What is the value of 0.8–0.6? Write your answer as a fraction in lowest terms
The Correct Answer and Explanation is :
The value of ( 0.8 – 0.6 ) is ( 0.2 ). Now, let’s express this as a fraction and simplify it.
- Convert the decimals to fractions:
- ( 0.8 = \frac{8}{10} )
- ( 0.6 = \frac{6}{10} )
- Subtract the fractions:
[
\frac{8}{10} – \frac{6}{10} = \frac{8 – 6}{10} = \frac{2}{10}
] - Simplify the fraction:
- ( \frac{2}{10} ) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
]
Thus, the value of ( 0.8 – 0.6 ) is ( \frac{1}{5} ) in its lowest terms.
Explanation (300 words):
The problem asks for the difference between 0.8 and 0.6 and requires the result to be expressed as a fraction in its simplest form. To tackle this, we first need to understand the connection between decimals and fractions.
Decimals are simply another way of representing fractions. The decimal 0.8 is equivalent to ( \frac{8}{10} ) because the number 0.8 can be read as “eight-tenths.” Similarly, 0.6 is equivalent to ( \frac{6}{10} ), or “six-tenths.” These fractions have the same denominator (10), which makes them easy to subtract.
Once we subtract the numerators (8 – 6), we get ( \frac{2}{10} ). While this is a correct representation of the difference, the fraction ( \frac{2}{10} ) is not in its simplest form. To simplify a fraction, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 2 and 10 is 2. Dividing both by 2 gives ( \frac{1}{5} ).
Therefore, ( 0.8 – 0.6 ) equals ( \frac{1}{5} ), which is the simplest form of the answer. This process demonstrates how decimals can be converted to fractions, subtracted, and then simplified for clarity and precision in mathematical expression.