Operations with Fractions

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 replying to comments. Calculate what fraction of the total time she spends recording and editing (remember to find a common denominator).

To make 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 it all together, they drink $\frac{2}{5}$ of a liter before putting it in the fridge, how much drink is left in total? Express the simplified answer in liters.

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

Perform the following fraction multiplications and simplify the results to the irreducible fraction:

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

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

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

In a café kitchen, they want to divide $3$ 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 $\frac{15}{2}$ meters long and we want to divide it into equal pieces measuring $\frac{3}{4}$ of a meter each. How many full pieces will we get? Will there be any wood left over?

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

Apply the laws of indices and roots to simplify the following numerical expression:

Calculate the result of the following mixed operation, simplifying the answer to its irreducible fraction:

Find the value of the following expression involving 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 equation with fractions:

Calculate the value of the unknown $x$ in the following equation with fraction operations:

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

A streaming platform divides its catalogue of series 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 is represented by the action series that they have not yet watched?

A drone takes off from the ground and ascends to a height of $12$ meters. Then, due to a gust of wind, it descends $\frac{14}{3}$ of a meter. If it then rises again by 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 located?

The publisher of a youth magazine is analyzing where its readers come from. It knows that $\frac{2}{5}$ of the total live in Mexico. Of the remaining readers, $\frac{3}{8}$ live in other Latin American countries. If there are still $1,500$ readers who live in the rest of the world, how many readers does the magazine have in total?

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

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 is left after Alba and Bruno have eaten.

1. a) What fraction of the pizza is left over?

1. b) If the pizza weighed $1.2$ kg, how many grams did each person eat?

A cyclist rides a stage of $120$ km in three legs. In the first hour, they cover $\frac{2}{5}$ of the journey. In the second hour, due to fatigue, their speed decreases and they only cover $\frac{1}{3}$ of the remaining distance. How many kilometers do they have left to cover for the third hour? What fraction of the total does that final leg represent?

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

A gardener has spent $\frac{2}{9}$ of the savings they had for tools on buying a lawnmower and $\frac{3}{10}$ of the initial budget on pruning shears. If they still have $172$ pesos left in their budget, how much money did they have at the start?

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