Given two fractions, \(\frac{a}{b}\) and \(\frac{c}{d}\), we say they are equivalent if they are:
In the following tutorial we explain what is meant by equivalent fractions as well as illustrate them with some examples.
This should help intriduce the topic, make sure to watch it now.
Given a fraction, for example \(\frac{1}{3}\), we'll somtimes need to express it over a different denominator. In other words we'll sometimes need to express it as equivalent fraction over a different denominator.
For example we may need to write \(\frac{1}{3}\) as an equivalent fraction over \(12\).
This leads to having to find the numerator, which we've called \(x\) here: \[\frac{1}{3} = \frac{x}{12}\] The method for doing this is explained in tutorial \(3\).
In the following tutorial we learn how to write a fraction as an equivalent fraction over a different denominator.
In particular we see how to write \(\frac{1}{2}\) as an equivalent fraction over \(6\), by solving \(\frac{1}{2} = \frac{x}{6}\).
Similarly we show how to write \(\frac{2}{3}\) as an equivalent fraction over \(12\) by solving \(\frac{2}{3} = \frac{x}{12}\) as well as how to write \(\frac{9}{15}\) as an equivalent fraction over \(5\) by solving\(\frac{9}{15} = \frac{x}{5}\).
Given a fraction, like \(\frac{2}{3}\), we can write it as an equivalent fraction over a given denominator, for instance\(\frac{x}{12}\), in two steps:
At times we'll need to write a fraction as an equivalent fraction for which the numerator has to equal a certain value.
For instance we may need to write \(\frac{4}{5}\) as an equivalent fraction with \(28\) as the numerator.
We do this by finding the value of \(x\) in: \[\frac{4}{5} = \frac{28}{x}\]
Given a fraction, such as \(\frac{1}{3}\), to write it as an equivalent fraction, whose numertor is imposed we can use the following two steps: