CBSE Class 7 Mathematics Fractions And Decimals Worksheet Set 02

Question 1. If a mixed fraction is converted into fraction, then its reciprocal is:
(a) proper
(b) improper
(c) equal to itself
(d) none of the options
Answer: (a) proper
When a mixed fraction is converted into an improper fraction, the numerator is greater than the denominator. The reciprocal of an improper fraction has a smaller numerator than denominator, which makes it a proper fraction.
In simple words: Flipping an improper fraction turns it into a proper fraction.
Exam Tip: Remember that a proper fraction always has a value less than 1.

Question 2. Reciprocal of \(1\frac{3}{4}\) is:
(a) \(1\frac{4}{3}\)
(b) \(4\frac{1}{3}\)
(c) \(3\frac{1}{4}\)
(d) none of the options
Answer: (d) none of the options
First, convert the mixed fraction into an improper fraction:
\(1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4}\)
The reciprocal of \(\frac{7}{4}\) is \(\frac{4}{7}\). Since \(\frac{4}{7}\) is not listed in options (a), (b), or (c), the correct choice is (d).
In simple words: Convert to an improper fraction first, then flip numerator and denominator to get \(\frac{4}{7}\).

Exam Tip: Always convert mixed fractions to improper fractions before finding their reciprocals.

Question 3. \(\frac{20}{3}\) litres milk is being distributed among 10 persons. How much milk would one person get?
(a) \(\frac{2}{3}\) litre
(b) \(\frac{1}{3}\) litre
(c) \(\frac{4}{3}\) litre
(d) \(\frac{2}{3}\) ml.
Answer: (a) \(\frac{2}{3}\) litre
Total milk = \(\frac{20}{3}\) litres
Number of persons = 10
Milk per person = \(\frac{20}{3} \div 10 = \frac{20}{3} \times \frac{1}{10} = \frac{2}{3}\) litre
In simple words: Divide the total quantity of milk by the number of people to find the share of one person.

Exam Tip: Division by a whole number is the same as multiplying by its reciprocal.

Question 4. 474 surgeons were invited for a conference and \(\frac{5}{6}\) of those invited actually participated in it. The number of participants was:
(a) 359
(b) 395
(c) 474
(d) 568
Answer: (b) 395
Total invited surgeons = 474
Fraction participating = \(\frac{5}{6}\)
Number of participants = \(\frac{5}{6} \times 474 = 5 \times 79 = 395\)
In simple words: Multiply the total number of invitees by the fraction who attended.

Exam Tip: Simplify fractions with large numbers by dividing first before multiplying.

Question 5. The number of months in \(\frac{3}{5}\)th of a century is:
(a) 60
(b) 600
(c) 720
(d) none of the options
Answer: (c) 720
1 century = 100 years
1 year = 12 months
Total months in a century = \(100 \times 12 = 1200\) months
Number of months in \(\frac{3}{5}\)th of a century = \(\frac{3}{5} \times 1200 = 3 \times 240 = 720\) months
In simple words: Find total months in 100 years and take \(\frac{3}{5}\) of that total.

Question 6. Arrange in ascending order: \(\frac{3}{4}, \frac{2}{3}, \frac{1}{2}, \frac{5}{6}, \frac{7}{8}\)
Answer:
First, find the LCM of the denominators \(4, 3, 2, 6, 8\).
LCM = 24
Convert each fraction to an equivalent fraction with denominator 24:
\(\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}\)
\(\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}\)
\(\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}\)
\(\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}\)
\(\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}\)
Comparing the numerators: \(12 < 16 < 18 < 20 < 21\)
Ascending order: \(\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8}\)
In simple words: Make all denominators the same using LCM, then compare the top numbers from smallest to largest.

Exam Tip: Finding the LCM of denominators makes comparing and ordering fractions very easy.

Question 7. Simplify:

(a) \(\frac{1}{12} + \frac{5}{12} + \frac{7}{12}\)
Answer:
\(= \frac{1 + 5 + 7}{12} = \frac{13}{12} = 1\frac{1}{12}\)
In simple words: Add the numerators when denominators are the same.

