Concept
In 1st ESO you learnt what a fraction is. Now it is time to put it in its proper place: inside a new set, $\mathbb{Q}$, which also includes negative numbers, and to learn how to work with its opposite and its reciprocal.
Fractions, integers and natural numbers: the set $\mathbb{Q}$
Every integer is rational: $5 = \frac{5}{1}$, $-2 = \frac{-4}{2}$. And any fraction whose numerator is a multiple of its denominator is really an integer in disguise: $\frac{15}{3} = 5$.
Classify the following expressions, stating whether they represent a natural number, an integer (but not a natural number), or a non-integer rational number: a)…
Classify the following expressions, stating whether they represent a natural number, an integer (but not a natural number), or a non-integer rational number:
- a) $\frac{15}{3}$
- b) $-\frac{12}{4}$
- c) $\frac{7}{5}$
- d) $\frac{0}{8}$
- e) $-\frac{1}{2}$
- f) $\frac{24}{6}$
Classify the following fractions as proper or improper. Remember that to distinguish them you must look at the relationship between the numerator and the denominator:…
Classify the following fractions as proper or improper. Remember that to distinguish them you must look at the relationship between the numerator and the denominator:
$$\frac{3}{5}, \quad \frac{7}{4}, \quad \frac{11}{12}, \quad \frac{9}{2}, \quad \frac{5}{5}, \quad \frac{1}{8}$$Negative fractions: opposite and reciprocal
A fraction can be negative, and the sign can be written in three equivalent places.
Write down the opposite and the reciprocal of each of the following fractions. Pay attention to the sign: a) $\frac{2}{5}$ b) $-\frac{3}{7}$ c) $4$ (remember that an…
Write down the opposite and the reciprocal of each of the following fractions. Pay attention to the sign:
- a) $\frac{2}{5}$
- b) $-\frac{3}{7}$
- c) $4$ (remember that an integer can also be written as a fraction)
Mixed numbers and fractions in their simplest form: a review
Your mobile phone battery has a total capacity of $4500$ mAh. If the screen shows that you have exactly $\frac{2}{9}$ of the total charge left, how many mAh of battery…
Your mobile phone battery has a total capacity of $4500$ mAh. If the screen shows that you have exactly $\frac{2}{9}$ of the total charge left, how many mAh of battery do you have available right now?
After an athletics training session, you have drunk $\frac{7}{3}$ of a litre of water. Express this amount as a mixed number to find out how many whole litres and what…
After an athletics training session, you have drunk $\frac{7}{3}$ of a litre of water. Express this amount as a mixed number to find out how many whole litres and what fraction of the next one you have drunk.
In the figure, each litre is divided into 3 equal parts (thirds) and is shown on a number line. You can use it to help you.
Simplify the following fractions to their simplest form: a) $\frac{15}{20}$ b) $\frac{24}{36}$ c) $\frac{10}{100}$
Simplify the following fractions to their simplest form:
- a) $\frac{15}{20}$
- b) $\frac{24}{36}$
- c) $\frac{10}{100}$
Fractions in real contexts: comparing proportions
When a fraction represents a success rate, the proportion of a mixture or a share, the first step is to write it correctly and, if you need to compare, to simplify it or find an equivalent fraction.
In a school basketball tournament, the "Tigers" team scored $48$ baskets out of $72$ attempts, while the "Hawks" scored $36$ baskets out of $54$ attempts. a) Write down…
In a school basketball tournament, the "Tigers" team scored $48$ baskets out of $72$ attempts, while the "Hawks" scored $36$ baskets out of $54$ attempts.
- a) Write down the success fraction for each team.
- b) Simplify both fractions to their simplest form using the Highest Common Factor (HCF) method.
- c) Looking at the results, which of the two teams has a better success rate?
To prepare a lilac paint mixture, an artist uses $\frac{4}{10}$ of a litre of blue paint for every litre of white paint. If the artist wants to keep exactly the same…
To prepare a lilac paint mixture, an artist uses $\frac{4}{10}$ of a litre of blue paint for every litre of white paint. If the artist wants to keep exactly the same shade but needs to produce a larger quantity:
- a) Find the value of $x$ in the following equality so that the fractions are equivalent: $\frac{4}{10} = \frac{x}{25}$.
- b) Write down three equivalent fractions to $\frac{4}{10}$ by multiplying (amplification) and one by simplifying.