1 1/15 X 5 2/5 X 4 7/12 As A Fraction

4 min read Jun 17, 2024
1 1/15 X 5 2/5 X 4 7/12 As A Fraction

Multiplying Mixed Numbers: A Step-by-Step Guide

This article will guide you through the process of multiplying mixed numbers, specifically focusing on the example of 1 1/15 x 5 2/5 x 4 7/12.

Converting Mixed Numbers to Improper Fractions

The first step is to convert each mixed number into an improper fraction. Remember that a mixed number represents a whole number plus a fraction.

Here's how to convert each mixed number:

  • 1 1/15: Multiply the whole number (1) by the denominator (15) and add the numerator (1). Keep the same denominator (15). This gives us 16/15.
  • 5 2/5: Multiply the whole number (5) by the denominator (5) and add the numerator (2). Keep the same denominator (5). This gives us 27/5.
  • 4 7/12: Multiply the whole number (4) by the denominator (12) and add the numerator (7). Keep the same denominator (12). This gives us 55/12.

Now our problem looks like this: 16/15 x 27/5 x 55/12

Multiplying Fractions

To multiply fractions, we simply multiply the numerators and the denominators.

(16 x 27 x 55) / (15 x 5 x 12)

Simplifying the Fractions

Before performing the multiplication, let's simplify the fractions by finding common factors in the numerators and denominators.

  • 16/15 cannot be simplified further.
  • 27/5 cannot be simplified further.
  • 55/12 cannot be simplified further.

However, we can notice that 12 and 55 both share a common factor of 4. We can simplify the fraction 55/12 by dividing both numerator and denominator by 4, resulting in 11/3.

Now our problem looks like this: 16/15 x 27/5 x 11/3

Performing the Multiplication

Now, we can multiply the numerators and the denominators:

(16 x 27 x 11) / (15 x 5 x 3)

This gives us 4752 / 225

Simplifying the Result

Finally, we can simplify the improper fraction by dividing both numerator and denominator by their greatest common factor, which is 9.

4752 / 225 = 528 / 25

Therefore, 1 1/15 x 5 2/5 x 4 7/12 = 528/25.

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