Is 5/8 greater than less than or equal to 1/2?
The Correct answer and Explanation is:
To determine whether ( \frac{5}{8} ) is greater than, less than, or equal to ( \frac{1}{2} ), we need to compare the two fractions. One common method for comparing fractions is to find a common denominator or convert them into decimal form.
Step 1: Finding a common denominator
Both ( \frac{5}{8} ) and ( \frac{1}{2} ) have different denominators. To compare them directly, we can rewrite them with the same denominator. The least common denominator (LCD) of 8 and 2 is 8.
- ( \frac{1}{2} ) can be converted to an equivalent fraction with a denominator of 8 by multiplying both the numerator and denominator by 4:
[
\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
]
Now, we can directly compare ( \frac{5}{8} ) with ( \frac{4}{8} ).
Step 2: Compare the numerators
- ( \frac{5}{8} ) has a numerator of 5, while ( \frac{4}{8} ) has a numerator of 4.
- Since 5 is greater than 4, we can conclude that:
[
\frac{5}{8} > \frac{4}{8}
]
Therefore, ( \frac{5}{8} ) is greater than ( \frac{1}{2} ).
Step 3: Decimal Conversion (Alternative Method)
We can also compare these fractions by converting them to decimals:
- ( \frac{5}{8} = 0.625 )
- ( \frac{1}{2} = 0.5 )
Since ( 0.625 > 0.5 ), this confirms that ( \frac{5}{8} ) is greater than ( \frac{1}{2} ).
Final Answer:
( \frac{5}{8} ) is greater than ( \frac{1}{2} ).
In conclusion, whether by using the common denominator approach or decimal conversion, ( \frac{5}{8} ) is larger than ( \frac{1}{2} ). This comparison shows that understanding the relationship between fractions involves either adjusting the denominators or converting to decimal form for direct comparison.