Question

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

at this rate, how much glue would she mix with 3 pounds of glitter?

\boxed{} gallons of glue

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Explanation:

Step1: Find the rate of glue per pound of glitter

The rate is the amount of glue divided by the amount of glitter. So, for \(\frac{7}{8}\) pound of glitter, we use \(\frac{1}{3}\) gallon of glue. The rate \(r\) is \(\frac{\frac{1}{3}}{\frac{7}{8}}\). To divide fractions, we multiply by the reciprocal: \(\frac{1}{3} \times \frac{8}{7}=\frac{8}{21}\) gallons per pound of glitter.

Step2: Calculate glue for 3 pounds of glitter

Multiply the rate by 3 pounds. So, \(3\times\frac{8}{21}\). Simplify the fraction: \(\frac{24}{21}=\frac{8}{7}\) (or \(1\frac{1}{7}\)).

Answer:

\(\frac{8}{7}\) (or \(1\frac{1}{7}\))