4.8: Exercise Supplement
- Page ID
- 52589
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Fractions of Whole Numbers
For Problems 1 and 2, name the suggested fraction.
Exercise \(\PageIndex{1}\)
- Answer
-
\(\dfrac{2}{6}\) or \(\dfrac{1}{3}\)
Exercise \(\PageIndex{2}\)
For problems 3-5, specify the numerator and denominator.
Exercise \(\PageIndex{3}\)
\(\dfrac{4}{5}\)
- Answer
-
numerator, 4; denominator, 5
Exercise \(\PageIndex{4}\)
\(\dfrac{5}{12}\)
Exercise \(\PageIndex{5}\)
\(\dfrac{1}{3}\)
- Answer
-
numerator, 1; denominator, 3
For problems 6-10, write each fraction using digits.
Exercise \(\PageIndex{6}\)
Three fifths
Exercise \(\PageIndex{7}\)
Eight elevenths
- Answer
-
\(\dfrac{8}{11}\)
Exercise \(\PageIndex{8}\)
Sixty-one forty firsts
Exercise \(\PageIndex{9}\)
Two hundred six-thousandths
- Answer
-
\(\dfrac{200}{6,000}\)
Exercise \(\PageIndex{10}\)
zero tenths
For problems 11-15, write each fraction using words.
Exercise \(\PageIndex{11}\)
\(\dfrac{10}{17}\)
- Answer
-
ten seventeenths
Exercise \(\PageIndex{12}\)
\(\dfrac{21}{38}\)
Exercise \(\PageIndex{13}\)
\(\dfrac{606}{1431}\)
- Answer
-
six hundred six, one thousand four hundred thirty-firsts
Exercise \(\PageIndex{14}\)
\(\dfrac{0}{8}\)
Exercise \(\PageIndex{15}\)
\(\dfrac{1}{16}\)
- Answer
-
one sixteenth
For problems 16-18, state each numerator and denominator and write each fraction using digits.
Exercise \(\PageIndex{16}\)
One minute is one sixtieth of an hour.
Exercise \(\PageIndex{17}\)
In a box that contains forty-five electronic components, eight are known to be defective. If three components are chosen at random from the box, the probability that all three are defective is fifty-six fourteen thousand one hundred ninetieths.
- Answer
-
numerator, 56; denominator, 14,190
Exercise \(\PageIndex{18}\)
About three fifths of the students in a college algebra class received a “B” in the course.
For problems 19 and 20, shade the region corresponding to the given fraction.
Exercise \(\PageIndex{19}\)
\(\dfrac{1}{4}\)
- Answer
-
Exercise \(\PageIndex{20}\)
\(\dfrac{3}{7}\)
Proper Fraction, Improper Fraction, and Mixed Numbers
For problems 21-29, convert each improper fraction to a mixed number.
Exercise \(\PageIndex{21}\)
\(\dfrac{11}{4}\)
- Answer
-
\(2 \dfrac{3}{4}\)
Exercise \(\PageIndex{22}\)
\(\dfrac{15}{2}\)
Exercise \(\PageIndex{23}\)
\(\dfrac{51}{8}\)
- Answer
-
\(6 \dfrac{3}{8}\)
Exercise \(\PageIndex{24}\)
\(\dfrac{121}{15}\)
Exercise \(\PageIndex{25}\)
\(\dfrac{356}{3}\)
- Answer
-
\(118 \dfrac{2}{3}\)
Exercise \(\PageIndex{26}\)
\(\dfrac{3}{2}\)
Exercise \(\PageIndex{27}\)
\(\dfrac{5}{4}\)
- Answer
-
\(1 \dfrac{1}{4}\)
Exercise \(\PageIndex{28}\)
\(\dfrac{20}{5}\)
Exercise \(\PageIndex{29}\)
\(\dfrac{9}{3}\)
- Answer
-
3
For problems 30-40, convert each mixed number to an improper fraction.
Exercise \(\PageIndex{30}\)
\(5 \dfrac{2}{3}\)
Exercise \(\PageIndex{31}\)
\(16 \dfrac{1}{8}\)
- Answer
-
\(\dfrac{129}{8}\)
Exercise \(\PageIndex{32}\)
\(18 \dfrac{1}{3}\)
Exercise \(\PageIndex{33}\)
\(3 \dfrac{1}{5}\)
- Answer
-
\(\dfrac{16}{5}\)
Exercise \(\PageIndex{34}\)
\(2 \dfrac{9}{16}\)
Exercise \(\PageIndex{35}\)
\(17 \dfrac{20}{21}\)
- Answer
-
\(\dfrac{377}{21}\)
Exercise \(\PageIndex{36}\)
\(1 \dfrac{7}{8}\)
Exercise \(\PageIndex{37}\)
\(1 \dfrac{1}{2}\)
- Answer
-
\(\dfrac{3}{2}\)
Exercise \(\PageIndex{38}\)
\(2 \dfrac{1}{2}\)
Exercise \(\PageIndex{39}\)
\(8 \dfrac{6}{7}\)
- Answer
-
\(\dfrac{62}{7}\)
Exercise \(\PageIndex{40}\)
\(2 \dfrac{9}{2}\)
Exercise \(\PageIndex{41}\)
Why does \(0 \dfrac{1}{12}\) not qualify as a mixed number?
