Describe how to use area models to find the quotient 2/3 divided by 1/5. Check your work by also finding the quotient 2/3 divided by 1/5 using numerical operations only.
To use area models to find the quotient, follow these steps:
Step 1: Draw a rectangle to represent the dividend, which in this case is 2/3.
Step 2: Divide the rectangle into three equal parts horizontally, representing the denominator of 2/3.
Step 3: Shade two of the three parts to represent the numerator of 2/3.
Step 4: Draw a smaller rectangle to represent the divisor, which is 1/5.
Step 5: Divide this rectangle into five equal parts horizontally, representing the denominator of 1/5.
Step 6: Shade one of the five parts to represent the numerator of 1/5.
Step 7: Count the shaded portions in the dividend rectangle (2) and divide it by the shaded portion in the divisor rectangle (1). The result is the quotient, which is 2.
To check your work using numerical operations, divide the numerators and denominators directly:
2/3 ÷ 1/5
Step 1: Invert the divisor and multiply: 2/3 * 5/1
(2 * 5) / (3 * 1)
10/3
The quotient using both methods matches, so the correct answer is 10/3 or 3 1/3.