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Example Questions
Example Question #1 : How To Find The Reciprocal Of A Fraction
What is the reciprocal of the fraction 3/727?
3/727
242
727/3
–727/3
–3/727
727/3
The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number.
3/727
Reciprocal 727/3
Example Question #1 : How To Find The Reciprocal Of A Fraction
What is the opposite reciprocal of 25/127?
–127/25
–5
127/25
–25/127
25/127
–127/25
The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The opposite reciprocal takes the negative of that number.
Example Question #2 : How To Find The Reciprocal Of A Fraction
Find the negative reciprocal of the following:
The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number.
Reciprocal
Negative Reciprocal
Example Question #1 : How To Find The Reciprocal Of A Fraction
What is the slope of any line perpendicular to 4y = 2x + 7 ?
First, we must solve the equation for y to determine the slope: y = (2/4)x + 7/4
By looking at the coefficient in front of x, we know that the slope of this line has a value of 1/2. To find the slope of any line perpendicular to this one, we take the negative reciprocal of it:
slope = m , perpendicular slope = –1/m
slope = 1/2 , perpendicular slope = –2
Example Question #1 : How To Find The Reciprocal Of A Fraction
Find the reciprocal of the following fraction
The reciprocal is defined such that a faction times its recprocal is 1. For you this just means turn the fraction upside down, ie the numerator is the denominator and vice versa.
Example Question #1 : How To Find The Reciprocal Of A Fraction
What is the reciprocal of 
This fraction doesn't have a reciprocal.
The reciprocal of a fraction is simply exchanging the denominator and numerator of a fraction.
You can double check that it works by making sure the product of a fraction and its reciprocal is 1.
Example Question #1 : How To Find The Lowest / Least Common Denominator
What is the difference between the LCM and GCF for the following set of numbers: 3, 12, and 30?
60
57
75
None of the answers are correct
48
57
LCM = least common multiple = 2 x 2 x 3 x 5 = 60
GCF = greatest common factor = 3
Prime factor each number
3 = 3 x 1
12 = 3 x 4 = 3 x 2 x 2
30 = 5 x 6 = 5 x 2 x 3
LCM – GCF = 60 – 3 = 57
Example Question #2 : Lowest Common Denominator
What is the least common denominator of 
16
32
24
48
16
In order to find the least common denominator, you must find the least common multiple of all three numbers. For this problem, the least common multiple of all three numbers is 16 (divisible by 2, 4, 8 , 1, and 16).
Example Question #1 : Lowest Common Denominator
What is the lowest common denominator for the following five fractions?
36
3
18
6
12
36
The lowest common denominator looks at the denominator (bottom number) of all of the fractions and finds the smallest number that all of the numbers divide into.
Of those numbers the largest is 18. First check to see if all the numbers divide into 18. 3 and 6 do, but 4 and 12 do not. Multiply 18 by 2 and get 36. Check to see if all the numbers divide into 36. 3 and 6 still do. 4 and 12 do now. therefore. 36 is the lowest common denominator.
Example Question #3 : Lowest Common Denominator
Find the lowest common denominator of these four fractions:
30
24
15
45
60
60
All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:
15 * 2 = 30 (NO)
15 * 3 = 45 (NO)
15 * 4 = 60 (YES!)
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