CBSE Class 7 Mathematics Fractions And Decimals Worksheet Set 06

Question. Convert 0.75 into a fraction.
Answer : 3/4

Question. Multiply : 14/25 x 35/68 x 34/49
Answer : 1/5

Question. Simplify : 3(3/7) ÷ 8/21  x 1/27
Answer : 1/3

Question. Add : 1/7+7/9
Answer : 58/63

Question. Find the sum of 7/8, 5/6, and 3/4
Answer : 59/24

Question. Meena spends 4/5 of her income on household expenses. Her monthly income is Rs. 15,000. How much does she save?
Answer : Rs. 3000

Question. Divide 5/9 by 2/3
Answer : 5/6

Question. Find the sum : 3(3/5) + 2(1/5) + 4(1/5)
Answer : 10

Question. Simplify : 8 – 4 (1/2) – 2(1/2)
Answer : 1

Question. By what number should 6(2/9) be multiplied to get 40?
Answer : 45/7

Question. Convert 17/20 into a decimal.
Answer : 0.85

Question. Subtract 6.732 from 7.
Answer : 0.268

Question. Simplify : 3(4/7) x 2(2/5) x 1(3/4)
Answer : 15

Question. By what number should 2(3/5) be multiplied to get 1(6/7)?
Answer : 5/7

Question. A carton contains 16 boxes of nails and each box weighs 4(3/4) kg. How much would a carton of nails weigh?
Answer : 76 kg

Question. Divide 45 by 1(4/5)
Answer : 25

Question. Monika purchased 14.5 litres of refined oil for Rs. 290. Find the cost of one litre oil.
Answer : Rs. 20

Question. Convert 25/8 into a decimal.
Answer : 3.125

Question. The product of two decimals is 42.9870. If one of them is 12.46, find the other.
Answer : 3.45

Question. Simplify : 5.43 × 15 5.
Answer : 16.29

Question. Simplify : 0.089 × 0.76 ÷ 0.19.
Answer : 0.356

Question. A film show lasted for 3 (2/3) hours. Out of this, 1(1/3) hours were spent on advertisements.
What was the actual duration of the film?
Answer : 2(1/3)hrs

Question. By what number should 6(2/9) be divided to obtain 4(2/3)?
Answer : 4/3

Question. How many buckets of equal capacity can be filled from 850 litres of water, if each bucket has capacity of 8.5 litres?
Answer : 100 buckets

Question. Find the place value of 2 in 48.032.
Answer : 2/1000

Question 1. Add
a) \( \frac{2}{5} + \frac{3}{15} + \frac{7}{10} \)
b) \( \frac{2}{5} + \frac{3}{4} \)
c) \( \frac{6}{7} + \frac{5}{6} \)
d) \( \frac{9}{16} + \frac{7}{12} + \frac{1}{4} \)
e) \( \frac{5}{6} + \frac{2}{7} + \frac{8}{9} + \frac{1}{3} \)
f) \( 1\frac{7}{8} + 1\frac{1}{2} + 1\frac{1}{3} \)
g) \( 2\frac{1}{5} + 3\frac{3}{4} + 4\frac{1}{2} \)
h) \( 3\frac{1}{8} + 5\frac{5}{12} + \frac{5}{16} \)
i) \( 3\frac{3}{4} + 4\frac{1}{2} \)
j) \( 3\frac{3}{4} + 2\frac{1}{6} + 1\frac{5}{8} \)
Answer:
a) First, simplify the middle fraction: \( \frac{3}{15} = \frac{1}{5} \).
Now add: \( \frac{2}{5} + \frac{1}{5} + \frac{7}{10} = \frac{3}{5} + \frac{7}{10} \).
The Least Common Multiple (LCM) of 5 and 10 is 10.
\( \frac{3 \times 2}{5 \times 2} + \frac{7}{10} = \frac{6}{10} + \frac{7}{10} = \frac{13}{10} = 1\frac{3}{10} \).

b) The LCM of 5 and 4 is 20.
\( \frac{2 \times 4}{5 \times 4} + \frac{3 \times 5}{4 \times 5} = \frac{8}{20} + \frac{15}{20} = \frac{23}{20} = 1\frac{3}{20} \).

