Write the decimal 5.6 as a fraction or mixed number in simplest form.
The correct answer and explanation is:
To write the decimal 5.6 as a fraction in its simplest form, follow these steps:
- Express the decimal as a fraction:
The number 5.6 is read as “five and six-tenths,” which means 5 and 6/10. Therefore, you can write: 5.6=5+6105.6 = 5 + \frac{6}{10} - Simplify the fraction:
Next, simplify the fraction 610\frac{6}{10}. To do this, find the greatest common divisor (GCD) of 6 and 10. The GCD of 6 and 10 is 2, so divide both the numerator and denominator of the fraction by 2: 610=6÷210÷2=35\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5} - Rewrite the mixed number:
Now you can express 5.6 as a mixed number: 5.6=5+35=255+35=2855.6 = 5 + \frac{3}{5} = \frac{25}{5} + \frac{3}{5} = \frac{28}{5}
Thus, the decimal 5.6 as a fraction in simplest form is: 285\frac{28}{5}
Explanation:
- Step 1: Start by expressing the decimal as a whole number plus a fraction. This helps visualize the decimal as a sum of its integer and fractional parts.
- Step 2: Simplifying the fraction is essential to express it in its simplest form. Dividing the numerator and denominator by their GCD ensures the fraction is in its lowest terms.
- Step 3: The final result is written as an improper fraction, 285\frac{28}{5}, which is mathematically equivalent to 5.6.