Whats 4 x 1/8 in simplest form
The Correct Answer and Explanation is:
To solve the multiplication of (4) and (\frac{1}{8}), we start by expressing (4) as a fraction. The number (4) can be represented as (\frac{4}{1}). Thus, the multiplication can be rewritten as follows:
[
4 \times \frac{1}{8} = \frac{4}{1} \times \frac{1}{8}
]
When multiplying two fractions, we multiply the numerators together and the denominators together. Therefore, we calculate the multiplication as follows:
[
\frac{4 \times 1}{1 \times 8} = \frac{4}{8}
]
Now, we need to simplify (\frac{4}{8}). To do this, we look for the greatest common divisor (GCD) of the numerator and the denominator. The GCD of (4) and (8) is (4). We can divide both the numerator and the denominator by their GCD:
[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
]
Thus, the simplified form of (4 \times \frac{1}{8}) is (\frac{1}{2}).
Explanation of the Steps
- Converting Whole Numbers to Fractions: In multiplication involving whole numbers and fractions, it’s often easier to convert the whole number into a fraction (in this case, (4) to (\frac{4}{1})).
- Multiplication of Fractions: The rule for multiplying fractions is straightforward: multiply the numerators together and the denominators together. This step is crucial as it forms the basis for simplifying the resultant fraction.
- Simplifying Fractions: After obtaining (\frac{4}{8}), the next step is simplification. Identifying the GCD allows us to reduce the fraction to its simplest form. Simplifying fractions is an essential skill in mathematics, ensuring that answers are expressed in the most concise way.
In conclusion, (4 \times \frac{1}{8}) simplifies to (\frac{1}{2}), demonstrating fundamental arithmetic operations involving fractions and the importance of simplification in mathematical expressions.