The concept of a fraction

Look at the following figure, which represents a bar of chocolate. What fraction of the bar remains if we have eaten the squares shaded in orange? State the numerator and the denominator.

Represent the following fractions visually in your exercise book using rectangles or circles:

1. a) $\dfrac{2}{5}$

1. b) $\dfrac{5}{4}$

You can do it on paper and send a photo with your answer.

What fraction of an hour do the following time intervals represent? (Express the fraction in its simplest form).

1. a) $30$ minutes.
2. b) $15$ minutes.
3. c) $20$ minutes.
4. d) $10$ minutes.

Identify whether the following pairs of fractions are equivalent using the cross-products method:

1. a) $\frac{12}{15}$ and $\frac{4}{5}$

1. b) $\frac{7}{3}$ and $\frac{21}{6}$

1. c) $\frac{10}{25}$ and $\frac{6}{15}$

For any pair that is not equivalent, state which of the two fractions is greater.

Write the following fractions using figures and classify them as proper or improper:

1. a) Three eighths.
2. b) Seven halves.
3. c) Eleven elevenths.
4. d) Four ninths.

Match each improper fraction with its corresponding mixed number:

A group of friends bought several bottles of soft drink for a party. Each bottle has a capacity of $\frac{1}{4}$ of a litre. If they consumed a total of $19$ bottles, express this quantity as an improper fraction and as a mixed number. How many full litres have they drunk?

On a digital gaming platform, Lucía has saved $180$ tokens. She decides to spend $\frac{4}{9}$ of her tokens on a new skin for her character and $\frac{2}{5}$ of what she has left on upgrading her protective gear. How many tokens has she spent in total and how many does she have left at the end?

To prepare a cookie recipe for $6$ people, $\frac{3}{4}$ kg of flour is needed. If we want to adapt the recipe to invite $15$ people:

1. a) What fraction of a kilogram of flour will we need?
2. b) Is that fraction greater or less than one? Justify whether it is a proper or improper fraction.