Class 8 Exam > Class 8 Questions > Divide as directed: 52pqr (p + q) (q + r) (r ...
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Divide as directed: 52pqr (p + q) (q + r) (r + p) ÷104pq (q + r) (r + p)
- a)r(p+q)
- b)1/2 r(p+q)
- c)1/2
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Divide as directed: 52pqr (p + q) (q + r) (r + p) ÷104pq (q + r...
Understanding the Division Problem
To solve the expression, we start with:
52pqr (p + q) (q + r) (r + p) ÷ 104pq (q + r) (r + p).
Step 1: Simplifying the Expression
- Identify the common terms in the numerator and denominator.
- In the expression, (q + r) and (r + p) are present in both the numerator and the denominator.
Step 2: Cancel Out Common Factors
- We can cancel (q + r) and (r + p) from the numerator and denominator:
52pqr (p + q) ÷ 104pq.
Step 3: Further Simplification
- Now, we simplify the coefficients:
52 ÷ 104 = 1/2.
- This gives us:
(1/2) * (pqr) ÷ (pq) = (1/2) * (r).
Final Result
The simplified expression is:
1/2 * r(p + q).
Thus, the correct answer is option 'B', which is 1/2 r(p + q).
Conclusion
- The process involved identifying and canceling common factors.
- The final outcome shows the simplified form clearly, confirming that option 'B' is indeed the correct answer.
To solve the expression, we start with:
52pqr (p + q) (q + r) (r + p) ÷ 104pq (q + r) (r + p).
Step 1: Simplifying the Expression
- Identify the common terms in the numerator and denominator.
- In the expression, (q + r) and (r + p) are present in both the numerator and the denominator.
Step 2: Cancel Out Common Factors
- We can cancel (q + r) and (r + p) from the numerator and denominator:
52pqr (p + q) ÷ 104pq.
Step 3: Further Simplification
- Now, we simplify the coefficients:
52 ÷ 104 = 1/2.
- This gives us:
(1/2) * (pqr) ÷ (pq) = (1/2) * (r).
Final Result
The simplified expression is:
1/2 * r(p + q).
Thus, the correct answer is option 'B', which is 1/2 r(p + q).
Conclusion
- The process involved identifying and canceling common factors.
- The final outcome shows the simplified form clearly, confirming that option 'B' is indeed the correct answer.
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