Question

Вычислите 1/12+1/9+5/6 4/15+2/5+1/6 7/8-4/5+1/20 11/18-5/12-1/9

Answer 1

1/12 + 1/9 + 5/6 = 3/36 + 4/36 + 30/36 = 37/36 = 1 1/36

4/15 + 2/5 + 1/6   = 8/30 + 12/30 + 5/30 = 25/30 = 5/6

7/8 - 4/5 + 1/20 = 35/40 - 32/40 + 2/40 = 5/40 = 1/8

11/18 - 5/12 - 1/9 = 22/36 - 15/36 - 4/36 = 3/36 = 1/12

Answer 2

To compute the sum of these fractions, we need to find a common denominator and then add the numerators. Let's go step by step.

Step 1: Finding the common denominator The denominators in the given fractions are 12, 9, 6, 15, 5, 6, 8, 5, 20, 18, 12, and 9. The least common multiple (LCM) of these denominators will be the common denominator we need to use.

The LCM of 12, 9, 6, 15, 5, 6, 8, 5, 20, 18, 12, and 9 is 360. Therefore, we will use 360 as the common denominator for all the fractions.

Step 2: Converting the fractions to have the common denominator We need to multiply the numerator and denominator of each fraction by the appropriate factor to make the denominators equal to 360.

1/12 = (1/12) * (30/30) = 30/360 1/9 = (1/9) * (40/40) = 40/360 5/6 = (5/6) * (60/60) = 300/360 4/15 = (4/15) * (24/24) = 96/360 2/5 = (2/5) * (72/72) = 144/360 1/6 = (1/6) * (60/60) = 60/360 7/8 = (7/8) * (45/45) = 315/360 4/5 = (4/5) * (72/72) = 288/360 1/20 = (1/20) * (18/18) = 18/360 11/18 = (11/18) * (20/20) = 220/360 5/12 = (5/12) * (30/30) = 150/360 1/9 = (1/9) * (40/40) = 40/360

Step 3: Adding the fractions Now that all the fractions have the same denominator, we can add the numerators.

(30/360) + (40/360) + (300/360) + (96/360) + (144/360) + (60/360) + (315/360) - (288/360) + (18/360) + (220/360) - (150/360) - (40/360)

Adding the numerators gives us:

(30 + 40 + 300 + 96 + 144 + 60 + 315 - 288 + 18 + 220 - 150 - 40) / 360

Simplifying the numerator gives us:

(1455) / 360

Finally, dividing the numerator by the denominator gives us the result:

Result: 4.041666666666667

Therefore, the sum of the given fractions is approximately 4.0417.