Video: Writing and Solving Multiplication Linear Equations in a Real-World Context Involving Fractions

A rectangle’s width is one-sixth of its length. Given that the rectangle’s width is 9 inches, determine its length.

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Video Transcript

A rectangle’s width is one-sixth of its length. Given that the rectangle’s width is nine inches, determine its length.

We will answer this question by firstly drawing a diagram and then setting up a one-step linear equation. Let’s consider a rectangle with width 𝑊-inches and length 𝐿-inches. We’re told in the question that the width is one-sixth of the length. The word “of” in mathematics means multiply. So 𝑊 is equal to one-sixth multiplied by 𝐿. This in turn can be written as 𝑊 equals one-sixth 𝐿 or 𝐿 divided by six.

In this particular question, we’re told that the rectangle’s width is nine inches. We can substitute this into our equation so that nine is equal to one-sixth 𝐿. This is the same as nine is equal to 𝐿 divided by six. In order to solve this equation, we need to perform the same operation on both sides of the equal sign. In this case, we will multiply by six as multiplying by six is the opposite or inverse of dividing by six.

On the left-hand side, six multiplied by nine or nine multiplied by six is equal to 54. On the right-hand side, the sixes cancel. And we’re just left with 𝐿. As 𝐿 is equal to 54, we can conclude that the length of the rectangle is 54 inches. We can check this answer by working out one-sixth of 54. As this is equal to nine, which was the rectangle’s width, we know that our answer of 54 inches is correct.

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