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Fractions on the number line
Halves on the number line: divide the units into two equal parts and write the appropriate fractions to the corresponding points.
\latex{ 0 }
\latex{ 0 }
\latex{ \frac{1}{2} }
\latex{ \frac{2}{2} }
\latex{ \frac{3}{2} }
\latex{ \frac{4}{2} }
\latex{ 1 }
\latex{ 2 }
Thirds on the number line: divide the units into three equal parts and write the appropriate fractions to the corresponding points.
\latex{ 0 }
\latex{ 0 }
\latex{ \frac{1}{3} }
\latex{ \frac{3}{3} }
\latex{ \frac{4}{3} }
\latex{ \frac{5}{3} }
\latex{ 1 }
\latex{ 2 }
\latex{ \frac{2}{3} }
\latex{ \frac{6}{3} }
Quarters on the number line: divide the units into four equal parts and write the appropriate fractions to the corresponding points.
\latex{ 0 }
\latex{ 0 }
\latex{ \frac{1}{4} }
\latex{ \frac{3}{4} }
\latex{ \frac{5}{4} }
\latex{ \frac{7}{4} }
\latex{ 1 }
\latex{ 2 }
\latex{ \frac{2}{4} }
\latex{ \frac{8}{4} }
\latex{ \frac{4}{4} }
\latex{ \frac{6}{4} }
Fractions with large denominators can be represented similarly on a number line.
Example 1
Show the fractions \latex{\frac{2}{3}} and \latex{\frac{3}{4}} on a number line.
Solution
\latex{ 12 } is a multiple of both \latex{ 3 } and \latex{ 4 }; therefore, expand both fractions so that their denominators become \latex{ 12 }.
\latex{\frac{2}{3}=\frac{8}{12}; \;\;\;\frac{3}{4}=\frac{9}{12}}
Fractions with common denominators.
Divide the distance between \latex{ 0 } and \latex{ 1 } into \latex{ 12 } equal parts, then mark the position of the numbers.
\latex{ 0 }
\latex{ \frac{1}{12} }
\latex{ \frac{2}{12} }
\latex{ \frac{3}{12} }
\latex{ \frac{4}{12} }
\latex{ \frac{5}{12} }
\latex{ \frac{6}{12} }
\latex{ \frac{7}{12} }
\latex{ \frac{8}{12} }
\latex{ \frac{9}{12} }
\latex{ \frac{10}{12} }
\latex{ \frac{11}{12} }
\latex{ \frac{12}{12} }
\latex{ \frac{3}{4} }
\latex{ \frac{2}{3} }
The number line shows you that \latex{\frac{2}{3}\lt \frac{3}{4}.}
Fractions can be compared using number lines.
Exercises
{{exercise_number}}. Mark the numbers on a number line.
a) \latex{\frac{2}{5};\frac{10}{5};\frac{5}{5};\frac{1}{5};\frac{7}{5};\frac{3}{5}}
b) \latex{\frac{1}{6};\frac{7}{6};\frac{5}{6};\frac{6}{6};\frac{11}{6};\frac{12}{6}}
c) \latex{\frac{3}{10};\frac{9}{10};\frac{4}{10};\frac{17}{10};\frac{13}{10};\frac{10}{10}}
{{exercise_number}}. Which numbers do the animals represent?
\latex{ 0 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 1 }
\latex{ 2 }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ G }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
{{exercise_number}}. Show both fractions on the same number line.
a) \latex{\frac{1}{2};\frac{3}{2}}
b) \latex{\frac{1}{2};\frac{3}{5}}
c) \latex{\frac{1}{4};\frac{5}{8}}
d) \latex{\frac{3}{4};\frac{4}{3}}
{{exercise_number}}. Show the position of the fractions on a number line. Draw a separate number line for each exercise.
a) \latex{\frac{7}{6};\frac{3}{2};\frac{2}{3}}
b) \latex{\frac{1}{2};\frac{1}{4};\frac{5}{8};\frac{3}{4}}
c) \latex{\frac{2}{5};\frac{7}{10};\frac{1}{2};\frac{6}{5}}
{{exercise_number}}. Which letters mark the position of \latex{ 0 } and \latex{ 1 } on the number lines?
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ G }
\latex{ H }
\latex{ I }
\latex{ J }
\latex{ K }
\latex{ L }
\latex{ M }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ G }
\latex{ H }
\latex{ I }
\latex{ J }
\latex{ K }
\latex{ L }
\latex{ M }
\latex{ \frac{2}{3} }
\latex{ \frac{4}{3} }
\latex{ \frac{3}{4} }
\latex{ \frac{6}{4} }
\latex{ \frac{2}{5} }
\latex{ \frac{7}{5} }
\latex{ \frac{1}{2} }
\latex{ \frac{5}{6} }
Quiz
The orange part of the parking meter shows the time remaining.
How many \latex{minutes} are left?
How many \latex{minutes} are left?
\latex{ 0 }
\latex{ 30 } \latex{ min }