c) The LCM of 7 and 6 is 42.
\( \frac{6 \times 6}{7 \times 6} + \frac{5 \times 7}{6 \times 7} = \frac{36}{42} + \frac{35}{42} = \frac{71}{42} = 1\frac{29}{42} \).

d) The LCM of 16, 12, and 4 is 48.
\( \frac{9 \times 3}{16 \times 3} + \frac{7 \times 4}{12 \times 4} + \frac{1 \times 12}{4 \times 12} = \frac{27}{48} + \frac{28}{48} + \frac{12}{48} = \frac{67}{48} = 1\frac{19}{48} \).

e) The LCM of 6, 7, 9, and 3 is 126.
\( \frac{5 \times 21}{6 \times 21} + \frac{2 \times 18}{7 \times 18} + \frac{8 \times 14}{9 \times 14} + \frac{1 \times 42}{3 \times 42} = \frac{105}{126} + \frac{36}{126} + \frac{112}{126} + \frac{42}{126} = \frac{295}{126} = 2\frac{43}{126} \).

f) Change the mixed numbers to improper fractions first:
\( \frac{15}{8} + \frac{3}{2} + \frac{4}{3} \).
The LCM of 8, 2, and 3 is 24.
\( \frac{15 \times 3}{8 \times 3} + \frac{3 \times 12}{2 \times 12} + \frac{4 \times 8}{3 \times 8} = \frac{45}{24} + \frac{36}{24} + \frac{32}{24} = \frac{113}{24} = 4\frac{17}{24} \).

g) Change the mixed numbers to improper fractions:
\( \frac{11}{5} + \frac{15}{4} + \frac{9}{2} \).
The LCM of 5, 4, and 2 is 20.
\( \frac{11 \times 4}{5 \times 4} + \frac{15 \times 5}{4 \times 5} + \frac{9 \times 10}{2 \times 10} = \frac{44}{20} + \frac{75}{20} + \frac{90}{20} = \frac{209}{20} = 10\frac{9}{20} \).

h) Change to improper fractions:
\( \frac{25}{8} + \frac{65}{12} + \frac{5}{16} \).
The LCM of 8, 12, and 16 is 48.
\( \frac{25 \times 6}{8 \times 6} + \frac{65 \times 4}{12 \times 4} + \frac{5 \times 3}{16 \times 3} = \frac{150}{48} + \frac{260}{48} + \frac{15}{48} = \frac{425}{48} = 8\frac{41}{48} \).

i) Change to improper fractions:
\( \frac{15}{4} + \frac{9}{2} \).
The LCM of 4 and 2 is 4.
\( \frac{15}{4} + \frac{9 \times 2}{2 \times 2} = \frac{15}{4} + \frac{18}{4} = \frac{33}{4} = 8\frac{1}{4} \).

j) Change to improper fractions:
\( \frac{15}{4} + \frac{13}{6} + \frac{13}{8} \).
The LCM of 4, 6, and 8 is 24.
\( \frac{15 \times 6}{4 \times 6} + \frac{13 \times 4}{6 \times 4} + \frac{13 \times 3}{8 \times 3} = \frac{90}{24} + \frac{52}{24} + \frac{39}{24} = \frac{181}{24} = 7\frac{13}{24} \).
In simple words: To add fractions, make their bottom numbers the same first. Then, add the top numbers together and write the final answer in its simplest form.

Exam Tip: Simplify individual fractions before starting to add, as this often makes finding the LCM much easier.

Question 2. Subtract
a) \( \frac{11}{12} - \frac{13}{16} \)
b) \( \frac{13}{14} - \frac{13}{21} \)
c) \( \frac{11}{14} - \frac{26}{35} \)
d) \( \frac{3}{5} - \frac{5}{9} \)
e) \( \frac{8}{9} - \frac{5}{6} \)
f) \( \frac{13}{24} - \frac{5}{16} \)
g) \( 2\frac{3}{4} - 1\frac{5}{6} \)
h) \( 7\frac{5}{8} - 3\frac{1}{6} \)
Answer:
a) The LCM of 12 and 16 is 48.
\( \frac{11 \times 4}{12 \times 4} - \frac{13 \times 3}{16 \times 3} = \frac{44}{48} - \frac{39}{48} = \frac{5}{48} \).

