Fraction Worksheet | Superprof

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Emma

November 14, 2020

Chapters

Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
Solution of exercise 4
Solution of exercise 5
Solution of exercise 6
Solution of exercise 7
Solution of exercise 8
Solution of exercise 9
Solution of exercise 10
Solution of exercise 11
Solution of exercise 12

Exercise 1

Associate the following fractions with the corresponding amount of minutes in an hour:

$\frac{1}{2}$ , $\frac{1}{4}$ , $\frac{3}{4}$ , $\frac{1}{10}$ , $\frac{1}{12}$ , $\frac{1}{3}$

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Exercise 2

Find the pairs of equivalent fractions and place them in pairs:

$\frac{4}{3}$ , $\frac{5}{7}$ , $\frac{8}{3}$ , $\frac{2}{11}$ , $\frac{6}{9}$

$\frac{16}{6}$ , $\frac{15}{21}$ , $\frac{4}{22}$ , $\frac{2}{3}$ , $\frac{12}{9}$

Exercise 3

Write the reciprocals of the following fractions:

$\frac{2}{3}$ , $\frac{5}{2}$ , $-\frac{3}{7}$ , 5, $\frac{4}{11}$ , $\frac{1}{8}$

Exercise 4

Write the sign > or <, to create a correct statement.

$\frac{3}{7} \square \frac{3}{9}$ , $\frac{2}{5} \square \frac{6}{5}$ , $\frac{3}{9} \square \frac{3}{4}$ , $\frac{2}{7} \square \frac{5}{7}$

Exercise 5

Write the sign > or <, to create a correct statement.

$\frac{2}{3} \square \frac{3}{5}$ , $\frac{2}{5} \square \frac{3}{7}$ , $\frac{5}{7} \square \frac{6}{8}$ , $\frac{4}{3} \square \frac{5}{4}$

Exercise 6

Order the following fractions from smallest to largest:

$\frac{5}{12}$ , $\frac{2}{15}$ , $\frac{5}{4}$ , $\frac{7}{5}$

Exercise 7

Classify the following fractions as either proper or improper fraction:

$\frac{2}{3}$ , $\frac{5}{6}$ , $\frac{8}{5}$ , $\frac{7}{9}$ , $\frac{5}{2}$ , $\frac{5}{12}$ , $\frac{3}{4}$ , $\frac{7}{5}$

Exercise 8

Solve:

$5\frac{1}{4} + 1 \frac{1}{6}$

Exercise 9

Solve using two different methods:

$\frac{1}{2} \cdot (\frac{3}{4} + \frac{1}{8})$

Exercise 10

Solve:
1. $(3 + \frac{1}{4}) - (2 + \frac{1}{6})$

2. $\frac{1}{2}: (\frac{1}{4} + \frac{1}{3})$

3. $(\frac{5}{3} - 1) \cdot (\frac{7}{2} - 2)$

4. $(\frac{3}{4} + \frac{1}{2}) : (\frac{5}{3} + \frac{1}{6})$

Exercise 11

Solve:

$\frac{2}{3} : [5 : (\frac{2}{4} + 1) - 3 (\frac{1}{2} - \frac{1}{4})]$

Exercise 12

Perform the divisions:

$1 : \frac{2}{3}$

$3 : \frac {1}{2}$

$\frac{3}{5} : \frac{1}{2}$

Solution of exercise 1

Associate the following fractions with the corresponding amount of minutes in an hour:

$\frac{1}{2}\cdot 60 = 30$ minutes

$\frac{1}{4}\cdot 60 = 15$ minutes

$\frac{3}{4}\cdot 60 = 45$ minutes

$\frac{1}{10}\cdot 60 = 6$ minutes

$\frac{1}{12}\cdot 60 = 5$ minutes

$\frac{1}{3}\cdot 60 = 20$ minutes

Solution of exercise 2

Find the pairs of equivalent fractions and place them in pairs:

$\frac{4}{3}$ , $\frac{5}{7}$ , $\frac{8}{3}$ , $\frac{2}{11}$ , $\frac{6}{9}$

$\frac{16}{6}$ , $\frac{15}{21}$ , $\frac{4}{22}$ , $\frac{2}{3}$ , $\frac{12}{9}$

$\frac{2}{3} = \frac{12}{9}$ $4 \cdot 9 = 3 \cdot 12$ $36 = 36$

$\frac{5}{7} = \frac{15}{21}$ $5 \cdot 21 = 7 \cdot 15$ $105 = 105$

$\frac{8}{3} = \frac{16}{6}$ $8 \cdot 6 = 3 \cdot 16$ $48 = 48$

$\frac{2}{11} = \frac{4}{22}$ $2 \cdot 22 = 4 \cdot 11$ $44 = 44$

$\frac{6}{9} = \frac{2}{3}$ $6 \cdot 3 = 9 \cdot 2$ $18 = 18$

Solution of exercise 3

Write the reciprocals of the following fractions:

$\frac{2}{3}$ , $\frac{5}{2}$ , $-\frac{3}{7}$ , 5, $\frac{4}{11}$ , $\frac{1}{8}$

$\frac{3}{2}$ , $\frac{2}{5}$ , $-\frac{7}{3}$ , $\frac{1}{5}$ , $\frac{11}{4}$ , 8

Solution of exercise 4

Write the sign > or <, to create a correct statement.

