Simplifying the Fraction: 1/3 × 3/5 × 2 1/4
In this article, we will explore how to simplify the fraction: 1/3 × 3/5 × 2 1/4. To do so, we need to follow the order of operations (PEMDAS) and perform the multiplication step by step.
Step 1: Convert Mixed Number to Improper Fraction
First, we need to convert the mixed number 2 1/4 to an improper fraction. To do this, we multiply the whole number part (2) by the denominator (4) and then add the numerator (1).
2 1/4 = (2 × 4) + 1 / 4 = 9/4
So, the expression becomes: 1/3 × 3/5 × 9/4
Step 2: Multiply the Fractions
Now, we can multiply the fractions:
- Multiply the numerators (numbers on top): 1 × 3 × 9 = 27
- Multiply the denominators (numbers at the bottom): 3 × 5 × 4 = 60
- Write the result as a fraction: 27/60
Step 3: Simplify the Fraction
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 27 and 60 is 3. So, we can divide both the numerator and the denominator by 3:
27 ÷ 3 = 9 60 ÷ 3 = 20
The simplified fraction is: 9/20
Therefore, the simplified form of the fraction 1/3 × 3/5 × 2 1/4 is 9/20.
