Question

put these numbers in order from greatest to least.
7.5
$\boldsymbol{-dfrac{28}{35}}$
$\boldsymbol{dfrac{12}{24}}$
$\boldsymbol{-dfrac{9}{10}}$

Explanation:

Step1: Simplify fractions

Simplify \(\frac{28}{35}\) to \(\frac{4}{5} = 0.8\), so \(-\frac{28}{35}=- 0.8\); simplify \(\frac{12}{24}\) to \(\frac{1}{2}=0.5\); \(-\frac{9}{10}=-0.9\).

Step2: Compare values

Positive numbers are greater than negative numbers. Among positive numbers, \(7.5>0.5\). Among negative numbers, the larger the absolute value, the smaller the number, so \(-0.8 > - 0.9\) (since \(|-0.8| = 0.8\) and \(|-0.9|=0.9\), and \(0.8<0.9\)).

Step3: Order from greatest to least

Arrange the numbers: \(7.5\), \(\frac{12}{24}\) (which is \(0.5\)), \(-\frac{28}{35}\) (which is \(-0.8\)), \(-\frac{9}{10}\) (which is \(-0.9\)).

Answer:

\(7.5,\frac{12}{24},-\frac{28}{35},-\frac{9}{10}\)