Let's analyze Rashid's work step-by-step to determine where he may have gone wrong. The problem involves dividing fractions, and Rashid applied the rule to "multiply by the reciprocal." Here, Rashid needs to divide [tex]\(\frac{3}{4}\)[/tex] by [tex]\(9\)[/tex].
1. Correct way to divide fractions:
- When you divide a fraction by a whole number, you should multiply by the reciprocal of the whole number.
- The given problem is [tex]\(\frac{3}{4} \div 9\)[/tex].
- To solve [tex]\(\frac{3}{4} \div 9\)[/tex], you should multiply [tex]\(\frac{3}{4}\)[/tex] by the reciprocal of [tex]\(9\)[/tex], which is [tex]\(\frac{1}{9}\)[/tex].
[tex]\[
\frac{3}{4} \div 9 = \frac{3}{4} \times \frac{1}{9} = \frac{3 \times 1}{4 \times 9} = \frac{3}{36} = \frac{1}{12}
\][/tex]
Therefore, the correct result of [tex]\(\frac{3}{4} \div 9\)[/tex] is [tex]\(\frac{1}{12}\)[/tex].
2. Analyzing Rashid's work:
- Rashid obtained a result of [tex]\(\frac{1}{12}\)[/tex].
- Let's understand how Rashid might have calculated it.
- Suppose Rashid mistakenly multiplied directly instead of dividing, or applied the reciprocal to the wrong term.
3. Explanation:
- Rashid should have multiplied [tex]\(\frac{3}{4}\)[/tex] by the reciprocal of [tex]\(9\)[/tex], which is [tex]\(\frac{1}{9}\)[/tex], and obtained [tex]\(\frac{1}{12}\)[/tex].
- An accurate analysis of his method suggests that Rashid might have handled the reciprocal part incorrectly.
The final understanding is that Rashid multiplied with the reciprocal of the dividend instead of multiplying by the reciprocal of the divisor (the term he should divide by).
Given these points, the accurate description of Rashid's work is:
- Rashid multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
