Worksheet on Fractions

In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced by the students to get more ideas on fractions.

1. Answer the following questions for each given shape:

(a)

(b)

(c)

(d)

(e)

(i) How many equals are there in each shape?

(ii) Express each equal part as a fraction.

(iii) Express the shaded part as a fraction.

(iv) Express each unshaded part as a fraction.

2. Write the fraction for the objects in the shaded part of the closed figure as a part of the whole collection.

3. Write the following fractions in words:

(i) \(\frac{5}{9}\) (five-ninth, five upon nine)

(ii) \(\frac{3}{7}\)

(iii) \(\frac{2}{11}\)

(iv) \(\frac{4}{7}\)

(v) \(\frac{7}{14}\)

(vi) \(\frac{9}{13}\)

(vii) \(\frac{3}{10}\)



4. Fill in the blanks:

(i) For two parts out of seven we say ‘two-seventh’ and write \(\frac{2}{7}\).

(ii) For ‘four parts out of five’ we say ……………… and write ……………….. .

(iii) For ‘nine parts out of seventeen’ we say …………… and write ………….. .

(iv) For ‘three parts out of six’ we say ……………… and write ……………… .

5. Write the fraction representing the coloured parts.

6. Write each of the following as a division.

(i) \(\frac{3}{7}\)

(ii) \(\frac{5}{19}\)

(iii) \(\frac{8}{19}\)

(iv) \(\frac{23}{29}\)

7. Write each of the following as a fraction.

(1) 1 ÷ 9

(ii) 2 ÷ 25

(iii) 3 ÷ 74

(iv) 3 ÷ 91

8. Find \(\frac{3}{9}\) of

(i) 54 m

(ii) 27 kg

(iii) 189 cm

(iv) 72 ml

9. Represent each of the following fractions on the number line.

(i) \(\frac{3}{4}\)

(ii) \(\frac{2}{3}\)

(iii) \(\frac{3}{7}\)

(iv) \(\frac{2}{5}\)

10. Nairitee has 45 pencils. She uses \(\frac{2}{9}\) of them. How many pencils does she have now?

11. What fraction of an ordinary year is 220 days?

12. Look at the number line given in Fig. and answer the following questions:

(i) What fraction does the point A represent?

(ii) What fraction does the point C represent?

(iii) What fraction does the point D represent?

13. Draw pictures to show the following:

(i) five-eighth of a collection

(ii) five-twelfth of a collection

(iii) four-ninth of a rectangular shape

(iv) three-fourth of a square

14. Change into an equivalent fraction with denominator 32.

(i) \(\frac{3}{4}\)

(ii) \(\frac{5}{8}\)

(iii) \(\frac{1}{2}\)

(iv) \(\frac{9}{16}\)

15. Fill in each box with >, < or = to make the statements true:

(i) \(\frac{3}{4}\) □ \(\frac{4}{3}\)

(ii) \(\frac{7}{8}\) □ \(\frac{4}{5}\)

(iii) \(\frac{5}{6}\) □ \(\frac{15}{18}\)

(iv) \(\frac{15}{13}\) □ \(\frac{15}{11}\)

(v) \(\frac{20}{32}\) □ \(\frac{1}{2}\)

(vi) \(\frac{7}{8}\) □ \(\frac{7}{10}\)

16. Reduce the following fractions into their lowest terms:

(i) \(\frac{12}{18}\) 

(ii) \(\frac{24}{36}\)

(iii) \(\frac{62}{96}\)

(iv) \(\frac{40}{120}\)

(v) \(\frac{40}{56}\)

17. Add the following fractions:

(i) \(\frac{2}{4}\) + \(\frac{1}{4}\)

(ii) \(\frac{7}{10}\) + \(\frac{3}{10}\)

(iii) \(\frac{1}{4}\) + \(\frac{1}{4}\)

(iv) \(\frac{3}{14}\) + \(\frac{1}{14}\) + \(\frac{4}{14}\)

(v) \(\frac{3}{18}\) + \(\frac{1}{18}\) + \(\frac{7}{18}\)

