Operations with rational numbers
A content creator cuts $\frac{1}{6}$ of a video because of sound errors and then removes $\frac{2}{5}$ of what is left. To find out what fraction of the original video survives, you need to be able to add, subtract, multiply and divide fractions confidently, even when negatives appear.
Adding and subtracting fractions
To make a healthy smoothie, you have mixed $\frac{3}{4}$ of a litre of oat milk with $\frac{1}{2}$ litres of orange juice. When serving it, $\frac{1}{8}$ of a litre is…
To make a healthy smoothie, you have mixed $\frac{3}{4}$ of a litre of oat milk with $\frac{1}{2}$ litres of orange juice. When serving it, $\frac{1}{8}$ of a litre is spilled. Work through the operation step by step to find out how much of the mixture remains in the jug.
Multiplying and dividing fractions
On a shelf in a comic shop, $\frac{2}{3}$ of the titles are about superheroes. Of those superhero comics, half ($\frac{1}{2}$) belong to a famous American publisher.…
On a shelf in a comic shop, $\frac{2}{3}$ of the titles are about superheroes. Of those superhero comics, half ($\frac{1}{2}$) belong to a famous American publisher. Calculate the fraction of the whole shelf represented by the comics of that specific publisher by carrying out a fraction multiplication.
We want to share $\frac{3}{2}$ of a kilogram of gummy sweets into small bags. If we put $\frac{1}{10}$ of a kilogram into each bag: a) How many bags can we fill…
We want to share $\frac{3}{2}$ of a kilogram of gummy sweets into small bags. If we put $\frac{1}{10}$ of a kilogram into each bag:
- a) How many bags can we fill completely?
- b) Carry out the operation using division of fractions: $\frac{3}{2} : \frac{1}{10}$
The opposite and the reciprocal of a fraction
Look at the following figure, which represents a chocolate cake divided into equal slices. Write down the fraction representing the missing part, and calculate the…
Look at the following figure, which represents a chocolate cake divided into equal slices. Write down the fraction representing the missing part, and calculate the opposite fraction and the reciprocal fraction of that amount.
Combined operations with fractions
Just as with integers: brackets first, then multiplication and division, and finally addition and subtraction.
Solve the following mixed operation respecting the order of operations: $$\frac{2}{5} \cdot \left( \frac{1}{2} + \frac{1}{3} \right) - \frac{1}{10}$$
Solve the following mixed operation respecting the order of operations:
$$\frac{2}{5} \cdot \left( \frac{1}{2} + \frac{1}{3} \right) - \frac{1}{10}$$Solve the following combined expression, simplifying the result to its simplest form: $$\frac{3}{5} - \left[ \frac{1}{2} : \left( \frac{2}{3} - \frac{1}{6} \right)…
Solve the following combined expression, simplifying the result to its simplest form:
$$\frac{3}{5} - \left[ \frac{1}{2} : \left( \frac{2}{3} - \frac{1}{6} \right) \right] \cdot \frac{5}{4}$$"Of the remainder" problems with fractions
When a problem gives a fraction of what is left, not of the total, you have to work step by step.
A teenager spends $\frac{1}{3}$ of their afternoon free time doing sport and $\frac{2}{5}$ studying maths. a) Calculate what fraction of their total free time these two…
A teenager spends $\frac{1}{3}$ of their afternoon free time doing sport and $\frac{2}{5}$ studying maths.
- a) Calculate what fraction of their total free time these two activities take up.
- b) What fraction of time do they have left to play on the games console?
Three friends decide to buy a gift for a classmate who is changing schools. The first contributes $\frac{2}{5}$ of the total price, the second contributes $\frac{1}{3}$…
Three friends decide to buy a gift for a classmate who is changing schools. The first contributes $\frac{2}{5}$ of the total price, the second contributes $\frac{1}{3}$ of what is left, and the third completes the payment with $16$ €.
- a) What fraction of the total does the amount contributed by the second friend represent?
- b) What is the total price of the gift?
- c) How much money did each person put in?