3/4 times 2 in a simplified fraction?
The Correct Answer and Explanation is:
To solve ( \frac{3}{4} \times 2 ) and express it as a simplified fraction, follow these steps:
Step 1: Express the number 2 as a fraction
The number 2 can be written as a fraction by expressing it over 1. This gives:
[
2 = \frac{2}{1}
]
Step 2: Multiply the fractions
To multiply fractions, multiply the numerators (top numbers) and the denominators (bottom numbers) separately:
[
\frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4}
]
Step 3: Simplify the fraction
The fraction ( \frac{6}{4} ) can be simplified. To do this, find the greatest common divisor (GCD) of the numerator (6) and the denominator (4). The GCD of 6 and 4 is 2.
Now, divide both the numerator and the denominator by 2:
[
\frac{6}{4} = \frac{6 \div 2}{4 \div 2} = \frac{3}{2}
]
Final Answer:
So, ( \frac{3}{4} \times 2 = \frac{3}{2} ).
Explanation:
The process of multiplying fractions involves straightforward multiplication of the numerators and denominators. In this case, ( \frac{3}{4} \times 2 ) becomes ( \frac{6}{4} ). After multiplying, the next step is simplifying the result. Simplifying a fraction involves dividing both the numerator and the denominator by their greatest common divisor (GCD). Here, the GCD of 6 and 4 is 2. By dividing both the numerator and denominator by 2, we get the simplified fraction ( \frac{3}{2} ).
Additional Notes:
- Fractions can be simplified by identifying and dividing by the GCD of the numerator and the denominator. This reduces the fraction to its simplest form.
- ( \frac{3}{2} ) is an improper fraction because the numerator (3) is larger than the denominator (2). It can also be expressed as a mixed number: ( 1 \frac{1}{2} ), but the fraction ( \frac{3}{2} ) is generally preferred in mathematical contexts when working with fractions.