Ms. Nellies has 2 pints of vinegar for her students to use in a science experiment. Each group of students needs 1/3 pint of vinegar. Trey draws the number line model and writes the equation below to help Ms. Nellies figure out how many 1/3-pint servings of vinegar she has. Are Trey’s number line model and equation correct? Click the arrows to choose an answer from each menu. Trey’s number line model is Choose… because it represents the expression Choose… The correct equation is Choose… Ms. Nellies has enough vinegar for Choose… groups of students.
The correct answer and explanation is:
The correct answers are:
- Trey’s number line model is correct because it represents the expression 2 ÷ 1/3.
- The correct equation is 2 ÷ 1/3 = 6.
- Ms. Nellies has enough vinegar for 6 groups of students.
Explanation:
Ms. Nellies has 2 pints of vinegar, and each group of students needs 1/3 pint of vinegar. To determine how many groups can be served, we need to divide 2 pints by 1/3 pint per group: 2÷132 \div \frac{1}{3}
When dividing by a fraction, we use the reciprocal of the divisor and multiply: 2×31=61=62 \times \frac{3}{1} = \frac{6}{1} = 6
This means there are 6 groups that can receive 1/3 pint of vinegar each.
Number Line Representation:
A number line model would correctly show 2 whole pints divided into sections of 1/3 pint. Each whole number from 0 to 2 would be split into three equal parts, representing the thirds. If the number line is correctly drawn, it should show six sections, confirming the correct calculation.
Why Trey’s Model and Equation Are Correct:
- The number line correctly represents the division of 2 into 1/3-pint sections. There should be 6 equal parts in total.
- The equation follows the correct mathematical operation: dividing a whole number by a fraction requires multiplying by the reciprocal.
- The solution (6 groups) matches the expected outcome when checking with a number line or by logical reasoning.
Now, let’s generate the image of the number line model.
The number line model visually represents the division of 2 pints into 1/3-pint sections. Each whole pint is split into three equal parts, resulting in a total of 6 groups. The equation 2 ÷ 1/3 = 6 is correct, confirming that Ms. Nellies has enough vinegar for 6 groups of students. Let me know if you need any further clarifications!
