Math worksheet with multiple choice questions on rational numbers, featuring problems involving fractions, equations, and real-world applications.

Final Answer:
(C) -125/462

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Explanation:
We need to find the value of x in this equation:
3/7 + x + (-8/21) + 5/22 = 2/462

Step 1: Move all the numbers (except x) to the right side.
That means we subtract them from both sides. So:

x = 2/462 - 3/7 - (-8/21) - 5/22

Remember: minus a negative is plus! So -(-8/21) becomes +8/21.

So now:
x = 2/462 - 3/7 + 8/21 - 5/22

Step 2: Find a common denominator for all fractions.
The denominators are 462, 7, 21, and 22.
462 is divisible by all of them (because 462 = 7 × 66, 21 × 22, 22 × 21).
So we’ll use 462 as the common denominator.

Convert each fraction:

- 3/7 = (3 × 66)/(7 × 66) = 198/462
- 8/21 = (8 × 22)/(21 × 22) = 176/462
- 5/22 = (5 × 21)/(22 × 21) = 105/462

Now plug them back in:

x = 2/462 - 198/462 + 176/462 - 105/462

Step 3: Combine all numerators over 462:

x = (2 - 198 + 176 - 105)/462

Do the math step by step:

2 - 198 = -196
-196 + 176 = -20
-20 - 105 = -125

So x = -125/462

That matches option (C).

✔ Final Answer: (C) -125/462