Operations with Fractions

At a snack with friends, several pizzas of the same size have been bought, all cut into 8 equal slices.

• Marcus has eaten $\frac{3}{8}$ of a pizza.

• Sara has eaten $\frac{2}{8}$ of a pizza.

Calculate what fraction of pizza they have eaten between the two of them and how many slices are left if only one pizza had been opened.

Calculate the following additions and subtractions of fractions with the same denominator, simplifying the result where possible:

1. a) $\frac{5}{12} + \frac{1}{12}$

1. b) $\frac{11}{15} - \frac{4}{15}$

1. c) $\frac{7}{9} + \frac{2}{9} - \frac{4}{9}$

A young influencer spends her afternoon organizing her videos. She spends $\frac{1}{4}$ of the time recording, $\frac{1}{3}$ editing and the rest of the time answering comments. Calculate what fraction of the total time she spends recording and editing (remember to find a common denominator).

A tablet battery indicates that it has $\frac{7}{10}$ of its charge left. If after watching some videos it has consumed $\frac{2}{5}$ of the total charge, what fraction of the battery is still left? (Hint: convert $\frac{2}{5}$ into a fraction with a denominator of $10$).

To prepare a tropical drink, a group of friends mixes $\frac{3}{4}$ of a liter of pineapple juice, $\frac{1}{3}$ of a liter of orange juice and $\frac{5}{6}$ of a liter of sparkling water. If after mixing everything, they drink $\frac{2}{5}$ of a liter before putting it in the fridge, what amount of drink is left in total? Express the simplified result in liters.

For an Art project, a group of students has a box with $60$ markers. If they have used $\frac{2}{5}$ of the markers to make a mural, how many markers have they used in total?

Perform the following multiplications of fractions and simplify the results to their irreducible fraction:

1. a) $\frac{2}{3} \cdot \frac{5}{7}$

1. b) $\frac{3}{4} \cdot \frac{2}{5}$

1. c) $5 \cdot \frac{3}{10}$

In a chemistry laboratory, a container $A$ contains $\frac{3}{4}$ of a liter of alcohol, and a container $B$ contains $\frac{2}{3}$ of a liter of water. Half of the contents of container $A$ is transferred to container $B$. What fraction of a liter of mixture is there now in container $B$? If $\frac{1}{5}$ of the total mixture of $B$ is then spilled, how many liters are left in that container?

In a café kitchen, they want to distribute $3$ liters of orange juice into glasses of $\frac{1}{4}$ of a liter each. How many glasses will they be able to fill completely? Illustrate your reasoning by dividing each liter into parts.

Solve these divisions using cross-multiplication:

1. a) $\frac{4}{5} : \frac{2}{3}$

1. b) $\frac{1}{6} : \frac{1}{2}$

1. c) $\frac{3}{7} : 3$

In the technology workshop, wooden battens are being cut. We have a batten $\frac{15}{2}$ feet long and we want to divide it into equal pieces measuring $\frac{3}{4}$ of a foot each. How many complete pieces will we get? Will there be any wood left over?

Calculate the result of the following combined operation, respecting the order of operations and simplifying the final result to obtain the irreducible fraction:

A drone takes off from the ground and ascends to a height of $12$ feet. Then, due to a gust of wind, it descends $\frac{14}{3}$ of a foot. If it then climbs back up a height equal to $\frac{2}{5}$ of the position it was in after the descent, at what height above the ground is the drone finally?

Calculate the result of the following combined operation, simplifying the result until you obtain the irreducible fraction:

Apply the properties of powers and roots to simplify the following numerical expression:

Find the value of the following expression with powers and roots of rational numbers. Remember to apply the order of operations and simplify fully:

Find the value of the unknown $x$ in the following equality of operations with fractions:

Calculate the value of the unknown $x$ in the following equality of operations with fractions:

A streaming platform divides its series catalogue into three parts: $\frac{2}{5}$ are action, $\frac{1}{3}$ are comedy and the rest are documentaries. If a user has already watched $\frac{3}{4}$ of all the available action series, what fraction of the total catalogue do the action series they have not yet watched represent?

A cyclist rides a $120$ mile stage in three sections. In the first hour, he covers $\frac{2}{5}$ of the route. In the second hour, due to fatigue, his speed decreases and he only covers $\frac{1}{3}$ of the remaining distance. How many miles does he have left to cover in the third hour? What fraction of the total does this last section represent?

Three friends, Alba, Bruno and Carla, buy a giant pizza for dinner. Alba eats $\frac{1}{4}$ of the pizza. Bruno eats $\frac{1}{3}$ of what is left. Carla eats $\frac{2}{5}$ of what Alba and Bruno have left together.

1. What fraction of the pizza is left over?

2. If the pizza weighed $1,2$ kg, how many grams has each person eaten?

A gardener has spent $\frac{2}{9}$ of his tool savings on buying a lawnmower and $\frac{3}{10}$ of the initial budget on pruning shears. If he still has $\$172$ left in his budget, how much money did he have at the beginning?

(Hint: First calculate what fraction of the total he has spent by adding both amounts).

A young video game streamer is analyzing the origin of his subscribers. He knows that $\frac{2}{5}$ of the total live in the United States. Of the rest of his subscribers, $\frac{3}{8}$ live in Latin American countries. If there are still $1.500$ subscribers who live in the rest of the world, how many subscribers does the channel have in total?

An architect is designing a sustainable house. The garden takes up $\frac{2}{7}$ of the total plot. The house takes up $\frac{3}{5}$ of the remaining area. If the garage and the swimming pool take up the final $120$ $m^2$, what is the total area of the plot?