How to Solve 7th Grade Math Proportions

By David McGuffin
Don't be confused by all the writing on the board, proportions are easily solved with some patience and by following a few simple steps.
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According to AlgebraHelp, proportions are algebraic equations that are used to compare two fractions or to make equivalent two fractions. Because the two fractions are equal, simple multiplication and division allow for proportion problems to be solved by keeping the fractional ratio consistent. Seventh grade math proportions may also come in the form of word problems, helping to sharpen a student's analytical skills. This article will explore how to solve proportions where one of the four numbers involved is an unknown.

Write the two fractions down on paper, putting an equal sign ("=") between them. Since a proportion compares two equal fractions, the equal sign between them allows you to solve for an unknown number ("y"). However, you are only able to solve for the unknown if you are given all the other three numbers in the fractions.

For example:

2 10

-- = --

6 y

Draw two lines across your fractions: one will connect the numerators, the other the denominators. Remember, the top numbers on the fractions are the numerators; the bottom numbers are the denominators. The line should cross through the equal sign. Visual learners can think of it this way: the four numbers are a box and you must connect the opposite corners of that box with two lines that will form an "X" across the box's center (where there is currently an equal sign).

Multiply each of the two number pairs that are connected by a line. This is called cross-multiplication. Use the space next to the fractions to write out the cross-multiplication sequence. Since the unknown number ("y") cannot be multiplied with a known number (2), the solution for cross-multiplication with a variable will be the known number times the unknown number, or 2y. The other cross-multiplication will yield a known number (60).


6 x 10 = 60

2 x y = 2y

Rewrite the cross-multiplied results so that they are equal to each other. Again, use the extra space on the page to re-write this equation.


60 = 2y

Divide both sides of the equation with the known number that remains with the unknown number in the equation. For example, the remaining number in the equation below is 2, which has been coupled with the "y" so far.


60 / 2 = 2y / 2

Solve the equation. Because the known integer on the right of the equation will be divisible by itself, it can be cancelled out. The result is the solution for the unknown number.


30 = y