Make a sketch to show each unit. Then use shading or some sort of marks to indicate the fractional part. Be sure that the thirds are clear. a. $\frac{2}{3}$ of the 6 children in the play were girls. b. $\frac{2}{3}$ of the 6 yards of cloth were needed for the play. c. $\frac{2}{3}$ of the 6 cartons of ice cream were chocolate. d. $\frac{2}{3}$ of each of the 6 cartons of ice cream were eaten. e. $\frac{2}{3}$ of the 6 moving vans were painted red. f. $\frac{2}{3}$ of each of the 6 moving vans were painted red. g. The store had 6 cartons of paper towels and used $\frac{2}{3}$ of them. h. The store had 6 cartons of paper goods and used $\frac{2}{3}$ of each of them.

a. First show $\frac{2}{5}$ of the pentagonal region to the right. b. Then show that $\frac{2}{5}$ is equivalent to $\frac{4}{10}$ by adding marks to the work for part (a). c. How might one show that $\frac{6}{5}=\frac{12}{10}$, with the pentagonal region as the whole?

Use sketches of regions or number lines to show each of the following: a. $\frac{2}{3}=\frac{10}{15}$ b. $1 \frac{4}{10}=1 \frac{2}{5}$ c. $\frac{5}{4}=\frac{15}{12}$

Shade six of the small squares in the rectangle we saw earlier. Using the diagram , explain how to determine each of the following : a. the percent of the area that is shaded b. the fractional part of the area that is shaded c. the fractional part expressed as a decimal

From memory, give familiar fractions that are roughly equal to the given decimals. a. $0.48176$ b. $0.3411$ c. $0.74622$ d. $0.655$ e. $0.67$

If 0 and $3-2 i$ are roots of a polynomial equation with rational coefficients, what other numbers must also be roots of the equation?

Determine all real solutions to the equation or inequality. For the inequalities, also sketch the graph of the solution set. $2 x-3>3 x-4$

How many possible remainders are there when you divide a whole number by eleven ? Test your conclusion on $\frac{3}{11}$ and revise your conclusion if necessary. Nonterminating, repeating decimals, like those you get for $\frac{1}{7}$ and $\frac{3}{11}$, are often abbreviated by putting a bar over the repeating part.

a. How many tens are in $357$ ? How many whole tens? b. How many hundreds are in $4362$ ? How many whole hundreds? c. How many tens are in $4362$ ? How many whole tens? d. How many thousands are in $456,654$ ? How many whole thousands? e. How many hundreds are in $456,654$ ? How many whole hundreds? f. How many tens are in $456,654$ ? How many whole tens? g. How many tenths are in $23.47$ ? How many whole tenths? h. How many thousandths are in $23.47$ ? How many whole thousandths? i. How many ones are in $23.47$ ? How many whole ones? j. How many hundredths are in $23.47$ ? How many whole hundredths? k. How many tenths are in $2347$ ? How many whole tenths? l. How many tenths are in $234.7$ ? How many whole tenths?

Which represents the greatest quantity of cheese? Be prepared to defend your answer. a. $1 \frac{3}{4}$ pounds b. $\frac{7}{4}$ pounds c. $1.75$ pounds d. $28$ ounces

Which of the following wholes is/are cut so that sixths can be shown?

Write the following decimals as fractions, if possible. Change to simplest form or lowest terms. a. $0.625$ b. $0.49$ c. $91.333 \ldots$ d. $1.7$ e. $0 . \overline{9}$ f. $0.9 \overline{3}$ g. $0 . \overline{53}$ h. $0.0 \overline{53}$ i. $4 . \overline{76}$ j. $8 . \overline{094}$ k. $0.1213141516171819110111112113114115 \ldots$ [There is a pattern in part $(\mathrm{k})$. Assume that the pattern you see continues. Is there a repeating block of digits?]

Using a rectangular or circular region as the whole, make sketches to show each of these: a. $\frac{2}{3}$ b. $\frac{7}{4}$ c. $2 \frac{3}{8}$ d. $\frac{0}{4}$ e. $\frac{3}{1}$

For each given pair of numbers, tell which fractional value is closer to $\frac{1}{2}$, Explain your reasoning. a. $\frac{11}{25}$ or $\frac{12}{25}$ b. $\frac{5}{8}$ or $\frac{9}{20}$ c. $\frac{12}{25}$ or $\frac{7}{15}$ d. $\frac{11}{24}$ or $\frac{9}{20}$ e. $\frac{7}{15}$ or $\frac{13}{25}$