Class 8 Exam > Class 8 Questions > What is the sum of3/7 + (-6/11) + (-8/21) + 5...
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What is the sum of
3/7 + (-6/11) + (-8/21) + 5/22 ?
- a)-125/462
- b)-125/446
- c)-100/462
- d)125/462
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What is the sum of3/7 + (-6/11) + (-8/21) + 5/22 ?a)-125/462b)-125/446...
3/7 + (-6/11) + (-8/21) + 5/22
= [3/7 + (-8/21)] + [(-6/11) + 5/22]
(by using commutativity and associativity)
(by using commutativity and associativity)
= [9/21 + (-8/21)] + [-12/22 + 5/22]
LCM of 7 and 21 is 21; LCM of 11 and 22 is 22
= 1/21 + (-7/22)
= 22/462 + (-147/462)
= -125/462
= 22/462 + (-147/462)
= -125/462
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What is the sum of3/7 + (-6/11) + (-8/21) + 5/22 ?a)-125/462b)-125/446...
Understanding the Problem
To find the sum of the fractions 3/7, -6/11, -8/21, and 5/22, we need to follow these steps:
Step 1: Find the Least Common Denominator (LCD)
- The denominators are 7, 11, 21, and 22.
- The LCD is the smallest number that all denominators can divide into evenly.
- The prime factorization gives us:
- 7 = 7
- 11 = 11
- 21 = 3 × 7
- 22 = 2 × 11
- The LCD is 462.
Step 2: Convert Each Fraction to the Common Denominator
- Convert each fraction:
- 3/7 = (3 * 66) / 462 = 198/462
- -6/11 = (-6 * 42) / 462 = -252/462
- -8/21 = (-8 * 22) / 462 = -176/462
- 5/22 = (5 * 21) / 462 = 105/462
Step 3: Add the Converted Fractions
- Now, sum the fractions:
- 198/462 + (-252/462) + (-176/462) + 105/462
- Combine the numerators:
- 198 - 252 - 176 + 105 = -125
Step 4: Write the Final Answer
- The sum is -125/462.
Thus, the final result is -125/462, confirming that option 'A' is correct.
To find the sum of the fractions 3/7, -6/11, -8/21, and 5/22, we need to follow these steps:
Step 1: Find the Least Common Denominator (LCD)
- The denominators are 7, 11, 21, and 22.
- The LCD is the smallest number that all denominators can divide into evenly.
- The prime factorization gives us:
- 7 = 7
- 11 = 11
- 21 = 3 × 7
- 22 = 2 × 11
- The LCD is 462.
Step 2: Convert Each Fraction to the Common Denominator
- Convert each fraction:
- 3/7 = (3 * 66) / 462 = 198/462
- -6/11 = (-6 * 42) / 462 = -252/462
- -8/21 = (-8 * 22) / 462 = -176/462
- 5/22 = (5 * 21) / 462 = 105/462
Step 3: Add the Converted Fractions
- Now, sum the fractions:
- 198/462 + (-252/462) + (-176/462) + 105/462
- Combine the numerators:
- 198 - 252 - 176 + 105 = -125
Step 4: Write the Final Answer
- The sum is -125/462.
Thus, the final result is -125/462, confirming that option 'A' is correct.
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