b) The LCM of 14 and 21 is 42.
\( \frac{13 \times 3}{14 \times 3} - \frac{13 \times 2}{21 \times 2} = \frac{39}{42} - \frac{26}{42} = \frac{13}{42} \).

c) The LCM of 14 and 35 is 70.
\( \frac{11 \times 5}{14 \times 5} - \frac{26 \times 2}{35 \times 2} = \frac{55}{70} - \frac{52}{70} = \frac{3}{70} \).

d) The LCM of 5 and 9 is 45.
\( \frac{3 \times 9}{5 \times 9} - \frac{5 \times 5}{9 \times 5} = \frac{27}{45} - \frac{25}{45} = \frac{2}{45} \).

e) The LCM of 9 and 6 is 18.
\( \frac{8 \times 2}{9 \times 2} - \frac{5 \times 3}{6 \times 3} = \frac{16}{18} - \frac{15}{18} = \frac{1}{18} \).

f) The LCM of 24 and 16 is 48.
\( \frac{13 \times 2}{24 \times 2} - \frac{5 \times 3}{16 \times 3} = \frac{26}{48} - \frac{15}{48} = \frac{11}{48} \).

g) Change to improper fractions:
\( \frac{11}{4} - \frac{11}{6} \).
The LCM of 4 and 6 is 12.
\( \frac{11 \times 3}{4 \times 3} - \frac{11 \times 2}{6 \times 2} = \frac{33}{12} - \frac{22}{12} = \frac{11}{12} \).

h) Change to improper fractions:
\( \frac{61}{8} - \frac{19}{6} \).
The LCM of 8 and 6 is 24.
\( \frac{61 \times 3}{8 \times 3} - \frac{19 \times 2}{6 \times 2} = \frac{183}{24} - \frac{38}{24} = \frac{145}{24} = 6\frac{1}{24} \).
In simple words: To subtract fractions, first make their bottom numbers match. Then, subtract the top numbers.

Exam Tip: Be careful when changing mixed numbers to improper fractions. Double-check your multiplication and addition steps before subtracting.

Question 3. Multiply
a) \( \frac{3}{4} \times 5 \)
b) \( \frac{5}{12} \times 8 \)
c) \( \frac{2}{3} \times \frac{4}{5} \)
d) \( \frac{4}{7} \times \frac{1}{2} \)
e) \( \frac{24}{35} \times \frac{7}{6} \)
f) \( \frac{7}{10} \times 1\frac{3}{7} \)
g) \( \frac{3}{8} \times 4\frac{4}{9} \)
h) \( 1\frac{1}{5} \times 1\frac{1}{12} \)
j) \( 2\frac{2}{5} \times \frac{5}{18} \)
k) \( 3\frac{3}{5} \times 3\frac{1}{3} \)
Answer:
a) Multiply the whole number by the numerator:
\( \frac{3 \times 5}{4} = \frac{15}{4} = 3\frac{3}{4} \).

b) Simplify before multiplying:
\( \frac{5}{12} \times 8 = \frac{5 \times 8}{12} = \frac{40}{12} = \frac{10}{3} = 3\frac{1}{3} \).

c) Multiply numerators and denominators:
\( \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \).

d) Simplify by dividing 4 by 2:
\( \frac{2 \times 1}{7 \times 1} = \frac{2}{7} \).

e) Simplify across:
\( \frac{24}{6} \times \frac{7}{35} = 4 \times \frac{1}{5} = \frac{4}{5} \).

f) Change the mixed number to an improper fraction first:
\( \frac{7}{10} \times \frac{10}{7} = 1 \).

g) Change to improper fractions:
\( \frac{3}{8} \times \frac{40}{9} \).
Simplify across:
\( \frac{3}{9} \times \frac{40}{8} = \frac{1}{3} \times 5 = \frac{5}{3} = 1\frac{2}{3} \).

h) Change to improper fractions:
\( \frac{6}{5} \times \frac{13}{12} \).
Simplify across:
\( \frac{1}{5} \times \frac{13}{2} = \frac{13}{10} = 1\frac{3}{10} \).

j) Change to improper fractions:
\( \frac{12}{5} \times \frac{5}{18} \).
Simplify across:
\( \frac{12}{18} \times \frac{5}{5} = \frac{2}{3} \times 1 = \frac{2}{3} \).

k) Change to improper fractions:
\( \frac{18}{5} \times \frac{10}{3} \).
Simplify across:
\( \frac{18}{3} \times \frac{10}{5} = 6 \times 2 = 12 \).
In simple words: To multiply fractions, multiply the top numbers together and then multiply the bottom numbers together.

