Question

7/15 : (6/10 + 8/3) + 19 * 2/31

Answer 1

Ответ:  $1\dfrac{80}{217}$

Решение:

$\displaystyle \frac{7}{15} : \bigg(\frac{6}{10} + \frac{8}{3} \bigg)+19 \cdot \frac{2}{31} =\frac{7}{15} : \bigg(\frac{18}{30} + 2\frac{20}{30} \bigg)+\frac{19 \cdot 2}{31}= \frac{7}{15} : 2\frac{38}{30} \bigg+\frac{38}{31}= \\\\= \frac{7}{15} : \frac{98}{30} + 1\frac{7}{31} =\frac{7 \cdot 30}{15 \cdot 98} + 1\frac{7}{31} =\frac{1}{7} + 1\frac{7}{31} =1\frac{31+49}{217} = 1\frac{80}{217}$

Answer 2

To evaluate the expression, let's break it down step by step:

Step 1: Add the fractions (6/10 + 8/3): To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 10 and 3 is 30. Let's convert the fractions:

6/10 = (6 * 3) / (10 * 3) = 18/30 8/3 = (8 * 10) / (3 * 10) = 80/30

Now we can add them:

18/30 + 80/30 = (18 + 80) / 30 = 98/30

Step 2: Multiply 19 by 2/31: To multiply a whole number by a fraction, we multiply the numerator of the whole number by the numerator of the fraction and keep the denominator the same:

19 * 2/31 = (19 * 2) / 31 = 38/31

Step 3: Add the results from step 1 and step 2: Now we can add the fraction 98/30 to the fraction 38/31. To add fractions, we need a common denominator. The LCM of 30 and 31 is 930. Let's convert the fractions:

98/30 = (98 * 31) / (30 * 31) = 3038/930 38/31 = (38 * 30) / (31 * 30) = 1140/930

Now we can add them:

3038/930 + 1140/930 = (3038 + 1140) / 930 = 4178/930

So, the simplified result of the expression 7/15 + (6/10 + 8/3) + 19 * 2/31 is 4178/930.