Multiplying Fractions: 1 1/2 x 3/4
This article will guide you through the process of multiplying the mixed number 1 1/2 by the fraction 3/4.
Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. To multiply a mixed number by a fraction, we first need to convert it into an improper fraction.
Converting 1 1/2 to an Improper Fraction:
- Multiply the whole number (1) by the denominator of the fraction (2): 1 * 2 = 2.
- Add the numerator of the fraction (1) to the result: 2 + 1 = 3.
- Keep the same denominator (2).
- The improper fraction equivalent of 1 1/2 is 3/2.
Multiplying Fractions
Now, we have the following multiplication problem: 3/2 x 3/4
To multiply fractions, we simply multiply the numerators and the denominators:
- Numerator: 3 x 3 = 9
- Denominator: 2 x 4 = 8
Therefore, 3/2 x 3/4 = 9/8
Simplifying the Result
The fraction 9/8 is an improper fraction (the numerator is larger than the denominator). We can simplify it into a mixed number:
- Divide the numerator (9) by the denominator (8): 9 ÷ 8 = 1 with a remainder of 1.
- The quotient (1) becomes the whole number part of the mixed number.
- The remainder (1) becomes the numerator of the fraction part.
- The denominator remains the same (8).
Therefore, the simplified form of 9/8 is 1 1/8.
Conclusion
The product of 1 1/2 and 3/4, when expressed in fraction form, is 1 1/8.