Multiplying Mixed Numbers: 1 1/2 x 2 1/3
This article will guide you through the process of multiplying mixed numbers, using the example of 1 1/2 x 2 1/3.
Converting Mixed Numbers to Improper Fractions
The first step is to convert both mixed numbers into improper fractions.
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1 1/2: To convert this, multiply the whole number (1) by the denominator (2) and add the numerator (1): 1 * 2 + 1 = 3. Keep the same denominator (2). This gives us 3/2.
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2 1/3: Follow the same process: 2 * 3 + 1 = 7. Keep the denominator (3). This gives us 7/3.
Multiplying the Fractions
Now, we can multiply the two improper fractions:
(3/2) x (7/3)
To multiply fractions, we multiply the numerators and the denominators:
(3 x 7) / (2 x 3) = 21/6
Simplifying the Result
The resulting fraction (21/6) can be simplified. Both the numerator and denominator are divisible by 3:
21/6 = (21 ÷ 3) / (6 ÷ 3) = 7/2
Converting Back to a Mixed Number
Finally, we can convert the improper fraction (7/2) back to a mixed number. Divide the numerator (7) by the denominator (2):
7 ÷ 2 = 3 with a remainder of 1.
The quotient (3) becomes the whole number, the remainder (1) becomes the numerator, and the denominator (2) stays the same.
Therefore, 1 1/2 x 2 1/3 = 3 1/2.