Question

6 3/20 - (1 5/6 + 2 1/15) + 7 13/60 - (5 5/82 - + 9/10)

Answer 1

Ответ:

$6 \frac{3}{20} - (1 \frac{5}{6} + 2 \frac{1}{15} ) + 7 \frac{13}{60} - (5 \frac{5}{82} + \frac{9}{10} ) = 3 \frac{311}{615}$

Answer 2

To simplify the given expression:

6 3/20 - (1 5/6 + 2 1/15) + 7 13/60 - (5 5/82 - + 9/10)

Let's break it down step by step:

1. Start with the addition/subtraction within parentheses: 1 5/6 + 2 1/15 = (1 + 2) + (5/6 + 1/15) = 3 + (5/6 + 1/15)

2. Find a common denominator for 6 and 15, which is 30: 5/6 + 1/15 = (25/30) + (2/30)

3. Add the fractions: (25/30) + (2/30) = 27/30

4. Simplify 27/30 by dividing both the numerator and denominator by their greatest common divisor, which is 3: (27/3) / (30/3) = 9/10

Now, we have simplified the expression to:

6 3/20 - 3 + 9/10 + 7 13/60 - (5 5/82 + 9/10)

Now, we'll deal with the second set of parentheses:

5 5/82 + 9/10 = (5 + 9/10) + (5/82)

To add 9/10 and 5, find a common denominator, which is 10:

(9/10) + (50/10) = 59/10

Now, we have:

6 3/20 - 3 + 9/10 + 7 13/60 - (59/10 + 5/82)

Next, let's add the whole numbers and fractions separately:

6 + 7 = 13

3/20 + 13/60 = (9/60) + (13/60) = 22/60

So, the expression becomes:

13 22/60 - 3 + 9/10 - (59/10 + 5/82)

Now, let's add or subtract the fractions and whole numbers:

13 - 3 = 10

22/60 = 11/30

9/10 - 59/10 = -50/10 = -5

So, the expression simplifies further to:

10 + 11/30 - 5 - 5/82

Now, let's work on subtracting fractions with different denominators. To do that, we need a common denominator for 30 and 82, which is 2460:

(11/30) = (807/2460) [by multiplying both numerator and denominator by 82] (5/82) = (150/2460) [by multiplying both numerator and denominator by 30]

Now, we can subtract these fractions:

(807/2460) - (150/2460) = (807 - 150) / 2460 = 657/2460

Now, we have:

10 + 657/2460 - 5

To simplify further, we can find a common denominator for 2460 and 10, which is 2460:

(10) = (24600/2460)

Now, we can subtract:

(24600/2460) + (657/2460) - (5) = (24600 + 657 - 5) / 2460 = 25252/2460

Finally, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:

(25252/4) / (2460/4) = 6313/615

So, the simplified expression is:

6313/615