- Answer
-
because the whole number part is zero
Exercise \(\PageIndex{42}\)
Why does 8 qualify as a mixed number?
Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Term
For problems 43-47, determine if the pairs of fractions are equivalent.
Exercise \(\PageIndex{43}\)
\(\dfrac{1}{2}, \dfrac{15}{30}\)
- Answer
-
equivalent
Exercise \(\PageIndex{44}\)
\(\dfrac{8}{9}, \dfrac{32}{36}\)
Exercise \(\PageIndex{45}\)
\(\dfrac{3}{14}, \dfrac{24}{110}\)
- Answer
-
not equivalent
Exercise \(\PageIndex{46}\)
\(2 \dfrac{3}{8}, \dfrac{38}{16}\)
Exercise \(\PageIndex{47}\)
\(\dfrac{108}{77}, 1 \dfrac{5}{13}\)
- Answer
-
not equivalent
For problems 48-60, reduce, if possible, each fraction.
Exercise \(\PageIndex{48}\)
\(\dfrac{10}{25}\)
Exercise \(\PageIndex{49}\)
\(\dfrac{32}{44}\)
- Answer
-
\(\dfrac{8}{11}\)
Exercise \(\PageIndex{50}\)
\(\dfrac{102}{266}\)
Exercise \(\PageIndex{51}\)
\(\dfrac{15}{33}\)
- Answer
-
\(\dfrac{5}{11}\)
Exercise \(\PageIndex{52}\)
\(\dfrac{18}{25}\)
Exercise \(\PageIndex{53}\)
\(\dfrac{21}{35}\)
- Answer
-
\(\dfrac{3}{5}\)
Exercise \(\PageIndex{54}\)
\(\dfrac{9}{16}\)
Exercise \(\PageIndex{55}\)
\(\dfrac{45}{85}\)
- Answer
-
\(\dfrac{9}{17}\)
Exercise \(\PageIndex{56}\)
\(\dfrac{24}{42}\)
Exercise \(\PageIndex{57}\)
\(\dfrac{70}{136}\)
- Answer
-
\(\dfrac{35}{68}\)
Exercise \(\PageIndex{58}\)
\(\dfrac{182}{580}\)
Exercise \(\PageIndex{59}\)
\(\dfrac{325}{810}\)
- Answer
-
\(\dfrac{65}{162}\)
Exercise \(\PageIndex{60}\)
\(\dfrac{250}{1000}\)
For problems 61-72, determine the missing numerator or denominator.
Exercise \(\PageIndex{61}\)
\(\dfrac{3}{7} = \dfrac{?}{35}\)
- Answer
-
15
Exercise \(\PageIndex{62}\)
\(\dfrac{4}{11} = \dfrac{?}{99}\)
Exercise \(\PageIndex{63}\)
\(\dfrac{1}{12} = \dfrac{?}{72}\)
- Answer
-
6
Exercise \(\PageIndex{64}\)
\(\dfrac{5}{8} = \dfrac{25}{?}\)
Exercise \(\PageIndex{65}\)
\(\dfrac{11}{9} = \dfrac{33}{?}\)
- Answer
-
27
Exercise \(\PageIndex{66}\)
\(\dfrac{4}{15} = \dfrac{24}{?}\)
Exercise \(\PageIndex{67}\)
\(\dfrac{14}{15} = \dfrac{?}{45}\)
- Answer
-
42
Exercise \(\PageIndex{68}\)
\(\dfrac{0}{5} = \dfrac{?}{20}\)
Exercise \(\PageIndex{69}\)
\(\dfrac{12}{21} = \dfrac{96}{?}\)
- Answer
-
168
Exercise \(\PageIndex{70}\)
\(\dfrac{14}{23} = \dfrac{?}{253}\)
Exercise \(\PageIndex{71}\)
\(\dfrac{15}{16} = \dfrac{180}{?}\)
- Answer
-
192
Exercise \(\PageIndex{72}\)
\(\dfrac{21}{22} = \dfrac{336}{?}\)
Multiplication and Division of Fractions ([link], [link])
For problems 73-95, perform each multiplication and division.
