Fractions. Equivalent fractions

In a video game, you collected $45$ coins out of a total of $60$ available in the level. On the other hand, your brother collected $15$ out of a total of $20$ in his game.

Use the cross-products rule to check whether the two fractions of coins collected are equivalent.

Two graphic designers are working with grids to create a logo. The first designer has shaded $\frac{12}{20}$ of their grid, while the second has shaded $\frac{18}{30}$ of theirs. Look at the following graphic representations and explain whether both have shaded the same proportion of area, by checking whether the fractions are equivalent.

A group of friends is comparing the success of their social media posts. Lucía says that $2$ out of every $5$ followers liked her latest photo.

1. a) Write down the fraction of "likes" for Lucía.
2. b) Find an equivalent fraction by multiplying both terms by $3$.
3. c) Find another equivalent fraction if Lucía had a total of $50$ followers.

In the school library, the librarian tells us that $\frac{12}{30}$ of the books are adventure books. Help him simplify this fraction to put on a poster:

1. a) Divide the numerator and the denominator by $2$.
2. b) Divide the previous result by $3$.
3. c) Is the fraction obtained in part b in its simplest form? Why?

Simplify the following fractions to their simplest form. To do this, use the method of dividing the numerator and denominator by their highest common factor (HCF):

1. a) $\dfrac{126}{180}$

1. b) $\dfrac{210}{315}$

1. c) $\dfrac{154}{198}$

Copy into your notebook and complete the missing value in each case so that the pairs of fractions are equivalent:

1. a) $\frac{1}{3} = \frac{\Box}{12}$

1. b) $\frac{10}{15} = \frac{2}{\Box}$

1. c) $\frac{\Box}{7} = \frac{20}{28}$

In an esports competition, one player has completed $42$ of the $60$ levels of a video game. Another player has completed the same proportion of levels, but the game they are playing has a total of $90$ levels. How many levels has the second player completed? Solve this by finding the unknown term $x$ in the equivalent fractions equation.

Find the value of the unknown $n$ in each of the following equalities so that the fractions are equivalent:

1. a) $\dfrac{n}{15} = \dfrac{12}{45}$

1. b) $\dfrac{7}{n} = \dfrac{28}{36}$

1. c) $\dfrac{10}{18} = \dfrac{25}{n}$

Identify, from the following list, which fractions are equivalent to $\frac{2}{3}$:

From the following fractions, identify which one does not belong to the group of equivalent fractions. Justify your answer by simplifying all of them to their simplest form.