Question

4 1/6 * (1 1/2 - 3/5) + (3/4 + 5/6)​

Answer 1

$4 \frac{1}{6} * (1 \frac{1}{2} - \frac{3}{5}) + (\frac{3}{4} + \frac{5}{6}) = 4 \frac{1}{6}(1 \frac{1}{2} - \frac{3}{5}) + \frac{3}{4} + \frac{5}{6} = 5 \frac{1}{3}\\\\1) 1 \frac{1}{2} - \frac{3}{5} = 1 \frac{5}{10} - \frac{6}{10} = \frac{9}{10}\\\\2) 4 \frac{1}{6} * \frac{9}{10} = \frac{25}{6} * \frac{9}{10} = \frac{25*9}{6*10} = \frac{5*3}{2*2} = \frac{15}{4}\\\\3) \frac{15}{4} + \frac{3}{4} = \frac{15+3}{4} = \frac{18}{4}$

$4) \frac{18}{4} + \frac{5}{6} = \frac{54}{12} + \frac{10}{12} = \frac{54+10}{12} = \frac{64}{12} = \frac{16}{3} = 5 \frac{1}{3}$

Ответ: $5 \frac{1}{3}$

Answer 2

To solve the given expression, follow these steps:

Step 1: Simplify the terms inside the parentheses. Step 2: Perform the subtraction inside the parentheses. Step 3: Multiply the result from Step 2 by the first fraction. Step 4: Simplify the fractions in the second parentheses. Step 5: Add the results from Step 3 and Step 4.

Let's proceed with the calculations:

Step 1: Simplify the terms inside the parentheses: 1 1/2 - 3/5 To subtract fractions with different denominators, we need a common denominator. The common denominator for 2 and 5 is 10.

1 1/2 = (2*1 + 1)/2 = 3/2 3/5 remains the same.

Step 2: Perform the subtraction inside the parentheses: 3/2 - 3/5 To subtract fractions with the same denominator, simply subtract their numerators:

(35 - 32) / 2*5 = (15 - 6) / 10 = 9 / 10

Step 3: Multiply the result from Step 2 by the first fraction: 4 1/6 * (9/10)

To multiply a whole number by a fraction, convert the whole number to a fraction by giving it a denominator of 1.

4 1/6 = (6*4 + 1) / 6 = 25/6

Now, multiply the fractions:

25/6 * 9/10 = (259) / (610) = 225 / 60

Step 4: Simplify the fractions in the second parentheses: 3/4 + 5/6

To add fractions with different denominators, we need a common denominator. The common denominator for 4 and 6 is 12.

3/4 = (33) / (43) = 9/12 5/6 remains the same.

Step 5: Add the results from Step 3 and Step 4: 225/60 + 9/12

To add fractions with the same denominator, simply add their numerators:

(225 + 9) / 60 = 234 / 60

Finally, simplify the fraction:

234/60 can be reduced to its simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 6:

234/60 = (639) / (610) = 39/10

So, the final result of the expression is:

4 1/6 * (1 1/2 - 3/5) + (3/4 + 5/6) = 39/10