1 2/3 X 2 3/5 In Fraction

3 min read Jun 17, 2024
1 2/3 X 2 3/5 In Fraction

Multiplying Mixed Numbers: 1 2/3 x 2 3/5

This article will guide you through the process of multiplying mixed numbers, specifically focusing on the example of 1 2/3 x 2 3/5.

Understanding Mixed Numbers

Mixed numbers are a combination of a whole number and a fraction. For example, 1 2/3 represents one whole and two-thirds of another.

Converting Mixed Numbers to Improper Fractions

Before multiplying mixed numbers, it's essential to convert them to improper fractions. Here's how:

  1. Multiply the denominator of the fraction by the whole number: In our case, 3 x 1 = 3.
  2. Add the numerator of the fraction: 3 + 2 = 5.
  3. Keep the same denominator: The improper fraction for 1 2/3 becomes 5/3.

Following the same steps for 2 3/5, we get:

  1. 5 x 2 = 10
  2. 10 + 3 = 13
  3. Keep the denominator: The improper fraction for 2 3/5 becomes 13/5.

Multiplying Improper Fractions

Now we have 5/3 x 13/5. To multiply fractions:

  1. Multiply the numerators: 5 x 13 = 65
  2. Multiply the denominators: 3 x 5 = 15

This gives us 65/15.

Simplifying the Result

The fraction 65/15 can be simplified. Both the numerator and denominator are divisible by 5:

65 ÷ 5 = 13 15 ÷ 5 = 3

Therefore, 65/15 simplifies to 13/3.

Converting Back to a Mixed Number

Finally, convert the improper fraction back to a mixed number:

  1. Divide the numerator by the denominator: 13 ÷ 3 = 4 with a remainder of 1.
  2. The quotient becomes the whole number: 4
  3. The remainder becomes the numerator: 1
  4. Keep the same denominator: 3

The final answer is 4 1/3.

Conclusion

By converting mixed numbers to improper fractions, multiplying them, and simplifying the result, we found that 1 2/3 x 2 3/5 equals 4 1/3. Remember to always simplify your answer to its lowest terms.

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