Question

1. $2\frac{2}{3}\cdot\frac{5}{6}=\underline{\quad\quad}$
2. $\frac{1}{8}\div\frac{1}{4}=\underline{\quad\quad}$
3. use the box plot below to answer the following question:

what is the minimum? $\underline{\quad\quad}$
maximum? $\underline{\quad\quad}$
(box plot with number line from 5 to 50, marks at 5,10,15,20,25,30,35,40,45,50, and a box plot drawn above)

Explanation:

Problem 8

Step1: Convert mixed number to improper fraction

To multiply a mixed number by a fraction, first convert the mixed number \(2\frac{2}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(2\frac{2}{3}\), we have \(a = 2\), \(b = 2\), \(c = 3\). Then \(\frac{2\times3 + 2}{3}=\frac{6 + 2}{3}=\frac{8}{3}\).

Step2: Multiply the two fractions

Now we multiply \(\frac{8}{3}\) by \(\frac{5}{6}\). When multiplying fractions, we multiply the numerators together and the denominators together. So \(\frac{8}{3}\times\frac{5}{6}=\frac{8\times5}{3\times6}=\frac{40}{18}\).

Step3: Simplify the fraction

Simplify \(\frac{40}{18}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. \(\frac{40\div2}{18\div2}=\frac{20}{9}\). Then convert \(\frac{20}{9}\) back to a mixed number. \(20\div9 = 2\) with a remainder of \(2\), so \(\frac{20}{9}=2\frac{2}{9}\).

Step1: Recall the rule for dividing fractions

To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of \(\frac{1}{4}\) is \(\frac{4}{1}\).

Step2: Multiply the fractions

So \(\frac{1}{8}\div\frac{1}{4}=\frac{1}{8}\times\frac{4}{1}\).

Step3: Simplify the multiplication

Multiply the numerators: \(1\times4 = 4\), multiply the denominators: \(8\times1 = 8\). Then simplify \(\frac{4}{8}\) by dividing both the numerator and the denominator by 4, which gives \(\frac{4\div4}{8\div4}=\frac{1}{2}\).

In a box - plot, the minimum value is represented by the left - most point (the whisker's left end). From the given box - plot, we can see that the left - most point is at 5.

Answer:

\(2\frac{2}{9}\)

Problem 9