(b) \(\frac{1}{12} + 2\frac{1}{3} + \frac{6}{15}\)
Answer:
Simplify \(\frac{6}{15} = \frac{2}{5}\)
Convert mixed fraction: \(2\frac{1}{3} = \frac{7}{3}\)
Expression: \(\frac{1}{12} + \frac{7}{3} + \frac{2}{5}\)
LCM of \(12, 3, 5 = 60\)
\(= \frac{5}{60} + \frac{140}{60} + \frac{24}{60} = \frac{5 + 140 + 24}{60} = \frac{169}{60} = 2\frac{49}{60}\)
In simple words: Simplify fractions, convert mixed numbers, find LCM, and add.

(c) \(2\frac{1}{3} + 3\frac{1}{2} - 1\frac{1}{4}\)
Answer:
Convert to improper fractions:
\(\frac{7}{3} + \frac{7}{2} - \frac{5}{4}\)
LCM of \(3, 2, 4 = 12\)
\(= \frac{28}{12} + \frac{42}{12} - \frac{15}{12} = \frac{28 + 42 - 15}{12} = \frac{55}{12} = 4\frac{7}{12}\)
In simple words: Convert mixed numbers to improper fractions, use LCM, and compute addition and subtraction.

(d) \(\frac{5}{7} - \frac{8}{35}\)
Answer:
LCM of \(7, 35 = 35\)
\(= \frac{5 \times 5}{35} - \frac{8}{35} = \frac{25 - 8}{35} = \frac{17}{35}\)
In simple words: Make denominators equal and subtract the numerators.

(e) \(2\frac{1}{3} + 3\frac{1}{2} - 1\frac{1}{4}\)
Answer:
(Same as part c)
\(= 4\frac{7}{12}\)
In simple words: Follow the same LCM steps as part (c).

(f) \(2\frac{1}{2} \times 3\frac{1}{4}\)
Answer:
Convert to improper fractions: \(\frac{5}{2} \times \frac{13}{4}\)
\(= \frac{5 \times 13}{2 \times 4} = \frac{65}{8} = 8\frac{1}{8}\)
In simple words: Multiply numerators together and denominators together.

(g) \(10 \times 4\frac{1}{4}\)
Answer:
\(= 10 \times \frac{17}{4} = \frac{170}{4} = \frac{85}{2} = 42\frac{1}{2}\)
In simple words: Multiply whole number by the improper fraction.

(h) \(\frac{5}{9} \times \frac{5}{8}\)
Answer:
\(= \frac{5 \times 5}{9 \times 8} = \frac{25}{72}\)
In simple words: Multiply top numbers and bottom numbers.

(i) \(\frac{1}{8}\) of Rs. 756
Answer:
\(= \frac{1}{8} \times 756 = \frac{756}{8} = \text{Rs. } 94.50 \text{ or } \text{Rs. } 94\frac{1}{2}\)
In simple words: Divide 756 by 8.

(j) \(\frac{3}{5}\) of \(62\frac{1}{2}\) m
Answer:
\(62\frac{1}{2} = \frac{125}{2}\)
\(= \frac{3}{5} \times \frac{125}{2} = \frac{3 \times 25}{1 \times 2} = \frac{75}{2} = 37\frac{1}{2}\text{ m}\)
In simple words: Convert mixed number and multiply by \(\frac{3}{5}\).

(k) \(\frac{5}{8} \div \frac{2}{3}\)
Answer:
\(= \frac{5}{8} \times \frac{3}{2} = \frac{15}{16}\)
In simple words: Multiply by the reciprocal of the second fraction.

(l) \(\frac{11}{13} \div 22\)
Answer:
\(= \frac{11}{13} \times \frac{1}{22} = \frac{1}{13 \times 2} = \frac{1}{26}\)
In simple words: Multiply by \(\frac{1}{22}\) and simplify.

