calculate the following, leaving your answer as a fraction (lowest) or in decimal. Show your work
8(2+3²
---------
2(5)²
Is the numerator supposed to be
8(2+3)^2
?
yes it is supposed to be 8(2+3)^2
To calculate the expression 8(2+3²) / 2(5)², let's start by simplifying the numerator and denominator separately.
First, let's simplify the numerator: 8(2 + 3²).
Step 1: Calculate the exponent: 3² = 3 * 3 = 9.
Now, we have 8(2 + 9) for the numerator.
Step 2: Perform the sum inside the parentheses: 2 + 9 = 11.
Now, we have 8(11) for the numerator.
Step 3: Multiply: 8 * 11 = 88.
Now, let's simplify the denominator: 2(5)².
Step 1: Calculate the exponent: 5² = 5 * 5 = 25.
Now, we have 2(25) for the denominator.
Step 2: Multiply: 2 * 25 = 50.
Now, we have the fraction 88/50.
To reduce the fraction to its lowest terms, we can find the greatest common divisor (GCD) of both numerator and denominator, and divide both by the GCD.
Step 1: Find the GCD of 88 and 50.
The factors of 88 are: 1, 2, 4, 8, 11, 22, 44, 88.
The factors of 50 are: 1, 2, 5, 10, 25, 50.
The GCD of 88 and 50 is 2.
Step 2: Divide both numerator and denominator by the GCD (2).
88 / 2 = 44
50 / 2 = 25
Therefore, the simplified fraction is 44/25.
The decimal representation of 44/25 is approximately 1.76.