Question

2÷3/5+3/5÷2+1 1/2÷6+6÷1 1/2=

Answer 1

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

Step 1: Simplify the division operations first. 2 ÷ 3/5 can be rewritten as 2 * 5/3 (by multiplying the numerator and denominator by the reciprocal of 3/5): 2 * 5/3 = 10/3

3/5 ÷ 2 can be rewritten as 3/5 * 1/2 (by multiplying the numerator and denominator by the reciprocal of 2): 3/5 * 1/2 = 3/10

1/2 ÷ 6 can be rewritten as 1/2 * 1/6 (by multiplying the numerator and denominator by the reciprocal of 6): 1/2 * 1/6 = 1/12

6 ÷ 1 can be simplified to just 6.

Step 2: Perform the additions and subtractions from left to right. 10/3 + 3/10 + 6 + 1/12 + 6 + 1/2

To add fractions, we need a common denominator. Let's find the least common denominator (LCD) for 3, 10, and 12, which is 60.

10/3 can be rewritten as 200/60 (by multiplying the numerator and denominator by 20): 200/60 + 3/10 + 6 + 1/12 + 6 + 1/2

3/10 can be rewritten as 18/60 (by multiplying the numerator and denominator by 6): 200/60 + 18/60 + 6 + 1/12 + 6 + 1/2

1/12 can be rewritten as 5/60 (by multiplying the numerator and denominator by 5): 200/60 + 18/60 + 6 + 5/60 + 6 + 1/2

Now we can add all the fractions together: (200 + 18 + 6 + 5)/60 + 6 + 1/2

Simplifying the fraction: 229/60 + 6 + 1/2

To add the mixed numbers, we need to convert 229/60 to a mixed number: 229 ÷ 60 = 3 remainder 29 So, 229/60 can be written as 3 29/60.

Now we can add the mixed numbers and the fraction together: 3 29/60 + 6 + 1/2

To add mixed numbers, we need a common denominator. The LCD for 60 and 2 is 120.

3 29/60 can be rewritten as 3 58/120 (by multiplying the whole number by 120 and adding it to the numerator): 3 58/120 + 6 + 1/2

Now we can add all the numbers together: (3 * 120 + 58)/120 + 6 + 1/2

(360 + 58)/120 + 6 + 1/2

418/120 + 6 + 1/2

Simplifying the fraction: (209/60) + 6 + 1/2

To add the fractions, we need a common denominator. The LCD for 60 and 2 is 120.

209/60 can be rewritten as 209/120 by multiplying the numerator and denominator by 2: 209/120 + 6 + 1/2

Now we can add all the numbers together: (209 + 6 * 120 + 1 * 120)/120

(209 + 720 + 120)/120

1049/120

The final result of the expression is 1049/120.