Question

(x- 10 1/8) : 1 7/8=2 2/5​

Answer 1

Ответ:

Пошаговое объяснение:

Вот

Answer 2

To solve the equation $(x - 10\frac{1}{8}) \div 1\frac{7}{8} = 2\frac{2}{5},$ you can follow these steps:

Step 1: Convert all mixed numbers to improper fractions.

• $10\frac{1}{8}$ as an improper fraction is $\frac{81}{8}$.
• $1\frac{7}{8}$ as an improper fraction is $\frac{15}{8}$.
• $2\frac{2}{5}$ as an improper fraction is $\frac{12}{5}$.

Now, the equation becomes: $(x - \frac{81}{8}) \div \frac{15}{8} = \frac{12}{5}.$

Step 2: To get rid of the fraction in the denominator, multiply both sides of the equation by the reciprocal of $\frac{15}{8}$, which is $\frac{8}{15}$.

• $(x - \frac{81}{8}) \div \frac{15}{8} \cdot \frac{8}{15} = \frac{12}{5} \cdot \frac{8}{15}$.

This simplifies to: $(x - \frac{81}{8}) = \frac{96}{75}.$

Step 3: Now, simplify the fraction on the right-hand side: $\frac{96}{75}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3: $\frac{96}{75} = \frac{96 ÷ 3}{75 ÷ 3} = \frac{32}{25}.$

So, the equation becomes: $x - \frac{81}{8} = \frac{32}{25}.$

Step 4: Add $\frac{81}{8}$ to both sides of the equation to isolate $x$: $x - \frac{81}{8} + \frac{81}{8} = \frac{32}{25} + \frac{81}{8}.$

This simplifies to: $x = \frac{32}{25} + \frac{81}{8}.$

Step 5: Find a common denominator and add the fractions on the right-hand side: To find a common denominator between 25 and 8, you can multiply them together (25 * 8 = 200). Then, convert both fractions to have a denominator of 200:

$\frac{32}{25} = \frac{32 \cdot 8}{25 \cdot 8} = \frac{256}{200}$

$\frac{81}{8} = \frac{81 \cdot 25}{8 \cdot 25} = \frac{2025}{200}$

Now, the equation becomes: $x = \frac{256}{200} + \frac{2025}{200}.$

Step 6: Add the fractions on the right-hand side: $x = \frac{256 + 2025}{200}.$

Step 7: Add the numerators: $x = \frac{2281}{200}.$

So, the solution to the equation is: $x=\frac{2281}{200}\mathrm{.}$ 0 0