Question

8 1/3:(3/13−1)−4⋅3 1/2.

Answer 1

Ответ:

$-24\frac{5}{6}$

Объяснение:

3/13-1=-10/13

4*3 1/2=4*7/2=28/2=14

8 1/3:(-10/13)=-25/3*13/10=-65/6=-10 5/6

-10 5/6-14=-24 5/6

Answer 2

To simplify the expression 8 1/3:(3/13 - 1) - 4 * 3 1/2, you should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right). Here's how you can simplify the expression step by step:

1. First, let's simplify within the parentheses: 3/13 - 1 = 3/13 - 13/13 = (3 - 13)/13 = (-10/13)

2. Now, substitute this value back into the expression: 8 1/3:(-10/13) - 4 * 3 1/2

3. Next, let's convert the mixed numbers into improper fractions: 8 1/3 = (3 * 8 + 1)/3 = (24 + 1)/3 = 25/3 3 1/2 = (2 * 3 + 1)/2 = (6 + 1)/2 = 7/2

4. Substitute these values back into the expression: (25/3) / (-10/13) - 4 * (7/2)

5. To divide fractions, you can multiply by the reciprocal of the second fraction: (25/3) * (-13/10) - 4 * (7/2)

6. Now, perform the multiplications and subtractions: = (-325/30) - (28/2) = (-325/30) - (14)

7. You can simplify the fractions further: = (-65/6) - (14)

8. To subtract fractions, find a common denominator, which is 6 in this case: = (-65/6) - (84/6)

9. Subtract the fractions: = (-65 - 84)/6 = (-149/6)

So, the simplified value of the expression is -149/6.

Answer 3

To simplify the expression 8 1/3:(3/13 - 1) - 4 * 3 1/2, you should follow the order of operations (PEMDAS/BODMAS):

1. First, simplify the fraction within the parentheses: 3/13 - 1 = 3/13 - 13/13 = (3 - 13)/13 = -10/13

2. Next, perform the division in the first part of the expression: 8 1/3 ÷ (-10/13)

To divide a whole number by a fraction, you can convert the whole number to an improper fraction:

8 1/3 = 25/3

Now, divide:

(25/3) ÷ (-10/13)

To divide fractions, multiply by the reciprocal of the divisor:

(25/3) * (-13/10)

Now, multiply the fractions:

(25 * -13) / (3 * 10) = (-325) / 30

You can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:

(-325/5) / (30/5) = (-65) / 6

So, the first part of the expression simplifies to -65/6:

8 1/3 ÷ (3/13 - 1) = -65/6

3. Now, move on to the second part of the expression, which is multiplication: -65/6 - 4 * 3 1/2

To multiply a whole number by a mixed number, first convert the mixed number to an improper fraction:

3 1/2 = 7/2

Now, perform the multiplication:

-65/6 - 4 * 7/2

To multiply, you can simplify the multiplication like this:

-65/6 - (4/1) * (7/2)

Now, multiply the fractions:

-65/6 - (28/2)

To subtract, you need to find a common denominator, which is 6:

-65/6 - (28 * 3/6)

Now, subtract the fractions:

-65/6 - 84/6 = (-65 - 84)/6 = -149/6

So, the second part of the expression simplifies to -149/6:

-4 * 3 1/2 = -149/6

4. Finally, subtract the results of the two simplified expressions:

-65/6 - (-149/6)

When you subtract a negative fraction, it's like adding its positive counterpart:

-65/6 + 149/6 = (149 - 65)/6 = 84/6

You can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6:

(84/6) ÷ (6/6) = (14/1) = 14

So, the final simplified result is 14:

8 1/3 ÷ (3/13 - 1) - 4 * 3 1/2 = 14