Hat sizes are determined by measuring the circumference of one's head in either inches or centimeters. Use ratio and porportion to complete the following table.
hat size Head circumference
7 1/4 (to nearest 1/5inch)
7 1/8 22 4/5
Head circumference
(to nearest centimeter)
58
Hat sizes are determined by measuring the circumference of one's head in either inches or centimeters. Use ratio and porportion to complete the following table.
hat sizes 7 1/4 7 1/8
Head circumference
(to nearest 1/5inch)
22 4/5
Head circumference
(to nearest centimeter)
58
To complete the table using ratio and proportion, we need to find the corresponding head circumference for each hat size.
First, let's convert the given head circumference of 22 4/5 inches to a decimal format. Since there are 5 parts in one whole, we can express 4/5 as 0.8. Therefore, the head circumference is 22.8 inches.
Since we are given the head circumference to the nearest 1/5 inch, we can assume that the hat size is rounded to the nearest 1/4 inch. So, to find the head circumference for a hat size of 7 1/4, we need to set up a proportion using the known head circumference (22.8 inches) and the unknown hat size.
Let x be the hat size for 7 1/4.
We can set up the proportion as:
x / 7 1/4 = 22.8 / 7 1/8
To simplify the proportion, let's convert the mixed numbers to improper fractions:
x / (29/4) = 22.8 / (57/8)
Next, we can simplify the fractions by multiplying both sides by the reciprocal of the denominator:
x / (29/4) = (22.8 * (8/57))
Simplifying further:
x / (29/4) = (182.4/57)
To solve for x, we can cross-multiply:
x * 57 = (182.4 * 4)
x * 57 = 729.6
Finally, divide both sides by 57 to isolate x:
x = 729.6 / 57
Using a calculator, we find that x is approximately 12.8.
Therefore, the head circumference for a hat size of 7 1/4, rounded to the nearest 1/5 inch, is 22.8 inches.
Now, let's use the same process to find the head circumference in centimeters.
Given head circumference = 58 centimeters.
Since we are given the head circumference to the nearest centimeter, we can assume that the hat size is rounded to the nearest 1/8 inch. So, to find the head circumference for a hat size of 7 1/8, we need to set up a proportion using the known head circumference (58 centimeters) and the unknown hat size.
Let x be the hat size for 7 1/8.
We can set up the proportion as:
x / 7 1/8 = 58 / 22.8
Using the same steps as above, we can solve for x. Cross-multiplying and simplifying, we find that x is approximately 11.9.
Therefore, the head circumference for a hat size of 7 1/8, rounded to the nearest centimeter, is 58 centimeters.
Completing the table:
hat size Head circumference (in inches) Head circumference (in centimeters)
7 1/4 22.8 -
7 1/8 - 58
(Note: The value for head circumference in inches is rounded to the nearest 1/5 inch, and the value in centimeters is rounded to the nearest centimeter.)
To complete the table using ratio and proportion, we need to convert the given head circumference measurements into the required format.
1. Let's start with the first row:
Hat size: 7 1/4
Head circumference: (to nearest 1/5 inch)
To convert the head circumference to the nearest 1/5 inch, we can multiply the given head circumference by 5:
22 4/5 * 5 = 114/5 = 22.8 inches
Therefore, the head circumference for a hat size of 7 1/4 (to the nearest 1/5 inch) is 22.8 inches.
2. Next, let's move to the second row:
Hat size: 7 1/8
Head circumference: 22 4/5
To convert the head circumference to the nearest centimeter, we can multiply the given head circumference by 2.54 (as there are 2.54 centimeters in an inch):
22 4/5 * 2.54 = (22 * 2.54) + (4/5 * 2.54)
= 55.88 + 2.032
= 57.912 centimeters (rounded to the nearest centimeter)
Therefore, the head circumference for a hat size of 7 1/8 (to the nearest centimeter) is 58 centimeters.
Now the completed table is as follows:
Hat size Head circumference
7 1/4 22.8 inches
7 1/8 58 centimeters