Question

problem 1 - part a
clare makes glitter glue by mixing \\(\frac{7}{8}\\) pound of glitter with \\(\frac{1}{3}\\) gallon of glue.

at this rate, how much glitter would she mix with 1 gallon of glue?

\\(\square\\) pounds of glitter

Explanation:

Step1: Identify the rate relationship

We know that for \(\frac{1}{3}\) gallon of glue, the amount of glitter is \(\frac{7}{8}\) pound. We need to find the amount of glitter for 1 gallon of glue. Let \(x\) be the amount of glitter for 1 gallon of glue. The rate of glitter to glue should be constant, so we can set up a proportion: \(\frac{\frac{7}{8}\text{ pound}}{\frac{1}{3}\text{ gallon}}=\frac{x\text{ pound}}{1\text{ gallon}}\).

Step2: Solve for \(x\)

To solve for \(x\), we can use the rule that \(x = \frac{7}{8}\div\frac{1}{3}\). Dividing by a fraction is the same as multiplying by its reciprocal, so \(x=\frac{7}{8}\times3\).

Step3: Calculate the product

\(\frac{7}{8}\times3=\frac{21}{8}\) (or \(2\frac{5}{8}\) as a mixed number).

Answer:

\(\frac{21}{8}\) (or \(2\frac{5}{8}\))