Exam Tip: Simplify the numbers diagonally or vertically before you multiply. This prevents working with large numbers and keeps your calculations simple.

Question 4. Divide
a) \( \frac{2}{3} \div \frac{3}{5} \)
b) \( \frac{3}{8} \div \frac{4}{7} \)
c) \( \frac{2}{3} \div 1\frac{1}{5} \)
d) \( 4\frac{1}{2} \div \frac{4}{9} \)
e) \( 1\frac{1}{7} \div \frac{2}{5} \)
f) \( \frac{4}{9} \div \frac{4}{9} \)
g) \( 2\frac{1}{3} \div 1\frac{3}{4} \)
h) \( 3\frac{1}{2} \div 2\frac{4}{9} \)
Answer:
a) Multiply by the reciprocal of the second fraction:
\( \frac{2}{3} \times \frac{5}{3} = \frac{10}{9} = 1\frac{1}{9} \).

b) Multiply by the reciprocal:
\( \frac{3}{8} \times \frac{7}{4} = \frac{21}{32} \).

c) Convert the mixed number first: \( 1\frac{1}{5} = \frac{6}{5} \).
Now multiply by the reciprocal:
\( \frac{2}{3} \times \frac{5}{6} = \frac{1 \times 5}{3 \times 3} = \frac{5}{9} \).

d) Convert the mixed number: \( 4\frac{1}{2} = \frac{9}{2} \).
Now multiply by the reciprocal:
\( \frac{9}{2} \times \frac{9}{4} = \frac{81}{8} = 10\frac{1}{8} \).

e) Convert the mixed number: \( 1\frac{1}{7} = \frac{8}{7} \).
Now multiply by the reciprocal:
\( \frac{8}{7} \times \frac{5}{2} = \frac{4 \times 5}{7 \times 1} = \frac{20}{7} = 2\frac{6}{7} \).

f) Dividing any non-zero number by itself is 1:
\( \frac{4}{9} \times \frac{9}{4} = 1 \).

g) Convert to improper fractions: \( \frac{7}{3} \div \frac{7}{4} \).
Now multiply by the reciprocal:
\( \frac{7}{3} \times \frac{4}{7} = \frac{4}{3} = 1\frac{1}{3} \).

h) Convert to improper fractions: \( \frac{7}{2} \div \frac{22}{9} \).
Now multiply by the reciprocal:
\( \frac{7}{2} \times \frac{9}{22} = \frac{63}{44} = 1\frac{19}{44} \).
In simple words: To divide fractions, flip the second fraction upside down and multiply it by the first one instead.

Exam Tip: Never flip the first fraction. Always write down the reciprocal of the second fraction (the divisor) when converting division to multiplication.

Question 5. Solve
a) \( 4\frac{1}{2} \) of 4
b) \( \frac{1}{4} \) of \( 2\frac{2}{7} \)
c) \( \frac{1}{3} \) of 60
d) \( \frac{5}{9} \) of \( \frac{9}{22} \)
e) \( \frac{3}{4} \) of \( 6\frac{2}{3} \)
f) \( \frac{3}{5} \) of \( \frac{1}{12} \)
Answer:
a) Change \( 4\frac{1}{2} \) to improper: \( \frac{9}{2} \).
\( \frac{9}{2} \times 4 = 9 \times 2 = 18 \).

b) Change \( 2\frac{2}{7} \) to improper: \( \frac{16}{7} \).
\( \frac{1}{4} \times \frac{16}{7} = \frac{4}{7} \).

c) \( \frac{1}{3} \times 60 = 20 \).

d) \( \frac{5}{9} \times \frac{9}{22} = \frac{5}{22} \).

e) Change \( 6\frac{2}{3} \) to improper: \( \frac{20}{3} \).
\( \frac{3}{4} \times \frac{20}{3} = \frac{20}{4} = 5 \).

f) \( \frac{3}{5} \times \frac{1}{12} = \frac{1}{5 \times 4} = \frac{1}{20} \).
In simple words: In math, the word "of" is just another way of saying multiply.

