How to Calculate X to Y Ratios

Calculating ratios is required in algebra class.

The ratio of x and y means x divided by y. The ratio shows the size of one value compared to another, which can be useful for all kinds of purposes, such as finding the slope of a hill or graph, or the rise over the run. You can also find the ratio of x and y in many algebraic equations, which is required in some mathematics classes. When calculating ratios, follow basic rules of mathematics and prove your work on paper.

Things You'll Need

• Calculator
• Lined paper

Instructions

Simple Ratios

1. Write x and y down separated by a colon, as in "x:y," on lined paper. This is the standard way that ratios are written.

2. Skip a line and write the value x, a line under it and then the y value under the line. This notation signifies x divided by y.

3. Enter the x value into a calculator, press the divide symbol ("÷"), enter the y value and press the equals button ("="). This value is the ratio of x and y.

4. Skip a line on the paper, write an equals sign and write the number on the calculator screen.

5. Multiply the value by 100 to transform the ratio of x to y into a percentage. This will give you the size of x as a percentage of y.

Linear Equations

1. Write the equation, such as y = 2x - 4. In this equation the slope of the line is the coefficient of x, 2, and the y-intercept is 4. The intercept is the point at which this linear equation would cross the y-axis if drawn on a graph. The slope stays constant, unlike the ratio of x/y, which changes depending on the values of x and y. This is because of the presence of the intercept.

2. Skip a line and rearrange the equation so that the x term alone is on one side:

   y + 4 = 2x

3. Divide all of the terms on both sides by y to achieve the form x/y:

   1 + 4/y = 2x/y

4. Divide both sides by 2 to get the ratio of x to y.

   1/2 + 2/y = x/y

5. Enter an x value into the original equation. For example, plug in x = 3:

   y = 2x - 4 = 6 - 4

   y = 2

6. Enter the y value into the equation to find the ratio of x to y when x is 3 and y is 2.

   x/y = 1/2 + 2/y

   = 1/2 + 1

   = 1 and 1/2, or 3/2

Tips & Warnings

• When reading ratio notation in words, x:y is the equivalent of "the ratio of x to y." The order of the numbers is important, as the first number is always divided by the second number.

• When changing ratios into percentages, if x and y are the same, x will be 100 percent of y. If x is 9 and y is 10, x is 90 percent of y. If x is 11 and y is 10, x is 110 percent of y.

• Do not get confused between finding the ratio of x/y in a linear equation and finding the gradient or slope of a straight line by differentiation. When finding the slope of a line in differentiation, you would find dx/dy, which means a small change in x divided by a small change in y. Dx/dy is not affected by the y intercept, and so for straight lines this value stays constant, and is equal to the coefficient of x.

References

• BBC: Maths, using ratios