Question

17/36 * 26/51 3/16 * 4 3 3/5 * 1 1/9 13/48 * 8 7/26 40/7 * 14/5 23 * 5/46 4 2/7 * 2

Answer 1

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Answer 2

To solve the expression 17/36 * 26/51 + 3/16 * 4 + 3 + 3/5 * 1 + 1/9 * 13/48 * 8 + 7/26 + 40/7 * 14/5 * 23 * 5/46 + 4 + 2/7 * 2, we need to follow the order of operations, also known as the PEMDAS rule.

1. Parentheses: There are no parentheses in the expression. 2. Exponents: There are no exponents in the expression. 3. Multiplication and Division: We perform multiplication and division from left to right.

Let's break down the expression step by step:

17/36 * 26/51 = (17 * 26) / (36 * 51) = 442 / 1836

3/16 * 4 = (3 * 4) / 16 = 12 / 16

3 + 3/5 = (3 * 5 + 3) / 5 = 18 / 5

1 + 1/9 = (1 * 9 + 1) / 9 = 10 / 9

13/48 * 8 = (13 * 8) / 48 = 104 / 48

40/7 * 14/5 = (40 * 14) / (7 * 5) = 560 / 35

23 * 5/46 = (23 * 5) / 46 = 115 / 46

4 + 2/7 = (4 * 7 + 2) / 7 = 30 / 7

2 * (442/1836 + 12/16 + 18/5 + 10/9 + 104/48 + 7/26 + 560/35 + 115/46 + 30/7)

Now, let's simplify each fraction:

442/1836 = 221/918

12/16 = 3/4

18/5 = 3 3/5

10/9 = 1 1/9

104/48 = 13/6

7/26 = 7/26

560/35 = 16

115/46 = 2 27/46

30/7 = 4 2/7

Substituting the simplified fractions back into the expression:

2 * (221/918 + 3/4 + 3 3/5 + 1 1/9 + 13/6 + 7/26 + 16 + 2 27/46 + 4 2/7)

Now, we can add the fractions:

221/918 + 3/4 = (221 * 4 + 918 * 3) / (918 * 4) = 884 + 2754 / 3672 = 3638 / 3672

3 3/5 + 1 1/9 = (3 * 5 + 3) / 5 + (1 * 9 + 1) / 9 = 18/5 + 10/9 = (18 * 9 + 10 * 5) / (5 * 9) = 162 + 50 / 45 = 212 / 45

2 27/46 + 4 2/7 = (2 * 46 + 27) / 46 + (4 * 7 + 2) / 7 = 92/46 + 30/7 = (92 + 30 * 46) / (46 * 7) = 92 + 1380 / 322 = 1472 / 322

Now, we substitute the simplified fractions back into the expression:

2 * (3638/3672 + 212/45 + 1 1/9 + 13/6 + 7/26 + 16 + 1472/322 + 115/46 + 30/7)

Next, we add the mixed numbers:

1 1/9 = 9/9 + 1/9 = 10/9

Now, we calculate the sums:

3638/3672 + 212/45 + 10/9 + 13/6 + 7/26 + 16 + 1472/322 + 115/46 + 30/7 = 1.742524

Finally, we multiply this sum by 2:

2 * 1.742524 = 3.485048

So, the answer to the given expression is approximately 3.485048.