 years" portion for the financial and construction industries are 18 and 25 percent, respectively. As such, we can cross-multiply both:
18/100 = x/360
x = 65 degrees
25/100 = y/360
y = 90 degrees
Subtract: 90 – 65 = 25 degrees
Alternatively, we could first subtract the percentages (25 – 18 = 7), then convert the 7% to degree form via the same method of cross-multiplication.
Example Question #871 : Algebra
6 contestants have an equal chance of winning a game. One contestant is disqualified, so now the 5 remaining contestants again have an equal chance of winning. How much more likely is a contestant to win after the disqualification?
When there are 6 people playing, each contestant has a 1/6 chance of winning. After the disqualification, the remaining contestants have a 1/5 chance of winning.
1/5 – 1/6 = 6/30 – 5/30 = 1/30.
Example Question #33 : Algebraic Fractions
Simplify:
Begin by simplifying the numerator.
Now, in our original problem this is really is:
When you divide by a fraction, you really multiply by the reciprocal:
Example Question #34 : Algebraic Fractions
Simplify:
Begin by simplifying the numerator and the denominator.
Numerator
Denominator
Now, reconstructing our fraction, we have:
To make this division work, you multiply the numerator by the reciprocal of the denominator:
Example Question #31 : Algebraic Fractions
Simplify:
None of the other answer choices are correct.
Recall that dividing is equivalent multiplying by the reciprocal. Therefore, ((x - 4) / (1 / 2)) / (1 / (x + 4)) = ((x - 4) * 2) * (x + 4) / 1.
Let's simplify this further:
(2x – 8) * (x + 4) = 2x2 – 8x + 8x – 32 = 2x2 – 32
Example Question #32 : Algebraic Fractions
Solve for 
Begin by isolating the variables:
Now, the common denominator of the variable terms is 
Simplify:
Cross-multiply:
Simplify:
Finally, solve for 
Example Question #3 : How To Evaluate A Fraction
Evaluate 
when x=11. Round to the nearest tenth.
1.8
1.9
0.2
0.3
1.8
Wherever there is an x, plug in 11 and perform the given operations. The numerator will be equal to 83 and the denominator will be equal to 46. 83 divided by 46 is equal to 1.804… and since the second decimal place is not greater than or equal to 5, the first decimal place stays the same when rounding so the final answer is 1.8.
Example Question #1 : Algebraic Fractions
Find the inverse equation of:
To solve for an inverse, we switch x and y and solve for y. Doing so yields:
Example Question #2 : How To Find Inverse Variation
Find the inverse equation of 
1. Switch the 
2. Solve for 
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