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Comparing fractions with a whole, mixed numbers

\latex{\frac{8}{8} =1}

\latex{\frac{10}{10} =1}

\latex{\frac{12}{12} =1}

A fraction is equal to \latex{1} if the numerator equals the denominator.

\latex{\frac{3}{8}\lt1}

\latex{\frac{7}{10} \lt1}

\latex{\frac{5}{12} \lt1}

A positive fraction is less than \latex{1} if the numerator is less than the denominator.

\latex{\frac{13}{8}\gt1}

\latex{\frac{19}{12} \gt1}

A positive fraction is greater than one if the numerator is greater than the denominator.

Mixed numbers

A fraction greater than one can be written as a mixed number.

\latex{\frac{13}{8}=\frac{8}{8}+\frac{5}{8}=1+\frac{5}{8}=1\frac{5}{8}}

\latex{\frac{19}{12}=\frac{12}{12}+\frac{7}{12}=1+\frac{7}{12}=1\frac{7}{12}}

Exercises

{{exercise_number}}. Which of the following fractions are

a) less than \latex{ 1 };

b) greater than \latex{ 1 };

c) equal to \latex{ 1 }?

\latex{\frac{2}{7}}

\latex{\frac{5}{5}}

\latex{\frac{5}{9}}

\latex{\frac{10}{3}}

\latex{\frac{28}{33}}

\latex{\frac{12}{11}}

\latex{\frac{17}{17}}

\latex{\frac{13}{4}}

\latex{\frac{42}{31}}

\latex{\frac{9}{14}}

\latex{\frac{7}{8}}

\latex{\frac{6}{11}}

{{exercise_number}}. Write the fractions in the correct sets. (→)

no less than \latex{ 1 }

no greater than \latex{ 1 }

{{exercise_number}}. Write fractions where the

a) numerator is smaller than the denominator by \latex{ 1 };
b) numerator is larger than the denominator by \latex{ 2 };
c) sum of the numerator and denominator is \latex{ 10 }.
b) Which fractions in exercises a), b), and c) are greater than \latex{ 1 }, less than \latex{ 1 } and equal to \latex{ 1 }?

{{exercise_number}}. Write fractions a) greater than \latex{ 1 }, b) less than \latex{ 1 }, whose numerator is a natural number smaller than \latex{ 5 }, and whose denominator cannot be greater than \latex{ 7 }. How many such fractions are there?

{{exercise_number}}.

a) Write positive fractions less than \latex{ 1 }, whose numerator is a natural number greater than \latex{ 6 }, and whose denominator cannot exceed \latex{ 10 }. How many such fractions are there?
b) Write fractions greater than \latex{ 1 }, whose numerator cannot exceed \latex{ 8 } and whose denominator is at least \latex{ 4 }. How many such fractions are there?

{{exercise_number}}. There are two sets: \latex{ A } = {\latex{ 1 }; \latex{ 3 }; \latex{ 5 }} and \latex{ B} = {\latex{ 2 }; \latex{ 3 }; \latex{ 4 }; \latex{ 5 }}. Make fractions using numbers from \latex{ A } for the numerator and numbers from \latex{ B } for the denominator. How many can you make?

Choose the ones that are

a) less than \latex{ 1 };

b) equal to \latex{ 1 };

c) greater than \latex{ 1 }.

{{exercise_number}}. List fractions where the \latex{\triangle} is the numerator and the \latex{\square} is the denominator according to the following rules:

a) greater than \latex{ 1 } and \latex{ 3 } \latex{\leq \triangle \leq} \latex{ 8 } and \latex{ 4 } \latex{\leq \square \leq} \latex{ 10 };

b) smaller than \latex{ 1 } and \latex{ 5 } \latex{\leq \triangle \leq} \latex{ 13 } and \latex{ 3 } \latex{\leq \square \leq} \latex{ 9 };

c) equal to \latex{ 1 } and \latex{ 7 } \latex{\leq \triangle \lt} \latex{ 14 } and \latex{ 9 } \latex{\lt \square \lt} \latex{ 17 }.

{{exercise_number}}. Convert the following fractions to mixed numbers.

a) \latex{\frac{7}{3}}

b) \latex{\frac{19}{15}}

c) \latex{\frac{17}{5}}

d) \latex{\frac{19}{7}}

e) \latex{\frac{11}{4}}

f) \latex{\frac{24}{9}}

g) \latex{\frac{23}{6}}

{{exercise_number}}. Convert the following mixed numbers to improper fractions.

a) \latex{1\frac{2}{3}}

b) \latex{5\frac{1}{2}}

c) \latex{2\frac{1}{4}}

d) \latex{1\frac{3}{7}}

e) \latex{3\frac{4}{5}}

f) \latex{7\frac{1}{2}}

g) \latex{5\frac{2}{3}}

Quiz

Piglet, Winnie the Pooh and Eeyore are playing with a ball. Everybody throws the ball the same number of times. In what proportion of all the throws does Piglet throw the ball to Winnie the Pooh?

Mathematics 5.

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