Operation Order: Evaluating 2 1/4 × 2/3
When dealing with mixed numbers and fractions, it's essential to follow the order of operations (PEMDAS) to ensure accurate calculations. In this article, we'll explore the step-by-step process of evaluating the expression 2 1/4 × 2/3.
Converting Mixed Numbers to Improper Fractions
Before we dive into the multiplication process, let's convert the mixed number 2 1/4 to an improper fraction.
2 1/4 = ?
To convert a mixed number to an improper fraction, we multiply the whole number part (2) by the denominator (4) and then add the numerator (1).
(2 × 4) + 1 = 9
So, the mixed number 2 1/4 is equivalent to the improper fraction:
9/4
Multiplying Fractions
Now that we have an improper fraction, we can multiply it by the other fraction 2/3.
9/4 × 2/3 = ?
To multiply fractions, we multiply the numerators (9 and 2) and multiply the denominators (4 and 3). Then, we simplify the resulting fraction.
(9 × 2) = 18
(4 × 3) = 12
18/12
Simplifying the Fraction
To simplify the resulting fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
GCD of 18 and 12 = 6
Divide both by 6:
18 ÷ 6 = 3
12 ÷ 6 = 2
3/2
Final Answer
The final result of the multiplication is:
2 1/4 × 2/3 = 3/2
or in decimal form:
1.5
By following the order of operations and converting mixed numbers to improper fractions, we can simplify complex expressions like 2 1/4 × 2/3 with ease.
