Multiplying Mixed Numbers: 1 1/4 x 2 2/3
To multiply mixed numbers, we need to convert them into fractions first. Here's how to do it:
Converting Mixed Numbers to Fractions
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1 1/4: Multiply the whole number (1) by the denominator of the fraction (4), and add the numerator (1). Keep the same denominator. (1 * 4) + 1 = 5, so 1 1/4 becomes 5/4.
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2 2/3: Multiply the whole number (2) by the denominator of the fraction (3), and add the numerator (2). Keep the same denominator. (2 * 3) + 2 = 8, so 2 2/3 becomes 8/3.
Multiplying Fractions
Now we have 5/4 * 8/3. To multiply fractions, we multiply the numerators and the denominators:
- (5 * 8) / (4 * 3) = 40/12
Simplifying the Fraction
40/12 can be simplified by finding the greatest common factor (GCF), which is 4. Dividing both numerator and denominator by 4:
- 40/12 = 10/3
Converting back to a Mixed Number (Optional)
10/3 is an improper fraction (numerator is larger than the denominator). To convert it back to a mixed number, divide the numerator (10) by the denominator (3):
- 10 ÷ 3 = 3 with a remainder of 1
The quotient (3) becomes the whole number, the remainder (1) becomes the numerator, and the denominator stays the same (3).
Therefore, 10/3 is equivalent to 3 1/3.
In conclusion, 1 1/4 x 2 2/3 is equal to 10/3 or 3 1/3.