To use ratio and proportion to complete the table, we need to establish a relationship between the hat size and the head circumference in both inches and centimeters.
Let's start with the hat size 7 1/4. To find the corresponding head circumference in inches, we need to round it to the nearest 1/5 inch.
Now, we can set up a proportion to find the head circumference:
Hat size / Head circumference (in inches) = 7 1/4 / X
Let's simplify the fraction 7 1/4 to a decimal: 7.25.
So the proportion becomes:
7.25 / X = 7 1/4 / X
To solve for X, we can cross-multiply:
7.25X = (7 * 4 + 1)X
7.25X = 29X
Now, divide both sides of the equation by 29:
X = 7.25 / 29
X ≈ 0.25
Since we are rounding to the nearest 1/5 inch, we can round 0.25 to 0.2. Therefore, the head circumference for hat size 7 1/4 in inches is approximately 0.2 inches.
To find the head circumference in centimeters, we need to convert 0.2 inches to centimeters.
1 inch is approximately equal to 2.54 centimeters.
Therefore:
0.2 inches * 2.54 cm/inch ≈ 0.508 cm
So the head circumference for hat size 7 1/4 in centimeters is approximately 0.508 cm.
Using this process, you can follow the same steps for other hat sizes and fill in the remaining values in the table.