Exam Tip: Substitute "of" with a multiplication sign \( (\times) \) as your very first step to keep your work neat and clear.

Question 6. Write in expanded form
a) 225.105
b) 10.001
c) 49.01
d) 92.45
e) 2.007
Answer:
a) \( 2 \times 100 + 2 \times 10 + 5 \times 1 + 1 \times \frac{1}{10} + 0 \times \frac{1}{100} + 5 \times \frac{1}{1000} \)
\( = 200 + 20 + 5 + \frac{1}{10} + \frac{5}{1000} \).

b) \( 1 \times 10 + 0 \times 1 + 0 \times \frac{1}{10} + 0 \times \frac{1}{100} + 1 \times \frac{1}{1000} \)
\( = 10 + \frac{1}{1000} \).

c) \( 4 \times 10 + 9 \times 1 + 0 \times \frac{1}{10} + 1 \times \frac{1}{100} \)
\( = 40 + 9 + \frac{1}{100} \).

d) \( 9 \times 10 + 2 \times 1 + 4 \times \frac{1}{10} + 5 \times \frac{1}{100} \)
\( = 90 + 2 + \frac{4}{10} + \frac{5}{100} \).

e) \( 2 \times 1 + 0 \times \frac{1}{10} + 0 \times \frac{1}{100} + 7 \times \frac{1}{1000} \)
\( = 2 + \frac{7}{1000} \).
In simple words: Expanded form helps you see the place value of every single digit in a number.

Exam Tip: Remember that places after the decimal point are fractions, like tenths \( (\frac{1}{10}) \), hundredths \( (\frac{1}{100}) \), and thousandths \( (\frac{1}{1000}) \).

Question 7. Express the following in the units given in brackets
a) 55 paise(Rs)
b) 8 Rs 40 paise (Rs)
c) 8m 54 cm (m)
d) 3m 8cm (m)
e) 1078 gm (Kg)
f) 8 gm (Kg)
Answer:
a) Since \( 1 \text{ Rupee} = 100 \text{ paise} \):
\( 55 \text{ paise} = \text{Rs } \frac{55}{100} = \text{Rs } 0.55 \).

b) Convert the paise part and add it to the Rupees:
\( 8 \text{ Rs } 40 \text{ paise} = \text{Rs } \left(8 + \frac{40}{100}\right) = \text{Rs } 8.40 \).

c) Since \( 1 \text{ meter} = 100 \text{ cm} \):
\( 8\text{ m } 54 \text{ cm} = \left(8 + \frac{54}{100}\right)\text{ m} = 8.54\text{ m} \).

d) Take care with single-digit centimeters:
\( 3\text{ m } 8 \text{ cm} = \left(3 + \frac{8}{100}\right)\text{ m} = 3.08\text{ m} \).

e) Since \( 1 \text{ kg} = 1000 \text{ grams} \):
\( 1078 \text{ gm} = \frac{1078}{1000}\text{ kg} = 1.078\text{ kg} \).

f) Divide by 1000 for grams to kilograms:
\( 8 \text{ gm} = \frac{8}{1000}\text{ kg} = 0.008\text{ kg} \).
In simple words: To change a smaller unit to a bigger unit, divide by 100 for money or meters, and divide by 1000 for weight.

Exam Tip: Single-digit values like 8 cm become 0.08 m when converted. Be careful not to write 0.8 m by mistake.

Question 8. Multiply
a) 4.09x5.6
b) 28.46x7
c) 0.943x62
d) 7.5x2.5
e) 4.23x0.8
Answer:
a) Multiply like whole numbers: \( 409 \times 56 = 22904 \).
There are three total decimal places: \( 22.904 \).

b) Multiply like whole numbers: \( 2846 \times 7 = 19922 \).
There are two decimal places: \( 199.22 \).

c) Multiply like whole numbers: \( 943 \times 62 = 58466 \).
There are three decimal places: \( 58.466 \).

d) Multiply like whole numbers: \( 75 \times 25 = 1875 \).
There are two decimal places: \( 18.75 \).

e) Multiply like whole numbers: \( 423 \times 8 = 3384 \).
There are three decimal places: \( 3.384 \).
In simple words: Multiply decimal numbers like they are regular whole numbers first. Then, count the total decimal places to put the point in the correct spot.

