What decimal represents $\frac{3}{4}$? What about $\frac{6}{8}$? What about $\frac{9}{12}$? Show answer
\begin{align*}\shortdiv{\ms{3}\ms{.}\ms{0}\ms{0}}{4}{\ms{0}\ms{.}\ms{7}\ms{5}}{\ms{}\ms{}\ms{^2}}\end{align*} \begin{align*}\shortdiv{\ms{6}\ms{.}\ms{0}\ms{0}}{8}{\ms{0}\ms{.}\ms{7}\ms{5}}{\ms{}\ms{}\ms{^4}}\end{align*} \begin{align*}\shortdiv{\ms{9}\ms{.}\ms{0}\ms{0}}{12}{\ms{0}\ms{.}\ms{7}\ms{5}}{\ms{}\ms{}\ms{^6}}\end{align*} The answer in all three cases is $0.75$. All three fractions are actually the same number.
Why did we get this answer? What is it about these three fractions? Show hint
There are a few ways to look at this. You might have noticed that the numerators are all multiples of $3$, so you decided to look at the fractions like this: \begin{align*} \frac{6}{8} &= \frac{3\times2}{4\times2}\\ \frac{9}{12} &= \frac{3\times3}{4\times3}. \end{align*} and realised that if we multiply the top and bottom of the fraction by the same number, then the numerator will still be $\frac{3}{4}$ of the denominator, and the fraction will always be equivalent to $\frac{3}{4}$.
Or you might have pictured the fractions a bit like this: and noticed that $\frac{6}{8}$ is the same as $\frac{3}{4}$ but with every part split into $2$, and similarly for $\frac{9}{12}$ split into $3$, but the amount shaded remains the same.