Question
16 - 12 + 5 * 8 + 2 / 5 cubed - 1 + 4 what is the simplified numerator
Answers
GPT-4o mini
Let's simplify the expression step by step:
The expression is:
\[ 16 - 12 + 5 \times 8 + \frac{2}{5^3} - 1 + 4 \]
We can break it down into parts. First, we will calculate \( 5^3 \) and the multiplication first, as per the order of operations (PEMDAS/BODMAS):
1. Calculate \( 5^3 \):
\[ 5^3 = 125 \]
2. Substitute this back into the expression:
\[ 16 - 12 + 5 \times 8 + \frac{2}{125} - 1 + 4 \]
3. Calculate \( 5 \times 8 \):
\[ 5 \times 8 = 40 \]
4. Substitute back:
\[ 16 - 12 + 40 + \frac{2}{125} - 1 + 4 \]
Now, combine all the whole numbers:
1. Calculate \( 16 - 12 = 4 \)
2. Then \( 4 + 40 = 44 \)
3. Then \( 44 - 1 = 43 \)
4. Finally, \( 43 + 4 = 47 \)
So, now we have:
\[ 47 + \frac{2}{125} \]
To combine these:
\[ \frac{47 \times 125 + 2}{125} \]
\[ = \frac{5875 + 2}{125} \]
\[ = \frac{5877}{125} \]
Thus, the numerator of the simplified fraction is:
\[ \boxed{5877} \]
The expression is:
\[ 16 - 12 + 5 \times 8 + \frac{2}{5^3} - 1 + 4 \]
We can break it down into parts. First, we will calculate \( 5^3 \) and the multiplication first, as per the order of operations (PEMDAS/BODMAS):
1. Calculate \( 5^3 \):
\[ 5^3 = 125 \]
2. Substitute this back into the expression:
\[ 16 - 12 + 5 \times 8 + \frac{2}{125} - 1 + 4 \]
3. Calculate \( 5 \times 8 \):
\[ 5 \times 8 = 40 \]
4. Substitute back:
\[ 16 - 12 + 40 + \frac{2}{125} - 1 + 4 \]
Now, combine all the whole numbers:
1. Calculate \( 16 - 12 = 4 \)
2. Then \( 4 + 40 = 44 \)
3. Then \( 44 - 1 = 43 \)
4. Finally, \( 43 + 4 = 47 \)
So, now we have:
\[ 47 + \frac{2}{125} \]
To combine these:
\[ \frac{47 \times 125 + 2}{125} \]
\[ = \frac{5875 + 2}{125} \]
\[ = \frac{5877}{125} \]
Thus, the numerator of the simplified fraction is:
\[ \boxed{5877} \]