Question

(-12,6×1 1/9+10,8)÷6 6/7+2 3/10

Answer 1

(-12,6 * 1 ¹/₉ + 10,8) : 6 ⁶/₇ + 2 ³/₁₀ = 1 ⁵/₆

1) - 12,6 * 1 ¹/₉ = - ¹²⁶/₁₀ * ¹⁰/₉ = - ¹²⁶/₉ = -¹⁴/₁ = - 14

2) - 14 + 10,8 = - (14,0 - 10,8) = -3,2

3) - 3,2 : 6 ⁶/₇ = - ³²/₁₀ : ⁴⁸/₇ = - ¹⁶/₅ * ⁷/₄₈ = - ⁽¹*⁷⁾ / ₍₅*₃₎ = - ⁷/₁₅

4) - ⁷/₁₅ + 2 ³/₁₀ = 2 ⁹/₃₀ - ¹⁴/₃₀ = 1 + (³⁹/₃₀ - ¹⁴/₃₀) = 1 ²⁵/₃₀ = 1 ⁵/₆

Answer 2

Let's break down the expression step by step:

1. (-12,6×1 1/9+10,8)÷6 6/7+2 3/10

First, perform the multiplication within the parentheses:

-12.6 × 1 1/9 = -12.6 × (9/9 + 1/9) = -12.6 × (10/9)

Now, simplify this multiplication:

-12.6 × (10/9) = -140.4/9

So the expression becomes:

(-140.4/9 + 10.8) ÷ 6 6/7 + 2 3/10

2. Next, add -140.4/9 and 10.8:

-140.4/9 + 10.8 = -140.4/9 + 97.2/9 = (-140.4 + 97.2)/9 = -43.2/9

3. Now, the expression becomes:

(-43.2/9) ÷ 6 6/7 + 2 3/10

4. To divide by a mixed number (6 6/7), you need to convert it to an improper fraction:

6 6/7 = (7 * 6 + 6)/7 = (42 + 6)/7 = 48/7

So, the expression now is:

(-43.2/9) ÷ (48/7) + 2 3/10

5. To divide fractions, you invert the second fraction (48/7) and multiply:

(-43.2/9) ÷ (48/7) = (-43.2/9) * (7/48)

Now, simplify this multiplication:

=(-43.2 * 7) / (9 * 48) = (-302.4) / 432

6. Simplify the fraction:

(-302.4) / 432 = -151.2 / 216

Now, reduce the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 6:

(-151.2 / 6) / (216 / 6) = -25.2 / 36

7. Simplify further by dividing both the numerator and denominator by their GCD, which is 12:

(-25.2 / 12) / (36 / 12) = -2.1 / 3

8. The expression now is:

-2.1 / 3 + 2 3/10

9. To add a fraction to a mixed number, you need to find a common denominator. In this case, the common denominator is 10. So, you need to convert -2.1/3 to a fraction with a denominator of 10:

-2.1/3 = (-2.1/3) * (10/10) = -21/30

Now, the expression becomes:

-21/30 + 2 3/10

10. To add these, you first need to add the whole numbers and then the fractions:

2 + 2 = 4

3/10 + (-21/30) = (3/10) + (-7/10) = (3 - 7)/10 = -4/10

Reduce the fraction by dividing both the numerator and denominator by their GCD, which is 2:

-4/10 = (-2/5)

So, the final result is:

4 - 2/5 = 3 3/5