Question

1. how much paint will each class get if there are 4 classes sharing 7 gallons of paint?
2. a mosaic tile art piece is on display at a local museum. on this mosaic, \\( \frac { 1 } { 8 } \\) of the tiles are triangles. out of these triangles, \\( \frac { 3 } { 4 } \\) will be painted blue. what fraction of the whole mosaic will be blue triangles?
3. at the high school, \\( \frac { 2 } { 3 } \\) of all the students play a team sport. \\( \frac { 1 } { 4 } \\) of these students are on a football team. what fraction of all the high school students are on a football team?
4. a cake recipe calls for \\( 2 \frac { 2 } { 3 } \\) cups of flour. if you are making a tiered cake and need \\( 3 \frac { 1 } { 2 } \\) times that amount, how much flour will you need?

Explanation:

Step1: Analyze problem 4

We need to find the fraction of blue - triangle tiles. We know that \(\frac{1}{8}\) of the tiles are triangles and \(\frac{3}{4}\) of these triangles are blue. We use the rule for multiplying fractions: \(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\).

Step2: Calculate the fraction

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Step3: Analyze problem 5

We know that \(\frac{2}{3}\) of students play a team sport and \(\frac{1}{4}\) of these play football. Again, using the fraction - multiplication rule \(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\).

Step4: Calculate the fraction

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Step5: Analyze problem 6

First, convert the mixed numbers to improper fractions. \(2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{8}{3}\) and \(3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{7}{2}\). Then, since we need \(3\frac{1}{2}\) times the amount of flour, we use multiplication of fractions \(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\).

Step6: Calculate the amount of flour

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Answer:

1. \(\frac{3}{32}\) of the whole mosaic will be blue triangles.
2. \(\frac{1}{6}\) of all the high - school students are on a football team.
3. You will need \(9\frac{1}{3}\) cups of flour.