Paul was given this math problem on a test to simplify: 1/4 + (5/8 + 1/2). after calculating, Paul mistakenly simplified to 9/32 as his final answer In which step did Paul make his first error? Show your work! My work
Paul's work 1/4 /9/8
1/4 /(5/8 + 4/8) 1/4 x 8/9
1/4 + 8/9 Paul's error 8/36
1/4 x 9/8 8/36 = 2/9
9/32 Is this correct
9/32
I apologize, but it seems that there was a mistake in the given work as well as Paul's work. Let's go step by step to solve the problem correctly.
The given expression is 1/4 + (5/8 + 1/2).
First, let's simplify the innermost parentheses by adding 5/8 and 1/2:
5/8 + 1/2 = 5/8 + 4/8 = 9/8.
Now, the expression becomes 1/4 + 9/8.
To add these fractions, we need to have a common denominator. The least common multiple of 4 and 8 is 8.
Converting 1/4 into a fraction with a denominator of 8:
1/4 = 2/8.
Now, the expression becomes 2/8 + 9/8.
When the fractions have the same denominator, we can add their numerators directly:
2/8 + 9/8 = 11/8.
Therefore, the correct simplified form of the expression is 11/8, and Paul made his first error when he calculated 1/4 + 9/8 as 8/36.
To find Paul's error, let's go through the steps one by one:
Step 1: Paul correctly wrote down the problem: 1/4 + (5/8 + 1/2)
Step 2: Paul made an error when simplifying the fraction 5/8 + 1/2. Let's break it down:
(5/8 + 1/2) = Common denominator is 8, so we need to rewrite 1/2 as an equivalent fraction with denominator 8:
(5/8 + 4/8) = 9/8
Step 3: Paul mistakenly wrote 1/4 divided by 9/8 instead of 1/4 multiplied by 9/8. The correct step should be:
1/4 * 9/8
Step 4: Paul's error continues when he adds 1/4 and 9/8 incorrectly. Let's go through the correct calculation:
1/4 * 9/8 = (1 * 9)/(4 * 8) = 9/32
Therefore, Paul's first error occurred in Step 2 when he incorrectly simplified (5/8 + 1/2) as 9/8 instead of 9/8.