# Word Problems on Fraction

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

### I. Word Problems on Addition of Fractions:

1. Nairitee took $$\frac{7}{8}$$ hour to paint a table and $$\frac{2}{3}$$ hour to paint a chair. How much time did he take in painting both items?

Solution:

Total time taken in painting both items = $$\frac{7}{8}$$ h + $$\frac{2}{3}$$ h
= ($$\frac{7}{8}$$ + $$\frac{2}{3}$$) h

= ($$\frac{21 + 16}{24}$$) h

= $$\frac{37}{24}$$ h

= 1$$\frac{13}{24}$$ h

Therefore, Nairitee took 1$$\frac{13}{24}$$ hours in painting both items.

2. Nitheeya and Nairitee $$\frac{3}{10}$$ and $$\frac{1}{6}$$ of a cake respectively. What portion of the cake did they eat together?

Solution:

The portion of cake ate by Nitheeya = $$\frac{3}{10}$$

The portion of cake ate by Nitheeya = $$\frac{1}{6}$$

The portion they ate together = $$\frac{3}{10}$$ + $$\frac{1}{6}$$

= $$\frac{9}{30}$$ + $$\frac{5}{30}$$; [Since, LCM of 10 and 6 = 30]

= $$\frac{9 + 5}{30}$$

= $$\frac{14}{30}$$

= $$\frac{7}{15}$$

Therefore, together Nitheeya and Nairitee ate $$\frac{7}{15}$$ of the cake.

3. Rachel took $$\frac{1}{2}$$ hour to paint a table and $$\frac{1}{3}$$ hour to paint a chair. How much time did she take in all?

Solution:

 Time taken to paint a table = $$\frac{1}{2}$$ hourTime taken to paint a chair = $$\frac{1}{3}$$ hourTotal time taken                = $$\frac{1}{2}$$ hour + $$\frac{1}{3}$$ hour                                       = $$\frac{5}{6}$$ hour $$\frac{1}{2}$$ + $$\frac{1}{3}$$L.C.M. of 2, 3 is 6.= $$\frac{3}{6}$$ + $$\frac{2}{6}$$$$\frac{1 × 3}{2 × 3}$$ = $$\frac{3}{6}$$ $$\frac{1 × 2}{3 × 2}$$ = $$\frac{2}{6}$$

### II. Word Problems on Subtraction of Fractions:

1. Out of $$\frac{12}{17}$$ m of cloth given to a tailor, $$\frac{1}{5}$$ m were used. Find the length of cloth unused.

Solution:

Length of the cloth given to the tailors = $$\frac{12}{17}$$ m

Length of cloth used = $$\frac{1}{5}$$ m

Length of the unused cloth = $$\frac{12}{17}$$ m - $$\frac{1}{5}$$ m

= ($$\frac{12}{17}$$ - $$\frac{1}{5}$$) m

= ($$\frac{12 × 5}{17 × 5}$$ - $$\frac{1 × 17}{5 × 17}$$) m; [Since, LCM of 17 and 5 = 85]

= ($$\frac{60}{85}$$ - $$\frac{17}{85}$$) m

= ($$\frac{60 - 17}{85}$$ m

= ($$\frac{43}{85}$$ m

2. Nairitee has $6$$\frac{4}{7}$$. She gives$4$$\frac{2}{3}$$ to her mother. How much money does she have now?

Solution:

Money with Nairitee = $6$$\frac{4}{7}$$ Money given to her mother =$4$$\frac{2}{3}$$

Money left with Nairitee = $6$$\frac{4}{7}$$ -$4$$\frac{2}{3}$$

= $(6$$\frac{4}{7}$$ - 4$$\frac{2}{3}$$) =$($$\frac{46}{7}$$ - $$\frac{14}{3}$$)

= $($$\frac{46 × 3}{7 × 3}$$ - $$\frac{14 × 7}{3 × 7}$$)[Since, LCM of 7 and 3 = 21] =$($$\frac{138}{21}$$ - $$\frac{98}{21}$$)

= $$$\frac{40}{21}$$ =$1$$\frac{19}{21}$$

Therefore, Nairitee has \$1$$\frac{19}{21}$$.

3. If 3$$\frac{1}{2}$$ m of wire is cut from a piece of 10 m long wire, how much of wire is left?

Total length of the wire = 10 m

Fraction of the wire cut out = 3$$\frac{1}{2}$$ m = $$\frac{7}{2}$$ m

Length of the wire left = 10 m – 3$$\frac{1}{2}$$ m

= [$$\frac{10}{1}$$ - $$\frac{7}{2}$$] m,    [L.C.M. of 1, 2 is 2]

= [$$\frac{20}{2}$$ - $$\frac{7}{2}$$] m,    [$$\frac{10}{1}$$ × $$\frac{2}{2}$$]

= [$$\frac{20 - 7}{2}$$] m

= $$\frac{13}{2}$$ m

= 6$$\frac{1}{2}$$ m

### III. Word Problems on Multiplication of Fractions:

1. $$\frac{4}{7}$$ of a number is 84. Find the number.

Solution:

According to the problem,

$$\frac{4}{7}$$ of a number = 84

Number = 84 × $$\frac{7}{4}$$

[Here we need to multiply 84 by the reciprocal of $$\frac{4}{7}$$]

= 21 × 7

= 147

Therefore, the number is 147.

2. One half of the students in a school are girls, $$\frac{3}{5}$$ of these girls are studying in lower classes. What fraction of girls are studying in lower classes?

Solution:

Fraction of girls studying in school = $$\frac{1}{2}$$

Fraction of girls studying in lower classes = $$\frac{3}{5}$$ of $$\frac{1}{2}$$

= $$\frac{3}{5}$$ × $$\frac{1}{2}$$

= $$\frac{3 × 1}{5 × 2}$$

= $$\frac{3}{10}$$

Therefore, $$\frac{3}{10}$$ of girls studying in lower classes.

3. Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson?

Solution:

Maddy reads = $$\frac{3}{5}$$ of 75

= $$\frac{3}{5}$$ × 75

= 45 pages.

= 30 pages.

### IV. Word Problems on Division of Fractions:

1. A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd?

Solution:

A herd of cows gives 4 litres of milk each day.

Each cow gives one-third of total milk each day = $$\frac{1}{3}$$ of 4

Therefore, each cow gives $$\frac{4}{3}$$ of milk each day.

Total no. of cows = 4 ÷ $$\frac{4}{3}$$

= 4 × $$\frac{3}{4}$$

= 3

Therefore there are 3 cows in the herd.

Worksheet on Word problems on Fractions:

1. Shelly walked $$\frac{1}{3}$$ km. Kelly walked $$\frac{4}{15}$$ km. Who walked farther? How much farther did one walk than the other?

2. A frog took three jumps. The first jump was $$\frac{2}{3}$$ m long, the second was $$\frac{5}{6}$$ m long and the third was $$\frac{1}{3}$$ m long. How far did the frog jump in all?

3. A vessel contains 1$$\frac{1}{2}$$ l of milk. John drinks $$\frac{1}{4}$$ l of milk; Joe drinks $$\frac{1}{2}$$ l of milk. How much of milk is left in the vessel?

4. Between 4$$\frac{2}{3}$$and 3$$\frac{2}{3}$$ which is greater and by how much?

5. What must be subtracted from 5$$\frac{1}{6}$$ to get 2$$\frac{1}{8}$$?

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