Question

dierdres work to solve a math problem is shown below.

problem: how many \\(1\frac{1}{2}\\)-foot pieces can be cut from a 12-foot length of ribbon?

step 1: \\(1\frac{1}{2} \div 12 = n\\)
step 2: \\(\frac{3}{2} \div 12 = n\\)
step 3: \\(\frac{3}{2} \times \frac{1}{12} = n\\)
step 4: \\(\frac{3}{24} = n\\)
answer: \\(\frac{1}{8} = n\\)

Explanation:

Identify the correct division setup

To find how many \(1\frac{1}{2}\)-foot pieces can be cut from a \(12\)-foot ribbon, we must divide the total length by the piece length.
Using the Modeling with Division and Fraction Division Word Problems knowledge points:

$$ 12 \div 1\frac{1}{2} = n $$

Analyze Dierdre's error in Step 1

Dierdre wrote \(1\frac{1}{2} \div 12 = n\).
She reversed the dividend and divisor, which is incorrect.

Calculate the correct answer

Convert the mixed number to an improper fraction:

$$ 1\frac{1}{2} = \frac{3}{2} $$

Now perform the division:

$$ 12 \div \frac{3}{2} = 12 \times \frac{2}{3} = \frac{24}{3} = 8 $$

Dierdre's setup led to \(n = \frac{1}{8}\), but the correct number of pieces is \(8\).

Answer:

Dierdre made an error in Step 1 by reversing the dividend and the divisor.

To find how many \(1\frac{1}{2}\)-foot pieces can be cut from a \(12\)-foot ribbon, the total length must be divided by the size of each piece:

$$12 \div 1\frac{1}{2} = n$$

The correct calculation is:

$$12 \div \frac{3}{2} = 12 \times \frac{2}{3} = 8$$

So, \(8\) pieces can be cut from the ribbon.