Equivalent fractions
Marcos has read $\frac{3}{4}$ of a book. Lucía says she has read $\frac{9}{12}$. Have they read the same amount? Even though the numbers are different, they might have: these are equivalent fractions.
What equivalent fractions are
Half a pizza, two quarters or four eighths: it is the same amount, even though it has been cut up differently.
Check whether the following fractions are equivalent using the method of cross-multiplication: $$\frac{4}{6} \text{ and } \frac{10}{15}$$ Show all your working.
Check whether the following fractions are equivalent using the method of cross-multiplication:
$$\frac{4}{6} \text{ and } \frac{10}{15}$$Show all your working.
Two friends, Marcos and Lucía, are comparing how much progress they have made in reading the same book. Marcos says he has read $\frac{3}{4}$ of the total, while Lucía…
Two friends, Marcos and Lucía, are comparing how much progress they have made in reading the same book. Marcos says he has read $\frac{3}{4}$ of the total, while Lucía claims to have completed $\frac{9}{12}$ of the pages. Use visual representation to check whether both have read the same proportion of the book and justify your answer using cross-multiplication.
Amplifying: making equivalent fractions
If you multiply the numerator and the denominator by the same number, you obtain an equivalent fraction: you have split the whole into more pieces, but you are also taking more of them.
Calculate the missing number so that the following pair of fractions is equivalent: $$\frac{3}{5} = \frac{\Box}{20}$$
Calculate the missing number so that the following pair of fractions is equivalent:
$$\frac{3}{5} = \frac{\Box}{20}$$Obtain three fractions equivalent to $\frac{2}{7}$ by amplification. To do this, multiply the numerator and the denominator by $2$, by $3$, and by $10$.
Obtain three fractions equivalent to $\frac{2}{7}$ by amplification. To do this, multiply the numerator and the denominator by $2$, by $3$, and by $10$.
Calculate the value of the unknown $x$ so that the following pairs of fractions are equivalent: a) $\dfrac{x}{15} = \dfrac{4}{5}$ b) $\dfrac{3}{7} = \dfrac{21}{x}$ c)…
Calculate the value of the unknown $x$ so that the following pairs of fractions are equivalent:
- a) $\dfrac{x}{15} = \dfrac{4}{5}$
- b) $\dfrac{3}{7} = \dfrac{21}{x}$
- c) $\dfrac{18}{x} = \dfrac{6}{11}$
Simplifying and the fraction in its simplest form
Dividing the numerator and the denominator by the same number is simplifying. When you cannot simplify any further, you have the fraction in its simplest form (an irreducible fraction).
Simplify the following fraction to its simplest form: $$\frac{18}{24}$$ State which number you divided the numerator and denominator by at each step.
Simplify the following fraction to its simplest form:
$$\frac{18}{24}$$State which number you divided the numerator and denominator by at each step.
Find the irreducible fraction of the following expressions using successive division or by calculating the Highest Common Factor ($M.C.D.$): a) $\dfrac{120}{180}$ b)…
Find the irreducible fraction of the following expressions using successive division or by calculating the Highest Common Factor ($M.C.D.$):
- a) $\dfrac{120}{180}$
- b) $\dfrac{45}{105}$
- c) $\dfrac{256}{512}$
From the following list of fractions, group together those that are equivalent to each other:…
From the following list of fractions, group together those that are equivalent to each other:
$\dfrac{1}{3}, \dfrac{5}{10}, \dfrac{2}{6}, \dfrac{1}{2}, \dfrac{4}{12}, \dfrac{3}{6}, \dfrac{10}{30}, \dfrac{7}{14}$
Finding the missing term
In a chain of equivalent fractions such as $\frac{2}{3} = \frac{4}{\Box} = \frac{\Box}{15}$, you use cross products to find what is missing.
Look at the following figure and determine what fraction the shaded part represents. Then, write an equivalent fraction with a denominator of $16$.
Look at the following figure and determine what fraction the shaded part represents. Then, write an equivalent fraction with a denominator of $16$.
Complete the following chains of equivalent fractions: a) $\dfrac{2}{3} = \dfrac{4}{\square} = \dfrac{\square}{15} = \dfrac{20}{\square}$ b)…
Complete the following chains of equivalent fractions:
- a) $\dfrac{2}{3} = \dfrac{4}{\square} = \dfrac{\square}{15} = \dfrac{20}{\square}$
- b) $\dfrac{60}{48} = \dfrac{30}{\square} = \dfrac{\square}{12} = \dfrac{5}{\square}$
Indicate which of the following statements are true and which are false, explaining your answer in your notebook: a) If we multiply the numerator of a fraction by $2$…
Indicate which of the following statements are true and which are false, explaining your answer in your notebook:
- a) If we multiply the numerator of a fraction by $2$ and the denominator by $2$, we get an equivalent fraction.
- b) When we add $3$ to the numerator and $3$ to the denominator of the fraction $\frac{1}{2}$, we get another equivalent fraction.
- c) The fraction $\frac{17}{13}$ is irreducible because both the numerator and the denominator are prime numbers.