Can you form different expressions for the same question?

Question

Homi · Accepted Answer

We need to find the length of rope left. Some pieces are cut from it.

Step 1 — Understand the problem

We have a rope. Its original length is 12.5 meters. A worker cuts off 3 pieces. Each piece is 1.5 meters long. We need to find the remaining rope length.

Diagram 1

Step 2 — Form Expression 1

Let us think about the total length cut first. We multiply the number of pieces. We multiply by the length of each piece. Then, we subtract this total. We subtract it from the original length. Let $L_R$ be the remaining length of the rope. $L_R = 12.5 - (3 \times 1.5)$ $= 12.5 - 4.5$ $= 8.0$

$\boxed{8.0 \text{ meters}}$

Step 3 — Form Expression 2

Let us think about cutting each piece one by one. We start with the original length. We subtract the first piece's length. Then, we subtract the second piece's length. Finally, we subtract the third piece's length. Let $L_R$ be the remaining length of the rope. $L_R = 12.5 - 1.5 - 1.5 - 1.5$ $= 11.0 - 1.5 - 1.5$ $= 9.5 - 1.5$ $= 8.0$

$\boxed{8.0 \text{ meters}}$

Step 4 — Form Expression 3 (using different units)

Let us convert all lengths to centimeters first. One meter equals 100 centimeters. Original rope length in centimeters: $12.5 \times 100 = 1250 \text{ cm}$ Length of one piece in centimeters: $1.5 \times 100 = 150 \text{ cm}$ Now, we write the expression in centimeters. Let $L_{R, \text{cm}}$ be the remaining length in centimeters. $L_{R, \text{cm}} = 1250 - (3 \times 150)$ $= 1250 - 450$ $= 800$

$\boxed{800 \text{ cm}}$ We need to convert this back to meters. $800 \div 100 = 8.0$ $\boxed{8.0 \text{ meters}}$

Answer

For the question: "A rope is 12.5 meters long. A worker cuts off 3 pieces, each 1.5 meters long. How much rope is left?"

(i) One expression is to calculate total cut length first: $12.5 - (3 \times 1.5)$ (ii) Another expression is to subtract each piece individually: $12.5 - 1.5 - 1.5 - 1.5$ (iii) A third expression uses centimeters as units: $(12.5 \times 100) - (3 \times (1.5 \times 100))$

Question 21

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