How to solve for a variable as part of a fraction - GRE Quantitative Reasoning
Card 1 of 56
If 
, then what is the value of 
?
If 
Tap to reveal answer
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
← Didn't Know|Knew It →
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
Tap to reveal answer
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
← Didn't Know|Knew It →
$\frac{4 }{x}$ = $\frac{2}{25}$
Find x.
$\frac{4 }{x}$ = $\frac{2}{25}$
Find x.
Tap to reveal answer
Cross multiply:
4 times 25 = 2x
100 = 2x
x = 50
Cross multiply:
4 times 25 = 2x
100 = 2x
x = 50
← Didn't Know|Knew It →
If 
, what is the value of 
?
If
Tap to reveal answer
Start by cross multiplying to get the equation
.
Then simplify by subtracting 
from each side to get the solution,
.
Start by cross multiplying to get the equation
Then simplify by subtracting
← Didn't Know|Knew It →
If 
, then what is 
equal to?
If
Tap to reveal answer
We start by solving for x in 
by multiplying 4 and 15, which gives us 
.
Then substituting 60 for x in,
gives us
which equals 0.
We start by solving for x in
Then substituting 60 for x in,
← Didn't Know|Knew It →
If 
, and 
, what is the value of 
?
If
Tap to reveal answer
Start by cross multiplying which gives us 
.
Simplify by dividing both sides by 
which gives us 
.
Isolate 
by dividing both sides by 
and then adding 
to both sides, which gives us 
.
Start by cross multiplying which gives us
Simplify by dividing both sides by
Isolate
← Didn't Know|Knew It →
If 
, and 
what is the value of 
?
If
Tap to reveal answer
Start by cross multiplying which gives us
.
Divide both sides by 12 and simplify which gives us 
.
Since 
, we only take the positive square root as the solution, 
.
Start by cross multiplying which gives us
Divide both sides by 12 and simplify which gives us
Since
← Didn't Know|Knew It →
If , then what is the value of ?
If
Tap to reveal answer
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
← Didn't Know|Knew It →
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
Tap to reveal answer
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
← Didn't Know|Knew It →
$\frac{4 }{x}$ = $\frac{2}{25}$
Find x.
$\frac{4 }{x}$ = $\frac{2}{25}$
Find x.
Tap to reveal answer
Cross multiply:
4 times 25 = 2x
100 = 2x
x = 50
Cross multiply:
4 times 25 = 2x
100 = 2x
x = 50
← Didn't Know|Knew It →
If , what is the value of ?
If
Tap to reveal answer
Start by cross multiplying to get the equation
.
Then simplify by subtracting from each side to get the solution,
.
Start by cross multiplying to get the equation
Then simplify by subtracting
← Didn't Know|Knew It →
If , then what is equal to?
If
Tap to reveal answer
We start by solving for x in by multiplying 4 and 15, which gives us .
Then substituting 60 for x in,
gives us
which equals 0.
We start by solving for x in
Then substituting 60 for x in,
← Didn't Know|Knew It →
If , and , what is the value of ?
If
Tap to reveal answer
Start by cross multiplying which gives us .
Simplify by dividing both sides by which gives us .
Isolate by dividing both sides by and then adding to both sides, which gives us .
Start by cross multiplying which gives us
Simplify by dividing both sides by
Isolate
← Didn't Know|Knew It →
If , and what is the value of ?
If
Tap to reveal answer
Start by cross multiplying which gives us
.
Divide both sides by 12 and simplify which gives us .
Since , we only take the positive square root as the solution, .
Start by cross multiplying which gives us
Divide both sides by 12 and simplify which gives us
Since
← Didn't Know|Knew It →
If , then what is the value of ?
If
Tap to reveal answer
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
← Didn't Know|Knew It →
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
Tap to reveal answer
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
← Didn't Know|Knew It →
$\frac{4 }{x}$ = $\frac{2}{25}$
Find x.
$\frac{4 }{x}$ = $\frac{2}{25}$
Find x.
Tap to reveal answer
Cross multiply:
4 times 25 = 2x
100 = 2x
x = 50
Cross multiply:
4 times 25 = 2x
100 = 2x
x = 50
← Didn't Know|Knew It →
If , what is the value of ?
If
Tap to reveal answer
Start by cross multiplying to get the equation
.
Then simplify by subtracting from each side to get the solution,
.
Start by cross multiplying to get the equation
Then simplify by subtracting
← Didn't Know|Knew It →
If , then what is equal to?
If
Tap to reveal answer
We start by solving for x in by multiplying 4 and 15, which gives us .
Then substituting 60 for x in,
gives us
which equals 0.
We start by solving for x in
Then substituting 60 for x in,
← Didn't Know|Knew It →
If , and , what is the value of ?
If
Tap to reveal answer
Start by cross multiplying which gives us .
Simplify by dividing both sides by which gives us .
Isolate by dividing both sides by and then adding to both sides, which gives us .
Start by cross multiplying which gives us
Simplify by dividing both sides by
Isolate
← Didn't Know|Knew It →