Question

1)12 3/5 - 7 1/6 + 2 3/102)4/5 : 2 2/3+ 3 1/23)170 8/51 - 2 4/9 : 3 2/3

Answer 1

1)5 12/30 (сокращаю) 5 4\10= 5, 4

Answer 2

Let's solve each of these arithmetic expressions step by step:

1. $12 \frac{3}{5} - 7 \frac{1}{6} + 2 \frac{3}{102}$

First, let's convert the mixed fractions into improper fractions:

$12 \frac{3}{5} = \frac{12 \cdot 5 + 3}{5} = \frac{63}{5}$

$7 \frac{1}{6} = \frac{7 \cdot 6 + 1}{6} = \frac{43}{6}$

$2 \frac{3}{102} = \frac{2 \cdot 102 + 3}{102} = \frac{207}{102}$

Now, let's add and subtract these fractions:

$= \frac{63}{5} - \frac{43}{6} + \frac{207}{102}$

To perform these calculations, we need a common denominator. The least common multiple of 5, 6, and 102 is 510.

$= \frac{63 \cdot 102}{5 \cdot 102} - \frac{43 \cdot 85}{6 \cdot 85} + \frac{207 \cdot 5}{102 \cdot 5}$

$= \frac{6426}{510} - \frac{3655}{510} + \frac{1035}{510}$

Now, combine the fractions:

$= \frac{6426 - 3655 + 1035}{510}$

$= \frac{3806}{510}$

Reduce the fraction:

$= \frac{1903}{255}$

Divide both the numerator and denominator by their greatest common divisor (which is 1):

$= \frac{1903}{255}$

2. $\frac{4}{5} : 2 \frac{2}{3} + 3 \frac{1}{2}$

First, convert the mixed fractions:

$2 \frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{8}{3}$

$3 \frac{1}{2} = \frac{3 \cdot 2 + 1}{2} = \frac{7}{2}$

Now, perform the division and addition:

$= \frac{4}{5} : \frac{8}{3} + \frac{7}{2}$

When dividing fractions, you can multiply the first fraction by the reciprocal of the second fraction:

$= \frac{4}{5} \cdot \frac{3}{8} + \frac{7}{2}$

$= \frac{12}{40} + \frac{7}{2}$

$= \frac{3}{10} + \frac{7}{2}$

To add these fractions, find a common denominator, which is 10:

$= \frac{3}{10} + \frac{35}{10}$