Exercise \(\PageIndex{73}\)
\(\dfrac{4}{5} \cdot \dfrac{15}{16}\)
- Answer
-
\(\dfrac{3}{4}\)
Exercise \(\PageIndex{74}\)
\(\dfrac{8}{9} \cdot \dfrac{3}{24}\)
Exercise \(\PageIndex{75}\)
\(\dfrac{1}{10} \cdot \dfrac{5}{12}\)
- Answer
-
\(\dfrac{1}{24}\)
Exercise \(\PageIndex{76}\)
\(\dfrac{14}{15} \cdot \dfrac{7}{5}\)
Exercise \(\PageIndex{77}\)
\(\dfrac{5}{6} \cdot \dfrac{13}{22} \cdot \dfrac{11}{39}\)
- Answer
-
\(\dfrac{5}{36}\)
Exercise \(\PageIndex{78}\)
\(\dfrac{2}{3} \div \dfrac{15}{7} \cdot \dfrac{5}{6}\)
Exercise \(\PageIndex{79}\)
\(3 \dfrac{1}{2} \div \dfrac{7}{2}\)
- Answer
-
1
Exercise \(\PageIndex{80}\)
\(2 \dfrac{4}{9} \div \dfrac{11}{45}\)
Exercise \(\PageIndex{81}\)
\(\dfrac{8}{15} \cdot \dfrac{3}{16} \cdot \dfrac{5}{24}\)
- Answer
-
\(\dfrac{1}{48}\)
Exercise \(\PageIndex{82}\)
\(\dfrac{8}{15} \div 3 \dfrac{3}{5} \cdot \dfrac{9}{16}\)
Exercise \(\PageIndex{83}\)
\(\dfrac{14}{15} \div 3 \dfrac{8}{9} \cdot \dfrac{10}{21}\)
- Answer
-
\(\dfrac{4}{35}\)
Exercise \(\PageIndex{84}\)
\(18 \cdot 5 \dfrac{3}{4}\)
Exercise \(\PageIndex{85}\)
\(3 \dfrac{3}{7} \cdot 2 \dfrac{1}{12}\)
- Answer
-
\(\dfrac{50}{7} = 7 \dfrac{1}{7}\)
Exercise \(\PageIndex{86}\)
\(4 \dfrac{1}{2} \div 2 \dfrac{4}{7}\)
Exercise \(\PageIndex{87}\)
\(6 \dfrac{1}{2} \div 3 \dfrac{1}{4}\)
- Answer
-
2
Exercise \(\PageIndex{88}\)
\(3 \dfrac{5}{16} \div 2 \dfrac{7}{18}\)
Exercise \(\PageIndex{89}\)
\(7 \div 2 \dfrac{1}{3}\)
- Answer
-
3
Exercise \(\PageIndex{90}\)
\(17 \div 4 \dfrac{1}{4}\)
Exercise \(\PageIndex{91}\)
\(\dfrac{5}{8} \div 1 \dfrac{1}{4}\)
- Answer
-
\(\dfrac{1}{2}\)
Exercise \(\PageIndex{92}\)
\(2 \dfrac{2}{3} \cdot 3 \dfrac{3}{4}\)
Exercise \(\PageIndex{93}\)
\(20 \cdot \dfrac{18}{4}\)
- Answer
-
90
Exercise \(\PageIndex{94}\)
\(0 \div 4 \dfrac{1}{8}\)
Exercise \(\PageIndex{95}\)
\(1 \div 6 \dfrac{1}{4} \cdot \dfrac{25}{4}\)
- Answer
-
1
Applications Involving Fractions
Exercise \(\PageIndex{96}\)
Find \(\dfrac{8}{9}\) of \(\dfrac{27}{2}\)
Exercise \(\PageIndex{97}\)
What part of \(\dfrac{3}{8}\) is \(\dfrac{21}{16}\)?
- Answer
-
\(\dfrac{7}{2}\) or \(3 \dfrac{1}{2}\)
Exercise \(\PageIndex{98}\)
What part of \(3 \dfrac{1}{5}\) is \(1 \dfrac{7}{25}\)?
Exercise \(\PageIndex{99}\)
Find \(6 \dfrac{2}{3}\) of \(\dfrac{9}{15}\).
- Answer
-
4
Exercise \(\PageIndex{100}\)
\(\dfrac{7}{20}\) of what number is \(\dfrac{14}{35}\)?
Exercise \(\PageIndex{101}\)
What part of \(4 \dfrac{1}{16}\) is \(3 \dfrac{3}{4}\)?
- Answer
-
\(\dfrac{12}{13}\)
Exercise \(\PageIndex{102}\)
Find \(8 \dfrac{3}{10}\) of \(16 \dfrac{2}{3}\)
Exercise \(\PageIndex{103}\)
\(\dfrac{3}{20}\) of what number is \(\dfrac{18}{30}\)?
- Answer
-
4
Exercise \(\PageIndex{104}\)
Find \(\dfrac{1}{3}\) of 0.
Exercise \(\PageIndex{105}\)
Find \(\dfrac{11}{12}\) of 1.
- Answer
-
\(\dfrac{11}{12}\)