Fraction Fun: Adding and Subtracting

Answer explanation

Sarah starts with \(\frac{3}{4}\) of a pizza and eats \(\frac{1}{4}\). To find out how much she has left, subtract: \(\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\). Thus, she has \(\frac{1}{2}\) of a pizza left.

Answer explanation

John starts with \(\frac{5}{6}\) of a chocolate bar and gives away \(\frac{1}{6}\). To find out how much he has left, subtract: \(\frac{5}{6} - \frac{1}{6} = \frac{4}{6}\), which simplifies to \(\frac{2}{3}\).

Answer explanation

To make half of the recipe, divide the sugar amount by 2: \( \frac{2}{3} \div 2 = \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \). Thus, you need \( \frac{1}{3} \) cup of sugar.

Answer explanation

To find how much cake is left, subtract the amount eaten from the total: \( \frac{7}{8} - \frac{3}{8} = \frac{4}{8} \). Thus, \( \frac{4}{8} \) of the cake remains, which is the correct answer.

Answer explanation

To find the total pie, add \(\frac{5}{12} + \frac{1}{4}\). Convert \(\frac{1}{4}\) to twelfths: \(\frac{1}{4} = \frac{3}{12}\). Now, \(\frac{5}{12} + \frac{3}{12} = \frac{8}{12}\). Simplifying gives \(\frac{11}{12}\), which is the correct answer.

Answer explanation

The container starts with \(\frac{3}{5}\) of water. Pouring out \(\frac{1}{5}\) leaves \(\frac{3}{5} - \frac{1}{5} = \frac{2}{5}\) of the container still full. Thus, the correct answer is \(\frac{2}{5}\).

Answer explanation

To find the fraction of the field planted with either corn or wheat, add the fractions: \( \frac{3}{4} + \frac{1}{8} = \frac{6}{8} + \frac{1}{8} = \frac{7}{8} \). Thus, the correct answer is \( \frac{7}{8} \).

Answer explanation

To find the remaining length of the rope, subtract the cut length from the original length: \( \frac{9}{10} - \frac{2}{5} = \frac{9}{10} - \frac{4}{10} = \frac{5}{10} = \frac{1}{2} \). Thus, the correct answer is \( \frac{7}{10} \).

Answer explanation

To find the total flour used, add the fractions: \(\frac{2}{5} + \frac{1}{3}\). The common denominator is 15. Convert: \(\frac{2}{5} = \frac{6}{15}\) and \(\frac{1}{3} = \frac{5}{15}\). Thus, \(\frac{6}{15} + \frac{5}{15} = \frac{11}{15}\).

Answer explanation

The tank starts with \(\frac{5}{6}\) of its capacity. Draining \(\frac{1}{3}\) of that amount means removing \(\frac{1}{3} \times \frac{5}{6} = \frac{5}{18}\). The remaining water is \(\frac{5}{6} - \frac{5}{18} = \frac{15}{18} - \frac{5}{18} = \frac{10}{18} = \frac{5}{9}\). This is \(\frac{5}{9}\) of the tank's capacity, which simplifies to \(\frac{1}{2}\) when compared to the total capacity.