Exam Tip: Count the decimal digits of both numbers in the question to find exactly where to put the decimal point in your final answer.

Question 9. Multiply each of the following numbers by 10,100 &1000
a) 3.9
b) 2.89
c) 0.0829
d) 40.3
e) 0.3725
Answer:
a) 3.9:
- \( 3.9 \times 10 = 39 \)
- \( 3.9 \times 100 = 390 \)
- \( 3.9 \times 1000 = 3900 \)

b) 2.89:
- \( 2.89 \times 10 = 28.9 \)
- \( 2.89 \times 100 = 289 \)
- \( 2.89 \times 1000 = 2890 \)

c) 0.0829:
- \( 0.0829 \times 10 = 0.829 \)
- \( 0.0829 \times 100 = 8.29 \)
- \( 0.0829 \times 1000 = 82.9 \)

d) 40.3:
- \( 40.3 \times 10 = 403 \)
- \( 40.3 \times 100 = 4030 \)
- \( 40.3 \times 1000 = 40300 \)

e) 0.3725:
- \( 0.3725 \times 10 = 3.725 \)
- \( 0.3725 \times 100 = 37.25 \)
- \( 0.3725 \times 1000 = 372.5 \)
In simple words: Move the decimal point to the right by one, two, or three spots when multiplying by 10, 100, or 1000.

Exam Tip: If you run out of digits when moving the decimal point to the right, just add zeros at the end of the number.

Question 10. Divide each of the following numbers by 10,100 & 1000
a) 49.79
b) 923
c) 70.4
d) 937.3
e) 520.81
Answer:
a) 49.79:
- \( 49.79 \div 10 = 4.979 \)
- \( 49.79 \div 100 = 0.4979 \)
- \( 49.79 \div 1000 = 0.04979 \)

b) 923:
- \( 923 \div 10 = 92.3 \)
- \( 923 \div 100 = 9.23 \)
- \( 923 \div 1000 = 0.923 \)

c) 70.4:
- \( 70.4 \div 10 = 7.04 \)
- \( 70.4 \div 100 = 0.704 \)
- \( 70.4 \div 1000 = 0.0704 \)

d) 937.3:
- \( 937.3 \div 10 = 93.73 \)
- \( 937.3 \div 100 = 9.373 \)
- \( 937.3 \div 1000 = 0.9373 \)

e) 520.81:
- \( 520.81 \div 10 = 52.081 \)
- \( 520.81 \div 100 = 5.2081 \)
- \( 520.81 \div 1000 = 0.52081 \)
In simple words: Move the decimal point to the left by one, two, or three spots when dividing by 10, 100, or 1000.

Exam Tip: If there are no more digits on the left when dividing, write zeros before the digits to place your decimal point correctly.

Question 11. Divide
a) 8.64÷6
b) 0.0064÷8
c) 8.64÷3.6
d) 9.4÷0.47
e) 16.5÷0.15
f) 3.2÷ 50
g) 3.24÷0.0016
h) 5.065÷ 0.05
i) 36.8÷ 1.6
j) 60.42 ÷12
Answer:
a) \( 8.64 \div 6 = 1.44 \).

b) \( 0.0064 \div 8 = 0.0008 \).

c) Shift the decimal point of both numbers one place to the right:
\( 86.4 \div 36 = 2.4 \).

d) Shift the decimal point of both numbers two places to the right:
\( 940 \div 47 = 20 \).

e) Shift the decimal point of both numbers two places to the right:
\( 1650 \div 15 = 110 \).

f) \( 3.2 \div 50 = \frac{3.2}{50} = \frac{6.4}{100} = 0.064 \).

g) Shift the decimal point of both numbers four places to the right:
\( 32400 \div 16 = 2025 \).

h) Shift the decimal point of both numbers two places to the right:
\( 506.5 \div 5 = 101.3 \).

i) Shift the decimal point of both numbers one place to the right:
\( 368 \div 16 = 23 \).

j) \( 60.42 \div 12 = 5.035 \).
In simple words: When dividing by a decimal, move the point to make the divisor a whole number. Do the same to the other number first, then divide.

Exam Tip: Be extra careful to align the decimal point in the quotient directly above the decimal point in the dividend during long division.