(m) \(6\frac{1}{4} \div 2\frac{1}{4}\)
Answer:
\(= \frac{25}{4} \div \frac{9}{4} = \frac{25}{4} \times \frac{4}{9} = \frac{25}{9} = 2\frac{7}{9}\)
In simple words: Convert both to improper fractions and multiply by the reciprocal.

(n) \(100 \div \frac{10}{7}\)
Answer:
\(= 100 \times \frac{7}{10} = 10 \times 7 = 70\)
In simple words: Multiply 100 by the reciprocal of \(\frac{10}{7}\).

Exam Tip: Always reduce fractions to their lowest terms in the final step.

Question 8. Sunita bought a 10 Kg. box of grapes from the market. She gave \(3\frac{1}{2}\) Kg. of the grapes to her friend Punita and \(2\frac{1}{4}\) Kg. to Anita. How many Kg. of grapes were left with her?
Answer:
Total weight of grapes = \(10\) Kg.
Grapes given to Punita = \(3\frac{1}{2} = \frac{7}{2}\) Kg.
Grapes given to Anita = \(2\frac{1}{4} = \frac{9}{4}\) Kg.
Total grapes given away = \(\frac{7}{2} + \frac{9}{4} = \frac{14}{4} + \frac{9}{4} = \frac{23}{4}\) Kg.
Grapes left with Sunita = \(10 - \frac{23}{4} = \frac{40}{4} - \frac{23}{4} = \frac{17}{4} = 4\frac{1}{4}\) Kg.
In simple words: Add the portions given to friends and subtract from the total 10 Kg.

Exam Tip: Find the total quantity given away first before subtracting from the initial stock.

Question 9. Anita jogs \(1\frac{1}{2}\) Km. in 1 hour. How many Km. can she cover in \(2\frac{1}{2}\) hours?
Answer:
Distance covered in 1 hour = \(1\frac{1}{2} = \frac{3}{2}\) Km.
Time = \(2\frac{1}{2} = \frac{5}{2}\) hours
Total distance covered = Speed \(\times\) Time
\(= \frac{3}{2} \times \frac{5}{2} = \frac{15}{4} = 3\frac{3}{4}\) Km.
In simple words: Multiply the speed per hour by the total hours.

Exam Tip: Distance equals speed multiplied by time.

Question 10. If 12 identical books kept together weigh \(6\frac{1}{3}\) Kg, what is the weight of each book?
Answer:
Weight of 12 books = \(6\frac{1}{3} = \frac{19}{3}\) Kg.
Weight of 1 book = \(\frac{19}{3} \div 12 = \frac{19}{3} \times \frac{1}{12} = \frac{19}{36}\) Kg.
In simple words: Divide the total weight by 12.

Exam Tip: To find the value of a single item, divide the total value by the number of items.

Question 11. Subtract:

(a) \(\frac{2}{11}\) from 4
Answer:
\(= 4 - \frac{2}{11} = \frac{44}{11} - \frac{2}{11} = \frac{42}{11} = 3\frac{9}{11}\)
In simple words: Convert whole number into a fraction with denominator 11 and subtract.

(b) \(1\frac{1}{4}\) from \(5\frac{1}{2}\)
Answer:
\(= 5\frac{1}{2} - 1\frac{1}{4} = \frac{11}{2} - \frac{5}{4} = \frac{22}{4} - \frac{5}{4} = \frac{17}{4} = 4\frac{1}{4}\)
In simple words: Convert both to improper fractions with a common denominator of 4.

(c) \(\frac{1}{2}\) from \(\frac{7}{6}\)
Answer:
\(= \frac{7}{6} - \frac{1}{2} = \frac{7}{6} - \frac{3}{6} = \frac{4}{6} = \frac{2}{3}\)
In simple words: Make denominators equal to 6 and subtract.

(d) \(3\frac{1}{2}\) from \(1\frac{1}{4}\)
Answer:
\(= 1\frac{1}{4} - 3\frac{1}{2} = \frac{5}{4} - \frac{7}{2} = \frac{5}{4} - \frac{14}{4} = -\frac{9}{4} = -2\frac{1}{4}\)
In simple words: Subtract the smaller number from the larger and apply a negative sign, since we subtract 3.5 from 1.25.

