Write 5.75 as a mixed number and as an improper fraction. Write your answers in simplest form.
mixed number: [ ]
improper fraction: [ ]
The value given is \(5.75\). This number can be split into its integer part, which is \(5\), and its decimal part, which is \(0.75\). To express this as a mixed number and an improper fraction, we first focus on converting the decimal part into a fraction.
The decimal part is \(0.75\), which is equivalent to \(\frac{75}{100}\). To simplify this fraction, we identify the greatest common divisor (GCD) of \(75\) and \(100\). Since both numbers are divisible by \(25\), we divide them: \(\frac{75 \div 25}{100 \div 25} = \frac{3}{4}\). Thus, \(0.75 = \frac{3}{4}\).
Combining the integer part \(5\) and the fractional part \(\frac{3}{4}\), we get the mixed number \(5 \frac{3}{4}\). To write this as an improper fraction, we multiply the integer by the denominator of the fraction and add the numerator: \(5 \times 4 + 3 = 20 + 3 = 23\). The result is the numerator over the original denominator, which is \(\frac{23}{4}\). Both forms are now in their simplest forms.
Imagine you are baking a cake and the recipe requires \(5.75\) cups of flour. Knowing this as a fraction helps you measure more accurately using standard measuring cups. Since your measuring cups are marked in fractions, you would recognize that \(5.75\) cups corresponds to \(5 \frac{3}{4}\) cups, or \(\frac{23}{4}\) cups if you are measuring by quarter-cup increments repeatedly. This skill is vital for cooking, construction, and any scenario where precise measurements with fractional parts are necessary.