Identify the given rate and write it as a fraction.
Write two quantities of the same unit as a fraction, one of which is the unknown quantity "x." Set the fraction equal to the given rate. Compare the ratio 4/9 to 12/x, for example.
Cross multiply the ratios by multiplying the numbers in the upper-left and lower-right corners together. Multiply the numbers in the lower-left and upper right corners together, as well. Set "4x" equal to "9 x 12", in this instance.
Solve the equation for x by dividing each side by the known variable. Divide "4x" by 4 and divide 108 (9 x 12) by 4 to obtain the value for x, which is 27.
Set two proportions, composed of fractions, equal to one another. Set "4/5 over 2/7" equal to "x over 3/4" in the following case.
Set the cross products equal to each other as done in Step 2 of the first section. Obtain "2/7 times x" equal to "4/5 x 3/4."
Cancel out common factors, or numbers that appear in both the numerator and denominator on one side of the equal sign. Cancel out 4 in the sample problem.
Multiply both sides by the reciprocal of the fraction located next to the "x." Multiply both sides by the reciprocal of 2/7, or 7/2, to isolate the x.
Calculate the value of x, which is 21/10.