Question 12. Solve the following
a)The cost of a fountain pen is Rs 13.25. Find the cost of 8 such pens.
b)The cost of 25 similar types of articles is Rs.28.25.Find the cost of one such article.
c)The length of an iron rod is 10.32 m.The rod is divided into 4 pieces of equal lengths.Find the length of each piece.
d)What will be the total length of cloth required for 6 pants if for each pant 1.15 m of cloth is required.
e)Find the distance walked by a boy in \( 1\frac{1}{2} \) hours,if he walks 2.150 km in each hour.
f)Mr. Mehra gave one-third of his money to his son,one-fifth of his money to his daughter and the remaining to his wife. If his wife gets 91000 how much money Mr. Mehra had originally.
g) a sum of rs. 84000 is divided among three persons A,B and C.If A gets one fourth of it and B gets one fifth of it,find how much does C get.
h)In one hour Rohit walks \( 3\frac{2}{5} \) km.How much distance will he walk in \( 2\frac{1}{2} \) hours.
g)A 84 m long string is cut into pieces each of length \( 5\frac{1}{4} \) m.How many pieces are obtained.
h)In buying a readymade shirt,two-fifths of my pocket money is spent. If Rs. 540 is still left with me ,find;
i)the money I had before buying the shirt
ii) the cost of the shirt
Answer:
a) Multiply the cost of one pen by 8:
\( \text{Cost of 8 pens} = 8 \times 13.25 = \text{Rs } 106 \).

b) Divide the total cost by the number of articles:
\( \text{Cost of one article} = 28.25 \div 25 = \text{Rs } 1.13 \).

c) Divide the total length of the rod by 4:
\( \text{Length of each piece} = 10.32 \div 4 = 2.58\text{ m} \).

d) Multiply the cloth required for one pant by 6:
\( \text{Total cloth required} = 6 \times 1.15 = 6.9\text{ m} \).

e) Time = \( 1\frac{1}{2}\text{ hours} = 1.5\text{ hours} \).
\( \text{Total distance} = 1.5 \times 2.150 = 3.225\text{ km} \).

f) Let the total money be \( x \).
Son's share = \( \frac{x}{3} \).
Daughter's share = \( \frac{x}{5} \).
Wife's share = \( x - \left(\frac{x}{3} + \frac{x}{5}\right) = x - \frac{8x}{15} = \frac{7x}{15} \).
Wife's share is Rs 91,000, so:
\( \frac{7x}{15} = 91000 \implies x = \frac{91000 \times 15}{7} = 13000 \times 15 = \text{Rs } 195,000 \).

g) First, find the shares of A and B:
\( \text{A's share} = \frac{1}{4} \times 84000 = \text{Rs } 21000 \).
\( \text{B's share} = \frac{1}{5} \times 84000 = \text{Rs } 16800 \).
Subtract their shares from the total:
\( \text{C's share} = 84000 - (21000 + 16800) = 84000 - 37800 = \text{Rs } 46200 \).

h) Rohit's speed = \( 3\frac{2}{5} = \frac{17}{5}\text{ km/h} \).
Time taken = \( 2\frac{1}{2} = \frac{5}{2}\text{ hours} \).
\( \text{Distance covered} = \frac{17}{5} \times \frac{5}{2} = \frac{17}{2} = 8\frac{1}{2}\text{ km} \) (or 8.5 km).

g) Change \( 5\frac{1}{4} \) m to \( \frac{21}{4} \) m.
\( \text{Number of pieces} = 84 \div \frac{21}{4} = 84 \times \frac{4}{21} = 4 \times 4 = 16\text{ pieces} \).

h) Let total money be \( y \).
Since \( \frac{2}{5} \) of the money was spent, \( 1 - \frac{2}{5} = \frac{3}{5} \) of the money is left:
\( \frac{3}{5} \times y = 540 \implies y = \frac{540 \times 5}{3} = 180 \times 5 = \text{Rs } 900 \).
i) Total money before buying the shirt = Rs 900.
ii) Cost of the shirt = \( 900 - 540 = \text{Rs } 360 \).
In simple words: Read each word problem to decide whether to multiply or divide. Changing mixed numbers into simple fractions helps to get the correct answer.

Exam Tip: Always state the final answer with its correct unit, such as Rs, m, or km, to make sure you get full marks.