Multi-Step The heights of the starting players for the Davis High School boy's basketball team are 78 1/2 in., 74 in., 71 5/8 in., 70 3/4 in., and 69 1/2 in. Find the average height of the starting players.
Change the fractions to decimals.
Add the heights. Divide by 5 to find the average height.
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To find the average height of the starting players, you need to add up all the heights and then divide the sum by the total number of players. Let's break down the steps:
Step 1: Add up all the heights.
To find the sum of the heights, add the given heights together:
78 1/2 in + 74 in + 71 5/8 in + 70 3/4 in + 69 1/2 in.
Step 2: Convert mixed numbers into improper fractions (if necessary).
The first height, 78 1/2 in, is a mixed number. Convert it to an improper fraction by multiplying the whole number (78) by the denominator (2), then adding the numerator (1). The result will be the new numerator:
78 * 2 + 1 = 157.
Write the new numerator (157) over the denominator (2) to get: 157/2 in.
Step 3: Find a common denominator (if necessary).
Since the fractions have different denominators (2, 8, and 4), you need to find a common denominator to be able to add them together. The least common multiple (LCM) of 2, 8, and 4 is 8.
Step 4: Convert all the fractions to have the same denominator.
To convert the fractions, multiply the numerator and denominator of each fraction by the same value that will make the denominator equal to the common denominator (8):
78 1/2 in = 157/2 in = 628/8 in.
71 5/8 in = (71 * 8 + 5)/8 in = 573/8 in.
70 3/4 in = (70 * 4 + 3)/4 in = 283/4 in.
69 1/2 in = (69 * 2 + 1)/2 in = 139/2 in.
Step 5: Add up the converted fractions.
Sum up the fractions:
628/8 in + 74 in + 573/8 in + 283/4 in + 139/2 in.
Step 6: Add up the whole numbers and fractions separately.
For simplicity, let's write the whole numbers separately from the fractions:
628/8 in + 74 in + 573/8 in + 283/4 in + 139/2 in
= (628/8 + 573/8) in + 74 in + 283/4 in + 139/2 in.
Step 7: Add up the fractions (numerator) and keep the denominator.
Add the numerators of the fractions that have the same denominator:
(628 + 573)/8 in + 74 in + (283 + 139)/4 in.
Step 8: Simplify the fractions.
Simplify where possible:
1201/8 in + 74 in + 422/4 in.
Step 9: Add up the fractions and whole numbers.
Add the fractions and whole numbers together:
1201/8 in + 74 in + 422/4 in = (1201 + 592 + 1688)/8 in.
Step 10: Divide the sum by the total number of players.
There are 5 players, so divide the sum by 5:
(1201 + 592 + 1688)/8 in ÷ 5 = 3481/40 in ÷ 5.
Step 11: Simplify the fraction (if necessary) to find the average height.
To simplify, divide the numerator by the denominator:
3481/40 in ÷ 5 = 696.2/40 in.
Step 12: Convert the fraction to a mixed number (if necessary) to find the average height.
To convert the improper fraction to a mixed number, divide the numerator by the denominator:
696.2/40 in ÷ 5 = 139.24/8 in.
The average height of the starting players for the Davis High School boy's basketball team is 139 3/8 inches.