Question

-1.(72)×0.2(6)-5.(123)​

Answer 1

-1,(72) · 0,2(6) - 5,(123) = - 5 целых 10691/18315

1) -1,(72) · 0,2(6) = -1 8/11 · 4/15 = -19/11 · 4/15 = -76/165

2) -76/165 - 5,(123) = -76/165 - 5 41/333 = - (8436/18315 + 5 2255/18315) = -5 целых 10691/18315

Ответ: - 5,5(837291).

Answer 2

To solve this expression, let's break it down step by step:

Step 1: Convert the repeating decimal 0.2(6) into a fraction.

Let x = 0.2(6) Multiply both sides of the equation by 10 to shift the decimal point: 10x = 2.(6) Subtract x from both sides: 10x - x = 2.(6) - 0.2(6) Simplifying the right side: 9x = 2.(6) - 0.2(6) 9x = 2.666... - 0.066... 9x = 2.6 Dividing both sides by 9: x = 2.6/9

So, 0.2(6) is equal to 2.6/9.

Step 2: Evaluate the expression -1.(72) × 0.2(6) - 5.(123).

Let's substitute the values we calculated:

-1.(72) × 0.2(6) - 5.(123) = -1.72 × 2.6/9 - 5.123

Performing the multiplication and subtraction:

= (-1.72 × 2.6)/9 - 5.123 = -4.472/9 - 5.123

To simplify the expression further, we need to find a common denominator for the fractions.

The common denominator is 9, so we multiply both the numerator and denominator of -4.472 by 9:

= (-4.472 × 9)/9 - 5.123 = -40.248/9 - 5.123

Now we can combine the fractions:

= (-40.248 - 45.207)/9 = -85.455/9

The final result is approximately:

-85.455/9 ≈ -9.494