Final answer:
To determine the total pounds of nails needed, one must use a double number line to align 1 3/4 pounds with 3/4 of the necessary amount. By dividing these numbers, the student finds that 2 1/3 pounds of nails are needed for the project.
Step-by-step explanation:
The question asks how many pounds of nails are needed for a project if 1 3/4 pounds is only 3/4 of what is necessary. To find the full amount needed, we use a double number line. One line represents the pounds of nails, and the other represents the fraction of the total amount needed.
- Mark the first number line at 0 for 0 pounds, and at the end for the total pounds needed. We don't know this number yet, so we can call it X.
- Mark the second number line at 0 for 0% of the nails needed, and at the end for 100% of the nails needed.
- Align the two lines so that 1 3/4 pounds on the first number line is directly above 3/4 (or 75%) on the second number line.
- To find the value of X, we calculate 1 3/4 lbs (which is the same as 7/4 or 1.75) divided by 3/4 (or 0.75). The equation is 1.75 ÷ 0.75 = 2 1/3 pounds, which will be the total amount needed for the project.
The student will need 2 1/3 pounds of nails for the project.