1 1/3 X 1 2/3 As A Fraction

3 min read Jun 17, 2024
1 1/3 X 1 2/3 As A Fraction

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

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

Understanding Mixed Numbers

Mixed numbers consist of a whole number and a fraction. For example, 1 1/3 represents one whole and one-third.

Converting Mixed Numbers to Improper Fractions

Before multiplying, we need to convert the mixed numbers into improper fractions. Here's how:

  1. Multiply the whole number by the denominator: 1 x 3 = 3
  2. Add the numerator: 3 + 1 = 4
  3. Keep the same denominator: 4/3

Therefore, 1 1/3 is equivalent to 4/3.

Applying the same process to 1 2/3, we get:

  1. Multiply the whole number by the denominator: 1 x 3 = 3
  2. Add the numerator: 3 + 2 = 5
  3. Keep the same denominator: 5/3

So, 1 2/3 is equivalent to 5/3.

Multiplying Fractions

Now that we have our improper fractions, we can multiply them:

(4/3) x (5/3)

To multiply fractions, we multiply the numerators and the denominators:

(4 x 5) / (3 x 3) = 20/9

Converting Back to Mixed Number

The result, 20/9, is an improper fraction. We can convert it back to a mixed number:

  1. Divide the numerator by the denominator: 20 ÷ 9 = 2 with a remainder of 2.
  2. The quotient (2) becomes the whole number part of the mixed number.
  3. The remainder (2) becomes the numerator of the fractional part.
  4. The denominator stays the same (9).

Therefore, 20/9 is equivalent to 2 2/9.

Conclusion

By converting the mixed numbers to improper fractions, multiplying the fractions, and converting the result back to a mixed number, we found that 1 1/3 x 1 2/3 = 2 2/9.

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