What is 1 3/4 times 2 1/2?
In this article, we'll walk through how to solve the problem of multiplying mixed numbers, specifically 1 3/4 times 2 1/2.
Understanding Mixed Numbers
First, let's understand mixed numbers. A mixed number combines a whole number and a fraction. For example, 1 3/4 means one whole and three-quarters.
Converting Mixed Numbers to Improper Fractions
To multiply mixed numbers, it's easier to convert them into improper fractions. Here's how:
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Multiply the whole number by the denominator of the fraction.
- For 1 3/4: 1 x 4 = 4
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Add the numerator of the fraction to the result.
- 4 + 3 = 7
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Keep the same denominator.
- The improper fraction for 1 3/4 is 7/4
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Repeat steps 1-3 for the other mixed number.
- For 2 1/2: 2 x 2 = 4
- 4 + 1 = 5
- The improper fraction for 2 1/2 is 5/2
Multiplying Improper Fractions
Now we have the problem: 7/4 times 5/2. To multiply fractions:
- Multiply the numerators (the top numbers).
- 7 x 5 = 35
- Multiply the denominators (the bottom numbers).
- 4 x 2 = 8
- The answer is the product of the numerators over the product of the denominators.
- 7/4 times 5/2 = 35/8
Converting Back to a Mixed Number (Optional)
The answer, 35/8, is an improper fraction. If you want to express it as a mixed number:
- Divide the numerator (35) by the denominator (8).
- 35 divided by 8 equals 4 with a remainder of 3.
- The whole number of the mixed number is the quotient (4).
- The fraction part of the mixed number is the remainder (3) over the original denominator (8).
Therefore, 35/8 is equivalent to 4 3/8.
Conclusion
So, 1 3/4 times 2 1/2 is equal to 35/8, or 4 3/8 when expressed as a mixed number.