Question

While working on a large portrait, Juan used 16 1/3tubes of paint and 5 1/4 ounces of brush cleaner. Juan is visiting an art supply store to get supplies for his next painting. Assuming his next painting requires the same amount of supplies, how many ounces of brush cleaner will he need to buy for every tube of paint? Complete the unit rate below. questions llc

Answer 1

To find out how many ounces of brush cleaner Juan needs for each tube of paint, we first convert the mixed numbers to improper fractions.

1. Convert paint tubes:

   • Juan used \(16 \frac{1}{3}\) tubes of paint.
   • Convert to an improper fraction: \[ 16 \frac{1}{3} = \frac{16 \times 3 + 1}{3} = \frac{48 + 1}{3} = \frac{49}{3}. \]

2. Convert brush cleaner:

   • Juan used \(5 \frac{1}{4}\) ounces of brush cleaner.
   • Convert to an improper fraction: \[ 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}. \]

3. Find the unit rate of brush cleaner per tube of paint:

   • To find the ounces of brush cleaner per tube of paint, divide the total ounces of brush cleaner by the total tubes of paint: \[ \text{Ounces per tube} = \frac{\frac{21}{4}}{\frac{49}{3}} = \frac{21}{4} \times \frac{3}{49} = \frac{21 \times 3}{4 \times 49} = \frac{63}{196}. \]

4. Simplify the fraction:

   • Both the numerator and denominator can be divided by 7: \[ \frac{63 \div 7}{196 \div 7} = \frac{9}{28}. \]

Thus, the unit rate is: \[ \text{Juan needs } \frac{9}{28} \text{ ounces of brush cleaner for each tube of paint.} \]