You can solve problems like this by cross multiplying. Multiply the numerator of one fraction by the denominator of the other and the denominator by the numerator. Then, solve for your variable ( Which, in this problem, is x.)
[tex] \frac{2}{5} [/tex] = [tex] \frac{x}{40} [/tex] Cross multiply (2 · 40) and (5 · x)
2 (40) = 5x Multiply 2(40)
80 = 5x Divide both sides by 5
16 = x Flip the equation to make this easier to read
x = 16
Check your answer.
[tex] \frac{2}{5} = \frac{16}{40} [/tex] Simplify [tex] \frac{16}{40} [/tex] by dividing both numbers by their greatest common factor.* (8)
[tex] \frac{2}{5} = \frac{16÷8}{40÷8} [/tex] Simplify
[tex] \frac{2}{5} = \frac{2}{5} [/tex]
Find the GCF of two numbers by listing all the factors of each number.
16: 1 , 2 , 4 , 8 , 16
40: 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40
So, x = 16 .
