Question

-5/12×2 2/3 - 7 2/3 × (- 1/6)​

Answer 1

Ответ:

$\frac{1}{6}$

Объяснение:

$-\frac{5}{12} * 2 \frac{2}{3} - 7 \frac{2}{3} *(-\frac{1}{6} )=-\frac{5}{12} * \frac{8}{3} - \frac{23}{3} *(-\frac{1}{6} )=\\=-\frac{5*8}{12*3} + \frac{23*1}{3*6}=-\frac{40}{36} + \frac{23}{18} =-\frac{20}{18} + \frac{23}{18} =\frac{23}{18} - \frac{20}{18}=\frac{3}{18} =\frac{1}{6}$

Answer 2

To solve this expression, you should follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).

Let's break down the expression step by step:

1. Start with the multiplication and division: -5/12 × 2 2/3 = -5/12 × 8/3

Now, let's multiply these fractions:

2. Multiply the numerators (top numbers) and the denominators (bottom numbers): -5 × 8 = -40 12 × 3 = 36

So, -5/12 × 2 2/3 = -40/36.

3. Simplify the fraction:

   -40/36 can be simplified by finding the greatest common divisor (GCD) of 40 and 36, which is 4.

   -40 ÷ 4 = -10 36 ÷ 4 = 9

So, -40/36 simplifies to -10/9.

Now, we have:

-10/9 - 7 2/3 × (-1/6)

Let's continue with the multiplication:

4. -7 2/3 × (-1/6) = -7 2/3 × 1/6

Now, let's multiply these fractions:

5. -7 2/3 × 1/6

To multiply a mixed number by a fraction, you should first convert the mixed number to an improper fraction. To do this:

6. Multiply the whole number (7) by the denominator (3) and then add the numerator (2):

   7 × 3 + 2 = 21 + 2 = 23

So, -7 2/3 is equivalent to -23/3.

Now, we have:

-23/3 × 1/6

7. Multiply the numerators and denominators:

   -23 × 1 = -23 3 × 6 = 18

So, -23/3 × 1/6 = -23/18.

Now, we have:

-10/9 - 23/18

To subtract these fractions, they need a common denominator, which is 18. You can convert -10/9 to have a denominator of 18:

-10/9 * 2/2 = -20/18

Now, the expression is:

-20/18 - 23/18

8. Subtract the fractions:

   -20/18 - 23/18 = (-20 - 23)/18 = -43/18

So, the final result is -43/18.