Converting 3 Yards to Feet: How-to & Tutorial

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will go through the steps of converting 3 yards into feet. We will learn how to set up equivalent ratios as fractions and cross-multiply those fractions in order to solve for a variable.

Steps to Solving the Problem

You are just starting a new sewing project. You went to the store and purchased 3 yards of some nice fabric. When you get home, you realize that the instructions for your project are in feet, not yards! Uh oh!! No need to panic, we will convert those yards right into feet and you can get that project started.

First of all, you need to know that 1 yard is equal to 3 feet. This is something you can memorize or look up if you forget. With this information, we will set up our first ratio as a fraction.

Original Fraction:


Fraction 1


The next step is to set up an equivalent ratio that is equal to the original fraction. In order to do so, you must put yards on top of the fraction in the numerator and feet on bottom of the fraction in the denominator. This is necessary because the units must match those of the original fraction.

Our equivalent fraction must have the 3 yards in the numerator and the unknown amount of feet in the denominator. This unknown amount of feet will be represented with an x which is called a variable.

Equivalent Fraction:


Fraction 2


Now we will set the two fractions equal to each other:


Equivalent


Now that we have an equation, we want to simplify it so we can solve for x. To do this, we will cross-multiply the fractions by multiplying the numerator of one fraction with the denominator of the other.

In our equation, we will multiply the numerator of the first fraction (1 yard) with the denominator of the second fraction (x feet). Then we will multiply the numerator of the second fraction (3 yards) with the denominator of the first fraction (3 feet).

Equation:


1 yard x x feet = 3 yards x 3 feet


Multiply 1 times x to get x and multiply 3 times 3 to get 9 for an even more simplified equation.

Simplified:


x (yards x feet) = 9 (yards x feet)


We are very close to our final answer; all that is left is to get x feet by itself. The way to do this is divide both sides by the unit yards. When this is done, yards will cancel out on both sides and you will be left with the solution.


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