(vi) \(\frac{6}{30}\) + \(\frac{4}{30}\)

(vii) \(\frac{4}{14}\) + \(\frac{8}{14}\) + \(\frac{2}{14}\)

(viii) \(\frac{8}{15}\) + \(\frac{1}{15}\) + \(\frac{3}{15}\)

18. Subtract the following fractions.

(i) \(\frac{9}{14}\) - \(\frac{4}{14}\)

(ii) \(\frac{5}{30}\) - \(\frac{4}{30}\)

(iii) \(\frac{7}{12}\) - \(\frac{2}{12}\)

(iv) \(\frac{8}{34}\) - \(\frac{5}{34}\)

19. Which of the following are proper fractions?

(i) \(\frac{4}{3}\)

(ii) \(\frac{7}{11}\)

(iii) \(\frac{6}{19}\)

(iv) \(\frac{5}{11}\)

(v) \(\frac{15}{11}\)

(vi) \(\frac{14}{8}\)

(vii) \(\frac{12}{17}\)

(viii) \(\frac{23}{24}\)

(ix) \(\frac{9}{8}\)

(x) \(\frac{6}{2}\)

20. Classify the following fractions as proper or improper or mixed fractions:

(i) \(\frac{15}{10}\)

(ii) \(\frac{2}{9}\)

(iii) 2\(\frac{6}{7}\)

(iv) \(\frac{35}{51}\)

(ν) \(\frac{16}{29}\)

(vi) \(\frac{41}{11}\)

(vii) \(\frac{327}{128}\)

(viii) 4\(\frac{20}{72}\)

21. Which of the following are groups of like fractions?

(i) \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{8}{14}\), \(\frac{6}{18}\)

(ii) \(\frac{3}{11}\), \(\frac{2}{11}\), \(\frac{15}{11}\), \(\frac{22}{11}\)

(iii) \(\frac{18}{7}\), \(\frac{13}{7}\), \(\frac{1}{7}\), \(\frac{22}{7}\)

(iv) \(\frac{4}{2}\), \(\frac{10}{21}\), \(\frac{21}{10}\), \(\frac{7}{6}\)

22. Check whether the given fractions are equivalent or not.

(i) \(\frac{3}{5}\), \(\frac{9}{15}\)

(ii) \(\frac{4}{7}\), \(\frac{19}{23}\)

(iii) \(\frac{4}{9}\), \(\frac{41}{42}\)

(iv) \(\frac{7}{12}\), \(\frac{32}{45}\)

(v) \(\frac{3}{11}\), \(\frac{21}{77}\)

(vi) \(\frac{8}{15}\), \(\frac{30}{65}\)

23. Write 🔲 in each of the following by the correct number:

(i) \(\frac{4}{5}\) = \(\frac{8}{🔲}\)

(ii) \(\frac{5}{7}\) = \(\frac{20}{🔲}\)

(iii) \(\frac{1}{6}\) = \(\frac{🔲}{18}\)

(iv) \(\frac{5}{12}\) = \(\frac{15}{🔲}\)

(v) \(\frac{7}{13}\) = \(\frac{🔲}{39}\)

(vi) \(\frac{7}{15}\) = \(\frac{🔲}{60}\)

24. Find the equivalent fraction of:

(i) \(\frac{5}{7}\) having numerator 25

(ii) \(\frac{5}{6}\) having denominator 42

(iii) \(\frac{7}{9}\) having denominator 72

(iv) \(\frac{6}{18}\) having numerator 3

(v) \(\frac{20}{30}\) having numerator 12

(vi) \(\frac{30}{33}\) having denominator 11

25. Convert each of the following mixed fractions into an improper fraction.

(i) 2\(\frac{1}{3}\)

(ii) 4\(\frac{3}{7}\)

(iii) 8\(\frac{4}{17}\)

(iv) 9\(\frac{6}{20}\)

26. Convert each of the following improper fractions into a mixed fraction.

(i) \(\frac{13}{7}\)

(ii) \(\frac{28}{7}\)

(iii) \(\frac{105}{7}\)

(iv) \(\frac{347}{12}\)

