[tex]3 \times \frac{16}{27} + 1 \times \frac{17}{27} - 2 \times \frac{25}{36} - 1 \times \frac{7}{36} = [/tex]
[tex]\frac{48}{27} + \frac{17}{27} - \frac{50}{36} - \frac{7}{36} = [/tex]
[tex]\frac{65}{27} - \frac{57}{36} = [/tex]
First, find a common denominator for 27 and 36:
[tex]27 = 3 \times 3 \times 3[/tex]
[tex]36 = 2 \times 2 \times 3 \times 3[/tex]
The least common multiple is 3 x 3 x 2 x 2 x 3 = 36 x 3 = 108.
Therefore:
[tex]\frac{65}{27} = \frac{65 \times 4}{27 \times 4} = \frac{260}{108}[/tex]
[tex]\frac{57}{36} = \frac{57 \times 3}{36 \times 3} = \frac{171}{108}[/tex]
Now, we can subtract the two fractions:
[tex]\frac{260}{108} - \frac{171}{108} = \frac{260 - 171}{108} = \frac{89}{108}[/tex]
So, the final answer is:
[tex]\frac{89}{108}[/tex]
[tex]3 \times \frac{16}{27} + 1 \times \frac{17}{27} - 2 \times \frac{25}{36} - 1 \times \frac{7}{36} = [/tex]
[tex]\frac{48}{27} + \frac{17}{27} - \frac{50}{36} - \frac{7}{36} = [/tex]
[tex]\frac{65}{27} - \frac{57}{36} = [/tex]
First, find a common denominator for 27 and 36:
[tex]27 = 3 \times 3 \times 3[/tex]
[tex]36 = 2 \times 2 \times 3 \times 3[/tex]
The least common multiple is 3 x 3 x 2 x 2 x 3 = 36 x 3 = 108.
Therefore:
[tex]\frac{65}{27} = \frac{65 \times 4}{27 \times 4} = \frac{260}{108}[/tex]
[tex]\frac{57}{36} = \frac{57 \times 3}{36 \times 3} = \frac{171}{108}[/tex]
Now, we can subtract the two fractions:
[tex]\frac{260}{108} - \frac{171}{108} = \frac{260 - 171}{108} = \frac{89}{108}[/tex]
So, the final answer is:
[tex]\frac{89}{108}[/tex]