Last week, Hayden rode his bike 5 times. Each time, he biked a 3-mile path, a 2-mile path, and a
2
1
4
-mile path. Which expression represents the total number of miles he biked?
A.
5
×
(
3
+
2
+
2
1
4
)
B.
5
+
(
3
×
2
×
2
1
4
)
C.
5
×
(
3
×
2
×
2
1
4
)
D.
5
+
(
3
+
2
+
2
1
4
)
Option A is the correct expression:
5 × (3 + 2 + 2 1/4)
This simplifies to:
5 × (7 1/4)
Multiplying across the mixed number:
5 × (29/4)
Converting to a common fraction:
145/4
This is the total number of miles Hayden biked, which cannot be simplified any further.
did u use pemdas
No, I did not use PEMDAS (or BEDMAS) explicitly in this problem. The problem only involves multiplying and adding, and these operations have the same priority, so you can just simplify from left to right. However, if there were parentheses or other grouping symbols involved, then PEMDAS would be helpful to ensure the correct order of operations.
use pemdas
Sure, we can use PEMDAS (or BEDMAS) to simplify the expression. Using the acronym, we perform the operations in the following order:
1. Parentheses (or other grouping symbols)
2. Exponents (powers, roots)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
The expression is:
5 × (3 + 2 + 2 1/4)
We don't have any exponents, so we can move to multiplication and division. There are no divisions, so let's multiply:
5 × (3 + 2 + 2 1/4) = 5 × (3 + 2 + 9/4)
Next, we need to simplify the expression inside the parentheses, taking into account the mixed number:
5 × (3 + 2 + 9/4) = 5 × (5 + 9/4)
Now, we can add the two whole numbers and the two fractions separately:
5 × (5 + 9/4) = 5 × (20/4 + 9/4)
5 × (20/4 + 9/4) = 5 × (29/4)
Finally, we multiply the two numbers:
5 × (29/4) = 145/4
So the total number of miles Hayden biked is 145/4, which cannot be simplified any further.