Question

Сравни числа 1/7/8и12/8. -14/5и2/4/52/8/15и32/15-3/3/14и-51/14

Answer 1

$\frac{ \frac{1}{7} }{8} < \frac{12}{8}$

$- \frac{14}{5} < \frac{ \frac{2}{4} }{5}$

$\frac{ \frac{2}{8} }{15} < \frac{32}{15}$

$- \frac{ \frac{3}{3} }{14} > - \frac{51}{14}$

Answer 2

To compare fractions, it's helpful to convert them to a common denominator. Let's compare the given fractions step by step:

1. $\frac{1}{7/8}$ and $\frac{12}{8}$

To simplify $\frac{1}{7/8}$, we can multiply the numerator and denominator by 8:

$\frac{1}{7/8} = \frac{8}{7}$

Now, we have $\frac{8}{7}$ and $\frac{12}{8}$. To compare them, we can convert them to decimals:

$\frac{8}{7} \approx 1.1429$ (rounded to four decimal places)

$\frac{12}{8} = 1.5$

Comparing $1.1429$ and $1.5$, we can see that $\frac{12}{8}$ is greater than $\frac{1}{7/8}$.

2. $\frac{-14}{5}$ and $\frac{2}{4/5}$

To simplify $\frac{2}{4/5}$, we can multiply the numerator and denominator by 5:

$\frac{2}{4/5} = \frac{2 \times 5}{4} = \frac{10}{4} = \frac{5}{2}$

Now, we have $\frac{-14}{5}$ and $\frac{5}{2}$. To compare them, we can convert them to decimals:

$\frac{-14}{5} = -2.8$

$\frac{5}{2} = 2.5$

Comparing $-2.8$ and $2.5$, we can see that $\frac{5}{2}$ is greater than $\frac{-14}{5}$.

3. $\frac{2}{8/15}$ and $\frac{32}{15}$

To simplify $\frac{2}{8/15}$, we can multiply the numerator and denominator by $\frac{15}{8}$:

$\frac{2}{8/15} = \frac{2 \times \frac{15}{8}}{1} = \frac{15}{4}$

Now, we have $\frac{15}{4}$ and $\frac{32}{15}$. To compare them, we can convert them to decimals:

$\frac{15}{4} = 3.75$

$\frac{32}{15} \approx 2.1333$ (rounded to four decimal places)

Comparing $3.75$ and $2.1333$, we can see that $\frac{15}{4}$ is greater than $\frac{32}{15}$.

4. $\frac{3}{3/14}$ and $\frac{-51}{14}$

To simplify $\frac{3}{3/14}$, we can multiply the numerator and denominator by $\frac{14}{3}$:

$\frac{3}{3/14} = \frac{3 \times \frac{14}{3}}{1} = 14$