Section 1
Introduction to Fractions and Mixed Numbers
Define the key terms.a. Fractionb. Numeratorc. Denominatord. Rational Numbere. Proper fractionf. Improper fractiong. Mixed number
Identify the numerator and the denominator for each fraction.$$\frac{2}{3}$$
Identify the numerator and the denominator for each fraction.$$\frac{8}{9}$$
Identify the numerator and the denominator for each fraction.$$\frac{12 x}{11 y^{2}}$$
Identify the numerator and the denominator for each fraction.$$\frac{7 p}{9 q}$$
Write a fraction that represents the shaded area.(FIGURE CAN'T COPY).
Write a fraction to represent the portion of gas in a gas tank represented by the gauge.(FIGURE CAN'T COPY).
The scoreboard for a recent men's championship swim meet in Melbourne, Australia, shows the final standings in the event. What fraction of the finalists are from the USA? (TABLE CAN'T COPY).
Refer to the scoreboard from Exercise $13 .$ What fraction of the finalists are from the Republic of South Africa (RSA)? (IMAGE CAN'T COPY).
The graph categorizes a sample of people by blood type. What fraction of the sample represents people with type O blood? (GRAPH CAN'T COPY).
Refer to the graph from Exercise $15 .$ What fraction of the sample represents people with type A blood? (IMAGE CAN'T COPY).
A class has 21 children $-11$ girls and 10 boys. What fraction of the class is made up of boys?
In a neighborhood in Ft. Lauderdale, Florida, 10 houses are for sale and 53 are not for sale. Write a fraction representing the portion of houses that are for sale.
Simplify if possible.$$\frac{-13}{1}$$
Simplify if possible.$$\frac{-14}{1}$$
Simplify if possible.$$\frac{2}{2}$$
Simplify if possible.$$\frac{8}{8}$$
Simplify if possible.$$\frac{0}{-3}$$
Simplify if possible.$$\frac{0}{7}$$
Simplify if possible.$$\frac{-3}{0}$$
Simplify if possible.$$\frac{-11}{0}$$
Simplify if possible.$$\frac{-9}{-10}$$
Simplify if possible.$$\frac{-13}{-6}$$
Which expressions are equivalent to $\frac{-9}{10} ?$$\begin{array}{cccc}\text { a. } \frac{9}{10} & \text { b. }-\frac{9}{10} & \text { c. } \frac{9}{-10} & \text { d. } \frac{-9}{-10}\end{array}$
Which expressions are equivalent to $-\frac{4}{5} ?$$\begin{array}{lll}\text { a. } \frac{-4}{5} & \text { b. } \frac{-4}{-5} & \text { c. } \frac{4}{-5} & \text { d. }-\frac{5}{4}\end{array}$
Which expressions are equivalent to $\frac{-4}{1} ?$a. $\frac{4}{-1} \quad$ b. $-4 \quad$ c. $-\frac{4}{1} \quad$ d. $\frac{1}{-4}$
Which expressions are equivalent to $\frac{-9}{1} ?$a. $\frac{-9}{-1} \quad$ b. $\frac{9}{-1} \quad$ c. $-9 \quad$ d. $-\frac{9}{1}$
For Exercises 33–38, label the fraction as proper or improper.$$\frac{7}{8}$$
Label the fraction as proper or improper.$$\frac{2}{3}$$
Label the fraction as proper or improper.$$\frac{10}{10}$$
Label the fraction as proper or improper.$$\frac{3}{3}$$
Label the fraction as proper or improper.$$\frac{7}{2}$$
Label the fraction as proper or improper.$$\frac{21}{20}$$
For Exercises 39–42, write an improper fraction for the shaded portion of each group of figures.(Figure cannot copy)
Write an improper fraction for the shaded portion of each group of figures.(Figure cannot copy)
For Exercises 43–44, write an improper fraction and a mixed number for the shaded portion of each group of figures.(Figure cannot copy)
Write an improper fraction and a mixed number for the shaded portion of each group of figures.(Figure cannot copy)
Write an improper fraction and a mixed number to represent the length of the nail.(Figure cannot copy)
Write an improper fraction and a mixed number that represent the number of cups of sugar needed for a batch of cookies, as indicated in the figure.(Figure cannot copy)
For Exercises 47–58, convert the mixed number to an improper fraction.$$1 \frac{3}{4}$$
Convert the mixed number to an improper fraction.$$6 \frac{1}{3}$$
Convert the mixed number to an improper fraction.$$-4 \frac{2}{9}$$
Convert the mixed number to an improper fraction.$$-3 \frac{1}{5}$$
Convert the mixed number to an improper fraction.$$-3 \frac{3}{7}$$
Convert the mixed number to an improper fraction.$$-8 \frac{2}{3}$$
Convert the mixed number to an improper fraction.$$6 \frac{3}{4}$$
Convert the mixed number to an improper fraction.$$10 \frac{3}{5}$$
Convert the mixed number to an improper fraction.$$11 \frac{5}{12}$$
Convert the mixed number to an improper fraction.$$12 \frac{1}{6}$$
Convert the mixed number to an improper fraction.$$-21 \frac{3}{8}$$
Convert the mixed number to an improper fraction.$$-15 \frac{1}{2}$$
How many thirds are in 10?
