Operations with fractions
At a tea party, Marcos eats $\frac{3}{8}$ of a pizza and Sara eats $\frac{2}{8}$. How much have they eaten between them? And what if the pizzas hadn't been cut in the same way? You are going to learn how to add, subtract, multiply and divide fractions without getting confused.
Adding and subtracting fractions
Calculate the following additions and subtractions of fractions with the same denominator, simplifying the result where possible: a) $\frac{5}{12} + \frac{1}{12}$ b)…
Calculate the following additions and subtractions of fractions with the same denominator, simplifying the result where possible:
- a) $\frac{5}{12} + \frac{1}{12}$
- b) $\frac{11}{15} - \frac{4}{15}$
- 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…
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 litre of pineapple juice, $\frac{1}{3}$ of a litre of orange juice, and $\frac{5}{6}$ of a litre of…
To make a tropical drink, a group of friends mixes $\frac{3}{4}$ of a litre of pineapple juice, $\frac{1}{3}$ of a litre of orange juice, and $\frac{5}{6}$ of a litre of sparkling water. If after mixing it all together, they drink $\frac{2}{5}$ of a litre before putting it in the fridge, how much drink is left in total? Express the simplified answer in litres.
Multiplying and dividing fractions
Perform the following fraction multiplications and simplify the results to the irreducible fraction: a) $\frac{2}{3} \cdot \frac{5}{7}$ b)…
Perform the following fraction multiplications and simplify the results to the irreducible fraction:
- a) $\frac{2}{3} \cdot \frac{5}{7}$
- b) $\frac{3}{4} \cdot \frac{2}{5}$
- c) $5 \cdot \frac{3}{10}$
Solve these divisions using cross-multiplication: a) $\frac{4}{5} : \frac{2}{3}$ b) $\frac{1}{6} : \frac{1}{2}$ c) $\frac{3}{7} : 3$
Solve these divisions using cross-multiplication:
- a) $\frac{4}{5} : \frac{2}{3}$
- b) $\frac{1}{6} : \frac{1}{2}$
- c) $\frac{3}{7} : 3$
In the technology workshop, wooden battens are being cut. We have a batten $\frac{15}{2}$ metres long and we want to divide it into equal pieces measuring $\frac{3}{4}$…
In the technology workshop, wooden battens are being cut. We have a batten $\frac{15}{2}$ metres long and we want to divide it into equal pieces measuring $\frac{3}{4}$ of a metre each. How many full pieces will we get? Will there be any wood left over?
Combined operations with fractions
Just as with integers, there is a fixed order: brackets first, then multiplications and divisions, and finally additions and subtractions.
At a snack with friends, several pizzas of the same size were bought, all cut into 8 equal slices. Marcos ate $\frac{3}{8}$ of a pizza. Sara ate $\frac{2}{8}$ of a…
At a snack with friends, several pizzas of the same size were bought, all cut into 8 equal slices.
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Marcos ate $\frac{3}{8}$ of a pizza.
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Sara ate $\frac{2}{8}$ of a pizza.
Calculate what fraction of a pizza they have eaten altogether and how many slices remain if only one pizza had been opened.
Calculate the result of the following mixed operation, respecting the order of operations and simplifying the final result to obtain the irreducible fraction:…
Calculate the result of the following mixed operation, respecting the order of operations and simplifying the final result to obtain the irreducible fraction:
$$\frac{2}{3} \cdot \left( \frac{5}{2} - \frac{3}{4} \right) + \frac{7}{6} : 2$$Find the value of the unknown $x$ in the following equation with fractions: $$\frac{x}{12} + \frac{5}{6} \cdot \frac{1}{2} = \frac{3}{4}$$
Find the value of the unknown $x$ in the following equation with fractions:
$$\frac{x}{12} + \frac{5}{6} \cdot \frac{1}{2} = \frac{3}{4}$$Problems with "of the rest"
Many problems say "a fraction of what is left", not of the total: you have to work step by step, not all at once.
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…
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…
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?
Back to the beginning: between them, Marcos and Sara have eaten $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$ of a pizza; if they had been cut differently (for example, into quarters and eighths), you would first have to convert them to a common denominator using the LCM before adding the numerators.