Answer:

3. (ii) three-seventh, three upon seven

(iii) two-eleventh, two upon eleven

(iv) four-seventh, four upon seven

(v) seven-fourteenth, seven upon fourteen

(vi) nine-thirteenth, nine upon thirteen

(vii) three-tenth, three upon ten



4. (ii) four-fifth, \(\frac{4}{5}\)

(iii) nine-seventeenth, \(\frac{9}{17}\)

(iv) three-sixth, \(\frac{3}{6}\)

5. (i) \(\frac{1}{2}\)

(ii) \(\frac{5}{8}\)

(iii) \(\frac{3}{6}\)

(iv) \(\frac{2}{4}\)

(v) \(\frac{2}{6}\)

(vi) \(\frac{1}{4}\)

6. (i) 3 ÷ 7

(ii) 5 ÷ 19

(iii) 8 ÷ 19

(iv) 23 ÷ 29

7. (i) \(\frac{1}{9}\)

(ii) \(\frac{2}{25}\)

(iii) \(\frac{3}{74}\)

(iv) \(\frac{3}{91}\)

8. (i) 18 m

(ii) 9 kg

(iii) 63 cm

(iv) 24 ml

9. 

10. 35 pencils

11. \(\frac{220}{365}\)

12. (i) A represents as \(\frac{1}{12}\)

(ii) C represents as \(\frac{7}{12}\)

(iii) D represents as \(\frac{9}{12}\)

13. 

14. (i) \(\frac{24}{32}\)

(ii) \(\frac{20}{32}\)

(iii) \(\frac{16}{32}\)

(iv) \(\frac{18}{32}\)

15. (i) <

(ii) <

(iii) =

(iv) <

(v) <

(vi) >

16. (i) \(\frac{2}{3}\) 

(ii) \(\frac{2}{3}\)

(iii) \(\frac{31}{48}\)

(iv) \(\frac{1}{3}\)

(v) \(\frac{5}{7}\)

17. (i) \(\frac{3}{4}\)

(ii) \(\frac{10}{10}\) = 1

(iii) \(\frac{2}{4}\) = \(\frac{1}{2}\)

(iv) \(\frac{8}{14}\) = \(\frac{4}{7}\)

(v) \(\frac{11}{18}\)

(vi) \(\frac{10}{30}\) = \(\frac{1}{3}\)

(vii) \(\frac{14}{14}\) = 1

(viii) \(\frac{12}{15}\) = \(\frac{4}{5}\)

18. (i) \(\frac{5}{14}\)

(ii) \(\frac{1}{30}\) 

(iii) \(\frac{5}{12}\)

(iv) \(\frac{3}{34}\)

19. (ii), (iii), (iv), (vii), (viii) are proper fractions because numerators are less than the denominators. 

20. (i) improper fraction 

(ii) proper fraction

(iii) mixed fraction

(iv) proper fraction

(ν) proper fraction

(vi) improper fraction

(vii) improper fraction

(viii) mixed fraction

21. (ii) and (iii) are like fractions.

22. (i) equivalent fraction

(ii) not equivalent fraction

(iii) not equivalent fraction

(iv) not equivalent fraction

(v) equivalent fraction

(vi) not equivalent fraction

23. (i) 10

(ii) 28

(iii) 3

(iv) 36

(v) 21

(vi) 28

24. (i) \(\frac{25}{35}\)

(ii) \(\frac{35}{42}\)

(iii) \(\frac{56}{72}\)

(iv) \(\frac{3}{9}\)

(v) \(\frac{12}{18}\)

(vi) \(\frac{10}{11}\)

25. (i) \(\frac{7}{3}\)

(ii) \(\frac{31}{7}\)

(iii) \(\frac{140}{17}\)

(iv) \(\frac{186}{20}\)

26. (i) 1\(\frac{6}{7}\)

(ii) 4

(iii) 15

(iv) 28\(\frac{11}{12}\)

If students have any queries regarding the Worksheet on expanded form of a number questions please fill-up the comment box so that we can help you.

However, suggestions for further improvement, from all quarters would be greatly appreciated.

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