A rod of length 2 m is cut into 1/4m pieces. How many pieces are obtained?
8
The question asks how many equal pieces a length can be divided into, which is a division of the whole length by the length of one piece.
Here the rod is 2 m long and each cut piece is \(\tfrac{1}{4}\) m, so the number of pieces is \(\dfrac{2}{\frac{1}{4}}\).
Dividing by a fraction is the same as multiplying by its reciprocal, so \(\dfrac{2}{\frac{1}{4}}=2\times4=8\) pieces.
A quick check confirms this: eight quarter-metre pieces give \(8\times\tfrac{1}{4}=2\) m, matching the rod length exactly.
The answers 4 and 6 come from dividing incorrectly, such as treating the piece as half a metre or subtracting instead of dividing, and give fewer pieces than the length allows.
The answer 10 overshoots, as would arise from multiplying by five instead of four, which does not fit the quarter-metre cut.
Hence, the answer is 8.
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Important Questions from Simplification
The value of {5 - 5 ÷ (10 - 12) × 8 + 9} × 3 + 5 + 5 × 5 ÷ 5 of 5 is:
What should come in place of the question mark (?) in the following question?
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Simplify the following expression.
\(\frac{{6\frac{1}{2} + 2\frac{5}{7} \times \frac{{14}}{{19}} - \frac{1}{2} \div 2\ of\frac{1}{4}}}{{11 \times 12 \div 12 + 12}}\)
The value of \(\left( {\frac{7}{5} \div \frac{7}{{10}}of\frac{3}{4}} \right) \div \frac{4}{9} + \left( {\frac{7}{{16}} \div 10\frac{1}{2} \times 7\frac{1}{5}} \right) \times \frac{5}{{12}} \) is:
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