Please give me a long answer! Thank you!

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

6 0

Answer:

10/12 can be approximated by 1

3/8 can be approximated by 1/2

so the answer to the subtraction must be really close to 1-1/2 = 1/2 = 0.5

Step-by-step explanation:

The real solution can be found by converting to numerator 24, which is the LCM, or Lowest Common Multiple of numerators 12 and 8.

10/12 = 20/24

3/8 = 9/24

Now the subtraction is (20-9)/24 = 11/24 ≈ 0.4583

So the actual result 0.4583 is actually pretty close to 0.5.

A benchmark value is nothing more than a really simple fraction or integer (1/2, 1/3, 1, 2, ...) that you know where to plot on the number line.

Making approximations can serve as a double check to see if you didn't make any mistakes on the actual calculation.

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Substitute $\mathbf{(ii)}$ into $\mathbf{(i)}:$

$\dfrac{7v}{13}+v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+1 \right )\cdot v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+\dfrac{13}{13} \right )\cdot v=180^{\circ}\\\\\\ \dfrac{20}{13}\cdot v=180^{\circ}\\\\\\ v=180^{\circ}\cdot \dfrac{13}{20}\\\\\\ \boxed{\begin{array}{c} v=117^{\circ} \end{array}}$

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