Exam Tip: Pay careful attention to the word "from" - "A from B" means \(B - A\).

Question 12. Find the reciprocal of the sum of \(1\frac{7}{9}\) and \(1\frac{9}{7}\)
Answer:
First number = \(1\frac{7}{9} = \frac{16}{9}\)
Second number = \(1\frac{9}{7} = \frac{16}{7}\)
Sum = \(\frac{16}{9} + \frac{16}{7}\)
LCM of \(9, 7 = 63\)
\(= \frac{16 \times 7}{63} + \frac{16 \times 9}{63} = \frac{112 + 144}{63} = \frac{256}{63}\)
Reciprocal of the sum = \(\frac{63}{256}\)
In simple words: Add the two numbers first, then flip the resulting fraction upside down.

Exam Tip: Always calculate the entire sum first before finding its reciprocal.

Question 13. On the occasion of birthday, Reena had eaten one-third of the cake and shared the rest equally among three of her friends.
(a) What fraction of the cake did each friend get?
(b) Do you share your lunch with your friends? Is sharing a good habit?
Answer:
(a) Total cake = 1
Cake eaten by Reena = \(\frac{1}{3}\)
Remaining cake = \(1 - \frac{1}{3} = \frac{2}{3}\)
Number of friends = 3
Fraction of cake each friend got = \(\frac{2}{3} \div 3 = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}\)
(b) Yes, sharing lunch with friends is a very good habit as it promotes friendship, caring, and togetherness.
In simple words: Subtract Reena's share from 1, then divide the remainder equally among 3 friends.

Exam Tip: "Rest" means the whole cake minus the part already consumed.

Question 14. The value of \(0.03784 \times 1000\) is:
(a) 3.784
(b) 37.84
(c) 378.4
(d) 3784
Answer: (c) 378.4
Multiplying by 1000 shifts the decimal point 3 places to the right: \(0.03784 \times 1000 = 37.84\)
In simple words: Move the decimal point three places to the right.

Exam Tip: Every zero in the multiplier shifts the decimal point one place to the right.

Question 15. The place value of the underlined digit in 78.0123 is:
(a) \(\frac{1}{100000}\)
(b) \(\frac{1}{1000}\)
(c) \(\frac{3}{1000}\)
(d) \(\frac{3}{10000}\)
Answer: (d) \(\frac{3}{10000}\)
In 78.0123, the digits after the decimal point are: tenths (0), hundredths (1), thousandths (2), and ten-thousandths (3). The underlined digit 3 is in the fourth decimal place, so its place value is \(\frac{3}{10000}\).
In simple words: Count the decimal positions after the dot. The fourth position represents ten-thousandths.

Exam Tip: Decimal place values go as tenths, hundredths, thousandths, ten-thousandths, etc.

Question 16. The value of the mixed fraction \(6\frac{7}{8}\) is:
(a) 7.875
(b) 6.785
(c) 6.875
(d) 6.985
Answer: (c) 6.875
\(6\frac{7}{8} = 6 + \frac{7}{8} = 6 + 0.875 = 6.875\)
In simple words: Divide 7 by 8 to get 0.875 and add it to 6.

Exam Tip: Remember standard fraction-to-decimal conversions like \(\frac{1}{8} = 0.125\).

Question 17. On subtracting 4.81 from 43.17, we get:
(a) 38.36
(b) 38.81
(c) 38.17
(d) 47.98
Answer: (a) 38.36
\(43.17 - 4.81 = 38.36\)
In simple words: Line up the decimal points and subtract.

Question 18. Amongst the following, the value of expression different from others is:
(a) \(6 \div 0.21\)
(b) \(60 \div 2.1\)
(c) \(0.6 \div 0.21\)
(d) \(600 \div 21\)
Answer: (c) \(0.6 \div 0.21\)
Expressions (a), (b), and (d) all simplify to equivalent ratios multiplying numerator and denominator by 100: \(\frac{600}{21}\), whereas (c) is \(\frac{60}{21}\), which is different.
In simple words: Check the ratio by shifting decimals equally in both numbers.

