SAT Math : Algebraic Fractions
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Example Question #41 : Algebraic Fractions
Evaluate:
Find the common denominator by multiplying both denominators together.
Multiply the top with what was multiplied on the bottom to get the denominator. Simplify the fraction.
Example Question #42 : Algebraic Fractions
Evaluate:
Multiply the denominators together to obtain the least common denominator, or LCD. Then multiply the numerators with what was multiplied on the denominator to get the LCD.
The answer is:
Example Question #41 : Algebraic Fractions
Simplify:
Find the common denominator and simplify.
Example Question #2653 : Sat Mathematics
Solve:
In order to evaluate this fraction, we will need to find the least common denominator. Multiply both denominators together.
Convert both fractions with the similar common denominator. Multiply the numerator with what was multiplied to get the denominator.
Add the numerators on the right side. The denominators will stay the same.
The answer is:
Example Question #42 : Algebraic Fractions
In a sample of 
To answer this question, we need to convert 
Example Question #43 : Algebraic Fractions
Mary walked to school at an average speed of 2 miles per hour and jogged back along the same route at an average speed of 6 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?
Since Mary traveled 3 times as quickly coming from school as she did going to school (6 miles per hour compared to 2 miles per hour), we know that Mary spent only a third of the time coming from school as she did going. If x represents the number of hours it took to get to school, then x/3 represents the number of hours it took her to return.
Knowing that the total trip took 1 hour, we have:
x + x/3 = 1
3x/3 + 1x/3 = 1
4x/3 = 1
x = 3/4
So we know it took Mary 3/4 of an hour to travel to school (and the remaining 1/4 of an hour to get back).
Remembering that distance = rate * time, the distance Mary traveled on her way to school was (2 miles per hour) * (3/4 of an hour) = 3/2 miles. Furthermore, since she took the same route coming back, she must have traveled 3/2 of a mile to return as well.
Therefore, the the total number of miles in Mary's round trip is 3/2 miles + 3/2 miles = 6/2 miles = 3 miles.
Example Question #44 : Algebraic Fractions
A school's tornado shelter has enough food to last 20 children for 6 days. If 24 children ended up taking shelter together, for how many fewer days will the food last?
4
8
1
6
2
1
Because the number of days goes down as the number of children goes up, this problem type is inverse variation. We can solve this problem by the following steps:
20*6=24*x
120=24x
x=120/24
x=5
In this equation, x represents the total number of days that can be weathered by 24 students. This is down from the 6 days that 20 students could take shelter together. So the difference is 1 day less.
Example Question #45 : 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 
Example Question #3 : How To Find Inverse Variation
When 
If 
If 
1. Using any of the two 
Using 
2. Use your new equation 
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