$\frac{3}{7} \square \frac{3}{9}$ , $\frac{2}{5} \square \frac{6}{5}$ , $\frac{3}{9} \square \frac{3}{4}$ , $\frac{2}{7} \square \frac{5}{7}$

$\frac{3}{7} > \frac{3}{9}$ , $\frac{2}{5} < \frac{6}{5}$ , $\frac{3}{9} < \frac{3}{4}$ , $\frac{2}{7} <\frac{5}{7}$

Solution of exercise 5

Write the sign > or <, to create a correct statement.

$\frac{2}{3} \square \frac{3}{5}$ , $\frac{2}{5} \square \frac{3}{7}$ , $\frac{5}{7} \square \frac{6}{8}$ , $\frac{4}{3} \square \frac{5}{4}$

$\frac{2}{3}> \frac{3}{5}$ , $\frac{2}{5}< \frac{3}{7}$ , $\frac{5}{7} <\frac{6}{8}$ , $\frac{4}{3} >\frac{5}{4}$

Solution of exercise 6

Order the following fractions from smallest to largest:

$\frac{5}{12}$ , $\frac{2}{15}$ , $\frac{5}{4}$ , $\frac{7}{5}$

We will make the denominators same by multiplying every fraction by a constant.

$\frac{25}{60}$ , $\frac{8}{60}$ , $\frac{75}{60}$ , $\frac{84}{60}$

$\frac{2}{12} < \frac{5}{12} < \frac{5}{4} < \frac{7}{5}$

Solution of exercise 7

Classify the following fractions as either proper or improper:

$\frac{2}{3}$ , $\frac{5}{6}$ , $\frac{8}{5}$ , $\frac{7}{9}$ , $\frac{5}{2}$ , $\frac{5}{12}$ , $\frac{3}{4}$ , $\frac{7}{5}$

Proper: $\frac{2}{3}$ , $\frac{5}{6}$ , $\frac{7}{9}$ , $\frac{5}{12}$ , $\frac{3}{4}$

Improper: $\frac{8}{5}$ , $\frac{5}{2}$ , $\frac{7}{5}$

Solution of exercise 8

Solve:

$5 \frac{1}{4} + 1 \frac{1}{6}$

$= \frac{5 \cdot 4 + 1}{4} + \frac{1 \cdot 6 + 1}{6} = \frac{21}{4} + \frac{7}{6} = \frac{63 + 14}{12} = \frac{77}{12}$

Solution of exercise 9

Solve using two different methods:

$\frac{1}{2} \cdot (\frac{3}{4} + \frac{1}{8})$

$= \frac{1}{2} \cdot (\frac{3}{4} + \frac{1}{8}) = \frac{1}{2} \cdot (\frac{6 + 1} {8}) = \frac{1}{2} \cdot \frac{7}{8} = \frac{7}{16}$

Solution of exercise 10

Solve:

$(3 + \frac{1}{4}) - (2 + \frac{1}{6}) = 3 + \frac{1}{4} - 2 - \frac{1}{6} = 1 + \frac{1}{4} - \frac{1}{6} = \frac{12 + 3 - 2}{12} = \frac{13}{12}$

$= \frac{1}{2}: (\frac{1}{4} + \frac{1}{3})$

$\frac{1}{2} : (\frac{1}{4} + \frac{1}{3}) = \frac{1}{2} : (\frac{3 + 4}{12}) = \frac{1}{2} : \frac{7}{12} = \frac{12}{14} = \frac{6}{7}$

$(\frac{5}{3} - 1) \cdot (\frac{7}{2} - 2) = (\frac{5 - 3}{2}) \cdot (\frac{7 - 4}{2}) = \frac{2}{3} \cdot \frac{3}{2} = \frac{6}{6} = 1$

$=(\frac{3}{4} + \frac{1}{2}) : (\frac{5}{3} + \frac{1}{6})$

$=(\frac{3}{4} + \frac{1}{2}) : (\frac{5}{3} + \frac{1}{6}) = (\frac{3 + 2}{4}) : (\frac{10 + 1}{6}) = \frac{5}{4} : \frac{11}{6} = \frac{30}{44} = \frac{15}{22}$

Solution of exercise 11

Solve:

$\frac{2}{3} : [ 5 : (\frac{2}{4} + 1) - 3 (\frac{1}{2} - \frac{1}{4})]$

$= \frac{2}{3}: [ 5 : (\frac{2 + 4} {4}) - 3 ( \frac{2 - 1}{4})]$

$= \frac{2}{3} : (5 : \frac{6}{4} - 3 \cdot \frac{1}{4})$

$= \frac{2}{3} : (\frac{10}{3} - \frac{3}{4})$

$\frac{2}{3} : (\frac{40 - 19}{12}) = \frac{2}{3} : \frac{31}{12} = \frac{24}{93} = \frac{8}{31}$

Solution of exercise 12

Perform the divisions:

1 $\frac{1}{2} : 3 = \frac{1}{6}$

2 $3 : \frac{1}{2} = 6$

3 $\frac{3}{5} : \frac{1}{2} = \frac{6}{5}$

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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