Question

order -2/3, -4/5, 8/15 and 3/5 from least to greatest
-2/3, 3/5, -4/5, 8/15
-4/5, -2/3, 8/15, 3/5
-2/3, -4/5, 3/5, 8/15
8/15, 3/5, -2/3, -4/5

Explanation:

Step1: Find a common denominator

The fractions are $-\frac{2}{3}$, $-\frac{4}{5}$, $\frac{3}{5}$, $\frac{8}{15}$. The least common denominator of 3, 5, and 15 is 15.
Convert each fraction:

• $-\frac{2}{3}=-\frac{2\times5}{3\times5}=-\frac{10}{15}$
• $-\frac{4}{5}=-\frac{4\times3}{5\times3}=-\frac{12}{15}$
• $\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}$
• $\frac{8}{15}$ remains as is.

Step2: Compare the numerators

For negative fractions, the larger the numerator (in absolute value), the smaller the fraction. So, $-\frac{12}{15}<-\frac{10}{15}$ (since $-12 < -10$).
For positive fractions, $\frac{8}{15}<\frac{9}{15}$ (since $8 < 9$).

Step3: Order the original fractions

From least to greatest: $-\frac{4}{5}$ (which is $-\frac{12}{15}$), $-\frac{2}{3}$ (which is $-\frac{10}{15}$), $\frac{8}{15}$, $\frac{3}{5}$ (which is $\frac{9}{15}$).

Answer:

-4/5, -2/3, 8/15, 3/5 (corresponding to the blue option: -4/5, -2/3, 8/15, 3/5)