Multiplying Mixed Numbers: A Step-by-Step Guide
This article will guide you through the process of multiplying mixed numbers, specifically the problem 1 2/3 x 2 1/3 x 2. We will break down the steps and simplify the final answer.
Converting Mixed Numbers to Fractions
The first step is to convert the mixed numbers into improper fractions.
1. Multiply the whole number and the denominator.
- 1 x 3 = 3
- 2 x 3 = 6
2. Add the numerator to the product from step 1.
- 3 + 2 = 5
- 6 + 1 = 7
3. Keep the same denominator.
- 1 2/3 becomes 5/3
- 2 1/3 becomes 7/3
4. Rewrite the problem:
- 5/3 x 7/3 x 2
Multiplying Fractions
1. Multiply the numerators.
- 5 x 7 x 2 = 70
2. Multiply the denominators.
- 3 x 3 x 1 = 9
3. The answer in fraction form is:
- 70/9
Simplifying the Answer
While 70/9 is a valid answer, we can simplify it to a mixed number.
1. Divide the numerator (70) by the denominator (9).
- 70 ÷ 9 = 7 with a remainder of 7
2. The quotient (7) becomes the whole number of the mixed number.
3. The remainder (7) becomes the numerator of the fraction.
4. The denominator (9) stays the same.
Therefore, the final answer is 7 7/9.
Conclusion
By converting the mixed numbers to fractions and then multiplying, we found that 1 2/3 x 2 1/3 x 2 equals 70/9, which simplifies to 7 7/9.