3/4 x 12
The Correct Answer and Explanation is:
To solve the problem ( \frac{3}{4} \times 12 ), let’s break it down step by step.
Step 1: Understand the Problem
The expression involves multiplying a fraction (( \frac{3}{4} )) by a whole number (12). When multiplying a fraction by a whole number, you treat the whole number as a fraction by writing it over 1. So, 12 can be rewritten as ( \frac{12}{1} ).
Step 2: Set Up the Multiplication
Now, we can set up the multiplication:
[
\frac{3}{4} \times \frac{12}{1}
]
Step 3: Multiply the Numerators and Denominators
To multiply fractions, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. So for our example:
[
\text{Numerator: } 3 \times 12 = 36
]
[
\text{Denominator: } 4 \times 1 = 4
]
Step 4: Simplify the Fraction
Now that we have the fraction ( \frac{36}{4} ), we simplify it by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of 36 and 4 is 4. So, we divide both the numerator and the denominator by 4:
[
\frac{36}{4} = \frac{36 \div 4}{4 \div 4} = \frac{9}{1}
]
Step 5: Final Answer
The simplified fraction ( \frac{9}{1} ) is just 9, because any fraction with 1 as the denominator is equivalent to the whole number in the numerator.
Thus, the solution to ( \frac{3}{4} \times 12 ) is 9.
Explanation of the Process
Multiplying fractions may seem tricky at first, but it is straightforward once you follow these steps. The key is to convert the whole number into a fraction by writing it as ( \frac{12}{1} ), then multiplying the numerators and denominators separately. Afterward, simplifying the result is important, especially when the numerator and denominator have common factors. In this case, the fraction simplifies to a whole number because 36 divided by 4 is 9. This is an essential skill for working with fractions, and the more you practice, the easier it will become!