Given that the amount of red paint and the amount of yellow paint needed to make tangerine, are:
[tex]\begin{gathered} 3\frac{9}{10}oz \\ \\ 3\frac{3}{8}oz \end{gathered}[/tex]
• You know that Gavin expects to have a total of:
[tex]6\frac{5}{8}oz[/tex]
Since:
[tex]\frac{5}{8}\approx0.6[/tex]
You know that the amount he expects to have is:
[tex]\approx6.6oz[/tex]
Knowing that:
[tex]\begin{gathered} 3\frac{9}{10}\approx4 \\ \\ 3\frac{3}{8}\approx3.4 \end{gathered}[/tex]
Therefore:
[tex]3\frac{9}{10}oz+3\frac{3}{8}oz\approx7oz[/tex]
Hence, you can conclude that it is a reasonable expectation.
• Given the Addition:
[tex]4+3\frac{1}{2}[/tex]
You can solve it as follows:
- Convert the Mixed Number to an Improper fraction by multiplying the whole number by the denominator and adding the result to the numerator. The denominator does not change:
[tex]=4+\frac{(3\cdot2)+1}{2}=4+\frac{7}{2}[/tex]
- Use this formula for adding fractions:
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}[/tex]
Then:
[tex]=\frac{(4\cdot2)+(1\cdot7)}{2}=\frac{8+7}{2}=\frac{15}{2}[/tex]
In order to write the Sum as a Mixed Number, you need to:
- Divide the numerator 15 by the denominator 2.
- The Quotient 7 will be the whole number
- The Remainder 1 will be the new numerator.
- The denominator does not change.
Then:
[tex]\frac{15}{2}=7\frac{1}{2}[/tex]
Notice that it is close to his estimate.
Hence, the answers are:
- Gavin's expectation is reasonable.
- Estimation of the amount of paint made:
[tex]4+3\frac{1}{2}=7.5[/tex]
- It is close to Gavin's estimate.