How many sixths are in 2?
How many eighths are in $2 \frac{3}{8} ?$
How many fifths are in $2 \frac{3}{5} ?$
How many fourths are in $1 \frac{3}{4}$ "
How many thirds are in $5 \frac{2}{3} ?$
For Exercises 65–76, convert the improper fraction to a mixed number.$$\frac{37}{8}$$
Convert the improper fraction to a mixed number.$$\frac{13}{7}$$
Convert the improper fraction to a mixed number.$$-\frac{39}{5}$$
Convert the improper fraction to a mixed number.$$-\frac{19}{4}$$
Convert the improper fraction to a mixed number.$$-\frac{27}{10}$$
Convert the improper fraction to a mixed number.$$-\frac{43}{18}$$
Convert the improper fraction to a mixed number.$$\frac{52}{9}$$
Convert the improper fraction to a mixed number.$$\frac{67}{12}$$
Convert the improper fraction to a mixed number.$$\frac{133}{11}$$
Convert the improper fraction to a mixed number.$$\frac{51}{10}$$
Convert the improper fraction to a mixed number.$$-\frac{23}{6}$$
Convert the improper fraction to a mixed number.$$-\frac{115}{7}$$
For Exercises 77–84, divide. Write the quotient as a mixed number.$$309 \div 7$$
Divide. Write the quotient as a mixed number.$$921 \div 4$$
Divide. Write the quotient as a mixed number.$$5281 \div 5$$
Divide. Write the quotient as a mixed number.$$7213 \div 8$$
Divide. Write the quotient as a mixed number.$$8913 \div 11$$
Divide. Write the quotient as a mixed number.$$4257 \div 23$$
Divide. Write the quotient as a mixed number.$$187 \div 15$$
Divide. Write the quotient as a mixed number.$$695 \div 34$$
For Exercises 85–94, plot the fraction on the number line.$$\frac{3}{4}$$
Plot the fraction on the number line.$$\frac{1}{2}$$
Plot the fraction on the number line.$$\frac{1}{3}$$
Plot the fraction on the number line.$$\frac{1}{5}$$
Plot the fraction on the number line.$$-\frac{2}{3}$$
Plot the fraction on the number line.$$-\frac{5}{6}$$
Plot the fraction on the number line.$$\frac{7}{6}$$
Plot the fraction on the number line.$$\frac{7}{5}$$
Plot the fraction on the number line.$$-\frac{4}{3}$$
Plot the fraction on the number line.$$-\frac{3}{2}$$
For Exercises 95–102, simplify.$$\left|-\frac{3}{4}\right|$$
Simplify.$$\left|-\frac{8}{7}\right|$$
Simplify.$$\left|\frac{1}{10}\right|$$
Simplify.$$\left|\frac{3}{20}\right|$$
Simplify.$$-\left|-\frac{7}{3}\right|$$
Simplify.$$-\left|-\frac{1}{4}\right|$$
Simplify.$$-\left(-\frac{7}{3}\right)$$
Simplify.$$-\left(-\frac{1}{4}\right)$$
True or false? Whole numbers can be written both as proper and improper fractions.
True or false? Suppose $m$ and $n$ are nonzero numbers, where $m>n .$ Then $\frac{m}{n}$ is an improper fraction.
True or false? Suppose $m$ and $n$ are nonzero numbers, where $m>n .$ Then $\frac{n}{m}$ is a proper fraction.
True or false? Suppose $m$ and $n$ are nonzero numbers, where $m>n .$ Then $\frac{n}{3 m}$ is a proper fraction.