To express the decimal 8.5 as a fraction, we can follow a straightforward method. First, we recognize that the number consists of two parts: the whole number (8) and the decimal part (0.5).
1. **Separate the Whole Number from the Decimal**: We start by separating 8.5 into its whole number and decimal components:
– Whole number: 8
– Decimal part: 0.5
2. **Convert the Decimal to a Fraction**: Next, we convert the decimal part (0.5) into a fraction. Since 0.5 is the same as 5 tenths, we can write it as:
– 0.5 = 5/10
3. **Simplify the Fraction**: The fraction 5/10 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
– 5 ÷ 5 = 1
– 10 ÷ 5 = 2
Thus, we have:
– 0.5 = 1/2
4. **Combine the Whole Number and the Fraction**: Now we can combine the whole number (8) with the simplified fraction (1/2). To do this, we can write:
– 8.5 = 8 + 0.5 = 8 + 1/2
5. **Express as an Improper Fraction**: If we want to express this combined value as a single proper fraction, we need to convert the whole number into a fraction. Since any whole number can be expressed as a fraction by using 1 as the denominator, we have:
– 8 = 8/1
To combine this with 1/2, we need a common denominator:
– The common denominator between 1 and 2 is 2. So, we can convert 8/1 to a fraction with 2 as the denominator:
– 8 = (8 x 2)/(1 x 2) = 16/2
6. **Final Combination**: Now we can add the two fractions:
– 16/2 + 1/2 = (16 + 1)/2 = 17/2
So, in conclusion, the decimal 8.5 can be expressed as the fraction:
16/2 or 17/2
This fraction can also be represented as a mixed number:
8 1/2
Thus, 8.5 as a fraction can be written as 17/2 or as the mixed number 8 1/2.