How do you compare mixed numbers?

To compare mixed numbers, convert them to improper fractions or decimals, then compare the values directly.

When comparing mixed numbers, the first step is to convert each mixed number into an improper fraction. A mixed number consists of a whole number and a fraction. To convert it, multiply the whole number by the denominator of the fraction, then add the numerator. This sum becomes the new numerator, while the denominator remains the same. For example, to convert \(2 \frac{3}{4}\) to an improper fraction, multiply 2 by 4 to get 8, then add 3 to get 11, resulting in \(\frac{11}{4}\).

Alternatively, you can convert mixed numbers to decimals. To do this, divide the numerator by the denominator to get the decimal part, then add this to the whole number. For instance, \(2 \frac{3}{4}\) can be converted to a decimal by dividing 3 by 4 to get 0.75, then adding 2 to get 2.75.

Once both mixed numbers are converted to either improper fractions or decimals, you can compare them directly. If using improper fractions, ensure they have a common denominator before comparing the numerators. If using decimals, simply compare the decimal values. For example, to compare \(2 \frac{3}{4}\) and \(3 \frac{1}{2}\), convert them to decimals (2.75 and 3.5, respectively) and observe that 3.5 is greater than 2.75.

By converting mixed numbers to a common format, you can easily determine which is larger or smaller.