Question

2 4/15−(2−1 1/15):4/9+9/2.

Answer 1

2 4/15−(2−1 1/15):4/9+9/2

34/15-(-2-16/15)*9/4+9/2

34/15-14/15*9/4+9/2

34/15-7/5*3/2+9/2

34/15-21/10+9/2

14/3=4 2/3=4.6

Answer 2

To solve the expression, let's follow the order of operations (PEMDAS/BODMAS):

1. Parentheses: Solve the expression within the parentheses first.
2. Exponents: If there were any exponents, we would solve them next (none in this case).
3. Multiplication and Division: Perform any multiplication or division from left to right.
4. Addition and Subtraction: Finally, perform any addition or subtraction from left to right.

Now, let's proceed step by step:

Step 1: Parentheses 2 4/15 − (2 − 1 1/15) : 4/9 + 9/2

Inside the parentheses: 2 - 1 1/15 = 2 - (1 + 1/15) = 2 - 16/15 = 30/15 - 16/15 = (30 - 16)/15 = 14/15

So the expression becomes: 2 4/15 − 14/15 : 4/9 + 9/2

Step 2: Division Now, let's perform the division from left to right: 2 4/15 − 14/15 : 4/9 + 9/2 = 2 4/15 − (14/15 : 4/9) + 9/2

Step 3: Division To divide fractions, you invert the divisor (second fraction) and then multiply: 14/15 : 4/9 = 14/15 * 9/4 = (14 * 9) / (15 * 4) = 126 / 60 = 21/10

So the expression becomes: 2 4/15 − 21/10 + 9/2

Step 4: Addition and Subtraction Convert the mixed number to an improper fraction: 2 4/15 = (2 * 15 + 4) / 15 = 34/15

Now, we can proceed with the addition and subtraction: 34/15 − 21/10 + 9/2

To add or subtract fractions, they must have the same denominator. The common denominator for 15 and 10 is 30.

Convert the fractions to have a common denominator: 34/15 = (34 * 2) / (15 * 2) = 68/30 21/10 = (21 * 3) / (10 * 3) = 63/30

Now the expression becomes: 68/30 − 63/30 + 9/2

Combine the fractions with the same denominator: 68/30 − 63/30 = (68 - 63)/30 = 5/30 = 1/6

So, the final expression is: 1/6 + 9/2

To add these fractions, we need to have a common denominator. The common denominator for 6 and 2 is 6.

Convert 9/2 to have a common denominator: 9/2 = (9 * 3) / (2 * 3) = 27/6

Now the expression becomes: 1/6 + 27/6

Finally, add the fractions: 1/6 + 27/6 = (1 + 27)/6 = 28/6 = 14/3

So the result of the expression is 14/3.