Question

The ratio of the length of a rectangle to its width is 4 1/2 : 2 1/4. What is the unit rate of the length per width of the rectangle?

Answer 1

The unit rate of the length per width of the rectangle, given the ratio 4 1/2 : 2 1/4, is 2 after converting to improper fractions and dividing the length by the width.

Step-by-step explanation:

The ratio of the length to the width of a rectangle is given as 4 1/2 : 2 1/4. To find the unit rate of the length per width, we need to convert each part of the ratio to improper fractions and then divide the length by the width. Converting to improper fractions, 4 1/2 becomes 9/2 and 2 1/4 becomes 9/4. Dividing 9/2 by 9/4, we get:

Length per Width = (9/2) ÷ (9/4) = 2

Thus, the unit rate of the length per width of the rectangle is simply 2.

Answer 2

The ratio simplifies fully to 2:1

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Work Shown:

4 & 1/2 = 4 + 1/2 = 4 + 0.5 = 4.5

2 & 1/4 = 2 + 1/4 = 2 + 0.25 = 2.25

The original ratio is the same as 4.5 : 2.25

Divide both parts by 2.25 and you'll end up with 2:1

4.5/2.25 = 2

2.25/2.25 = 1

This means the length is twice as long compared to the width.