Question

You and your sister ordered two individual pizzas. You ate \(\frac{3}{4}\) of your pizza and your sister ate \(\frac{5}{8}\) of her pizza. Who ate more pizza?

Short answer

Answer: You ate more pizza than your sister.

Step-by-step solution

Identify the Least Common Denominator (LCD)

The first step is to find the least common denominator (LCD) for the two given fractions. The LCD is the smallest multiple that the denominators share. In this case, the denominators are 4 and 8. Since 8 is a multiple of 4 (8 = 4 * 2), the least common denominator for the fractions \(\frac{3}{4}\) and \(\frac{5}{8}\) is 8.

Convert the fractions to equivalent fractions with the common denominator

Now that we have identified the least common denominator (LCD), we can convert the given fractions to equivalent fractions using the LCD. To do this, multiply the numerator and the denominator of each fraction by the same number to get the equal fractions with the common denominator. For the fraction \(\frac{3}{4}\), we need to multiply both the numerator and the denominator by 2 to get the LCD 8: \(\frac{3}{4} * \frac{2}{2} = \frac{3*2}{4*2} = \frac{6}{8}\) For the fraction \(\frac{5}{8}\), the denominator is already 8, so there is no need to convert to an equivalent fraction.

Compare the equivalent fractions

Now that we have the equivalent fractions with the same denominator, we can compare their numerators: \(\frac{6}{8}\) versus \(\frac{5}{8}\) Since 6 is greater than 5, we can conclude that \(\frac{6}{8}\) is greater than \(\frac{5}{8}\).

Draw the conclusion

As a result of the comparison, we can determine that \(\frac{6}{8}\), which represents the portion of pizza eaten by you, is more than \(\frac{5}{8}\), which represents the portion of pizza eaten by your sister. Therefore, you ate more pizza than your sister.