Question

8+(-2 5/7) -4 2/5+3,4 -6,5+3 1/2 7 2/3+(-9)

Answer 1

1)37/7

2)-1

3)-3

4)-4/3

Answer 2

Let's break down each calculation step by step:

8 + (-2 5/7)

To add mixed numbers like these, we need to convert them to improper fractions first:

-2 5/7 = -(2*7 + 5)/7 = -19/7

So we have:

8 + (-19/7)

To add these two numbers, we can find a common denominator of 7:

8*7/7 + (-19/7)

56/7 - 19/7 = 37/7

So, the first part of the expression simplifies to:

37/7

-4 2/5 + 3,4

Here, we have a mix of fractions and decimals. To add them, we can convert the decimals to fractions with the same denominator as the fraction:

-4 2/5 = -4 4/10 = -4 2/5

3,4 = 3 4/10 = 3 2/5

Now, we can add the fractions:

-4 2/5 + 3 2/5 = -1/5

So, the second part of the expression simplifies to:

-1/5

-6,5 + 3 1/2

Similarly, we can convert the mixed number to a fraction:

-6,5 = -6 5/10 = -6 1/2

3 1/2 = 3 5/10 = 3 1/2

-6 1/2 + 3 1/2 = -3

So, the third part of the expression simplifies to:

-3

7 2/3 + (-9)

Again, we can convert the mixed number to a fraction:

7 2/3 = 7*3/3 + 2/3 = 23/3

So, we have:

23/3 + (-9)

To add these two numbers, we can find a common denominator of 3:

23/3 - 27/3 = -4/3

So, the fourth part of the expression simplifies to:

-4/3

Putting it all together, we have:

37/7 - 1/5 - 3 - 4/3

To subtract fractions, we need a common denominator. The smallest common multiple of 5, 7, and 3 is 105, so we can convert all fractions to this denominator:

37/7 * 15/15 = 555/105 1/5 * 21/21 = 21/105 4/3 * 35/35 = 140/105

Now, we can subtract the fractions:

555/105 - 21/105 - 140/105 = 394/105

So, the final simplified expression is:

394/105, which can also be expressed as a mixed number: 3 59/105.