1/8 x 2/3
The Correct Answer and Explanation is :
To calculate ( \frac{1}{8} \times \frac{2}{3} ), we follow the standard rule for multiplying fractions, which is to multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
Step-by-Step Process:
- Multiply the numerators:
The numerators are 1 and 2, so:
[
1 \times 2 = 2
] - Multiply the denominators:
The denominators are 8 and 3, so:
[
8 \times 3 = 24
] - Combine the results:
Now, put the product of the numerators over the product of the denominators:
[
\frac{1}{8} \times \frac{2}{3} = \frac{2}{24}
] - Simplify the fraction:
To simplify ( \frac{2}{24} ), find the greatest common divisor (GCD) of 2 and 24. The GCD is 2. Divide both the numerator and denominator by 2:
[
\frac{2}{24} = \frac{2 \div 2}{24 \div 2} = \frac{1}{12}
]
Final Answer:
The simplified result of ( \frac{1}{8} \times \frac{2}{3} ) is ( \frac{1}{12} ).
Explanation:
When multiplying fractions, it’s crucial to understand the concept of “parts of parts.” Each fraction represents a division of a whole into parts. In this case, ( \frac{1}{8} ) means one part out of 8, and ( \frac{2}{3} ) means two parts out of 3. When you multiply the two fractions, you’re essentially finding a portion of a portion.
Another way to visualize this is to imagine dividing a pizza into 8 slices (for ( \frac{1}{8} )) and then taking 2 out of every 3 slices from a smaller portion. When combined, you’re left with ( \frac{1}{12} ) of the whole pizza.
The multiplication of fractions works by multiplying the parts directly, and simplification is necessary to ensure the result is in its simplest form, making the fraction easier to understand and use.