Question

(/-обозначение дроби) 3/8*2/5-4/7*21/24=? (-1/4)*(2/7)-(-5/9)*(3/10)=?

Answer 1

Ответ:

3/8*2/5-4/7*21/24=-7/20

-7/20=-0,35

(-1/4)*(2/7)-(-5/9)*(3/10)=2/21

Answer 2

Let's solve each expression step by step:

1. $\frac{3}{8} \times \frac{2}{5} - \frac{4}{7} \times \frac{21}{24}$

   First, multiply the numerators together and the denominators together for each fraction:

   $$\frac{3 \times 2}{8 \times 5} - \frac{4 \times 21}{7 \times 24}$$

   Simplify the fractions:

   $$\frac{6}{40} - \frac{84}{168}$$

   Now, find a common denominator (in this case, it's 168) and combine the fractions:

   $$\frac{6 \times 4}{40 \times 4} - \frac{84}{168} = \frac{24}{160} - \frac{84}{168}$$

   Combine the numerators and keep the common denominator:

   $$\frac{24 - 84}{168}$$

   Simplify the numerator:

   $$\frac{-60}{168}$$

   Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common factor (which is 12):

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

2. $\left(-\frac{1}{4}\right) \times \left(\frac{2}{7}\right) - \left(-\frac{5}{9}\right) \times \left(\frac{3}{10}\right)$

   Perform the multiplications first:

   $$\frac{-1 \times 2}{4 \times 7} - \frac{-5 \times 3}{9 \times 10}$$

   Simplify the fractions:

   $$\frac{-2}{28} + \frac{15}{90}$$

   Find a common denominator (in this case, it's 90) and combine the fractions:

   $$\frac{-2 \times 3}{28 \times 3} + \frac{15 \times 4}{90 \times 4} = \frac{-6}{84} + \frac{60}{360}$$

   Combine the numerators and keep the common denominator:

   $$\frac{-6 + 60}{360}$$

   Simplify the numerator:

   $$\frac{54}{360}$$

   Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common factor (which is 18):

   $$\frac{3}{20}$$

So, the solutions are:

1. $\frac{3}{8} \times \frac{2}{5} - \frac{4}{7} \times \frac{21}{24} = -\frac{5}{14}$

2. $\left(-\frac{1}{4}\right) \times \left(\frac{2}{7}\right) - \left(-\frac{5}{9}\right) \times \left(\frac{3}{10}\right) = \frac{3}{20}$