Simplify the following fractions:
Simplify the following fractions, writing your answers as mixed numbers:
Evaluate the following, writing your answers in simplest form:
\dfrac {5}{9} + \dfrac {8}{9}
\dfrac {11}{9} \times \dfrac {2}{99}
- \dfrac {3}{7} \times \dfrac {2}{3}
\left(\dfrac {4}{9}\right)^{2}
\dfrac {3}{8} \div \dfrac {3}{4}
\dfrac {11}{35} \div \dfrac {55}{49}
\left( - \dfrac {4}{5} \right) \div \dfrac {3}{4}
\dfrac{3}{5} \times \dfrac{2}{3} + \dfrac{5}{15}
\left(\dfrac{2}{3} + \dfrac {3}{5}\right) \times \dfrac{3}{7}
Evaluate:
A class has 40 students. \dfrac{2}{5} of the class are boys.
What fraction of the class is girls?
How many girls are in the class?
Ellie wants to install a rectangular swimming pool in her backyard.
If the space available for a pool in her backyard measures 10\dfrac{1}{4}\text{ m} by 4\text{ m}, what will be the total area of the pool?
Sally is a sales assistant. She earns \$192 per week, plus a commission of \dfrac{1}{3} on anything she sells. Last week, she sold \$726 of printers.
What was Sally's commission for last week?
What was Sally's pay for last week?
In a survey of 270 people, \dfrac{1}{10} said their favourite sport was soccer, and \dfrac{1}{9} said their favourite sport was tennis.
What is the total fraction of people who said their favourite sport was soccer or tennis?
What is the fraction of people who did not put soccer or tennis as their favourite sport?
How many people did not put soccer or tennis as their favourite sport?
At the end of last month, a dam was \dfrac{5}{7} full. Over the current month, \dfrac{52}{63} of the dam's capacity was used up by the town. Meanwhile, rain filled \dfrac{5}{9} of the dam's capacity over the duration of the month. What fraction of the dam is full at end of this month?
After an earthquake, \dfrac{3}{7} of all claims were paid within a month. Of the remaining claims that had not yet been paid, \dfrac{5}{7} of them were paid within the second month. What fraction of all claims were paid in the second month?
During a sale, a number of computers were sold. 6 computers were sold at a loss, which represents \dfrac{1}{6} of the total number of computers that were sold.
If 89 computers were up for sale, how many weren't sold?
A bottle is \dfrac{2}{7} full of cordial. If 230\text{ ml} of cordial is added to it, the bottle is \dfrac{5}{6} full. How much cordial does the bottle hold when full?
At the Easter Show, Tobias spends half an hour visiting chickens and \dfrac{1}{3} of an hour visiting alpacas. What fraction of an hour has he spent visiting animals?
A bag of oranges weighing \dfrac{8}{9} \text{ kg} was divided among 6 children. What was the mass of the oranges given to each child?
Katrina and Luigi ordered a pizza to share. Katrina ate \dfrac{3}{7} of the pizza while Luigi ate \dfrac{1}{2}.
Who ate more pizza?
What fraction of the pizza did they eat together?
What fraction of pizza is left?
Luke has a dice tin that is \dfrac{1}{4} full. He puts 8 extra dice in and the tin is now \dfrac{1}{3} full.
What fraction of the tin do the 8 extra dice take up?
How many dice can fit inside the tin?
Victoria borrows a 360-page novel from the library. She reads \dfrac{3}{4} of the novel.
How many pages did she read?
How many more pages does she have to read to finish her novel?
In the morning, a dam contains 635\text{ L} of water. Throughout the day, \dfrac{1}{5} of the water is lost through evaporation and cattle drinking from it.
How many litres of water are lost throughout the day?
How many litres of water are left in the dam at the end of the day?
Maria is a sales assistant. She earns \$293 per week, plus a commission of \dfrac{2}{9} on anything she sells. Last week she sold \$1377 of sofas.
Find Maria's commission for last week.
Find Maria's pay for last week.