Exam Tip: Multiplying both dividend and divisor by the same power of 10 keeps the quotient unchanged.

Question 19. Find the length of wire required to fence a field of length 290 m. and width of 75.25 m.
Answer:
Length \((l) = 290\) m.
Width \((b) = 75.25\) m.
Perimeter of the field = \(2 \times (l + b)\)
\(= 2 \times (290 + 75.25) = 2 \times 365.25 = 730.50\) m.
In simple words: Fencing requires the perimeter, which is twice the sum of length and width.

Exam Tip: Perimeter of a rectangle formula is \(2(l + b)\).

Question 20. Find the value of:

(a) \(432.24 + 23.268 + 910.9 + 76.007\)
Answer:
\(= 1442.415\)
In simple words: Align decimal points and add column by column.

(b) \(15 + 16.21 + 109\)
Answer:
\(= 140.21\)
In simple words: Treat whole numbers as having .00 at the end.

(c) \(26.5 - 1.50\)
Answer:
\(= 25.00\)
In simple words: Subtract 1.50 from 26.50.

(d) \(5.721 - 0.89\)
Answer:
\(= 4.831\)
In simple words: Pad 0.89 with a zero to make it 0.890 and subtract.

(e) \(0.097 \times 19\)
Answer:
\(= 1.843\)
In simple words: Multiply normally and place the decimal 3 places from the right.

(f) \(1.07 \times 0.02\)
Answer:
\(= 0.0214\)
In simple words: Total decimal places in factors is 4, so result has 4 decimal places.

(g) \(18.673 \times 100\)
Answer:
\(= 1867.3\)
In simple words: Move decimal point two places to the right.

(h) \(15.28 \times 1000\)
Answer:
\(= 15280\)
In simple words: Move decimal point three places to the right.

(i) \(56.8 \div 4\)
Answer:
\(= 14.2\)
In simple words: Divide 56.8 by 4.

(j) \(4.29 \div 0.003\)
Answer:
\(= \frac{4.29}{0.003} = \frac{4290}{3} = 1430\)
In simple words: Multiply both numbers by 1000 to remove decimals, then divide.

(k) \(0.07525 \div 2.15\)
Answer:
\(= \frac{0.07525}{2.15} = \frac{7.525}{215} = 0.035\)
In simple words: Shift decimals equally and divide.

(l) \(48 \div 0.008\)
Answer:
\(= \frac{48}{0.008} = \frac{48000}{8} = 6000\)
In simple words: Multiply 48 by 1000 and divide by 8.

Exam Tip: Count decimal places carefully when multiplying or dividing decimals.

Question 21. 76.8 m. of cloth has been cut into pieces 1.2 m. long. Find the number of pieces that can be cut.
Answer:
Total length of cloth = 76.8 m.
Length of each piece = 1.2 m.
Number of pieces = \(76.8 \div 1.2 = \frac{76.8}{1.2} = \frac{768}{12} = 64\)
In simple words: Divide total length by the length of one piece.

Exam Tip: Cancel out the decimal points by multiplying both numbers by 10.

Question 22. Subtract (a) 42.89 from 760 (b) 33.07 from 330.7
Answer:
(a) \(760 - 42.89 = 717.11\)
(b) \(330.7 - 33.07 = 297.63\)
In simple words: Add trailing zeros to whole numbers to match decimal places, then subtract.

Exam Tip: Place decimal points and zeros carefully before subtracting from a whole number.

Question 23. Find the product of \(0.2 \times 0.2 \times 0.2\)
Answer:
\(0.2 \times 0.2 = 0.04\)
\(0.04 \times 0.2 = 0.008\)
In simple words: Multiply digits (2 \(\times\) 2 \(\times\) 2 = 8) and place the decimal 3 places to the right.

Exam Tip: The total number of decimal places in the product equals the sum of decimal places in all factors.

Question 24. Anju on her birthday wants to treat 4 of her friends along with herself an ice cream cone costing Rs. 17.65 each. She has only Rs. 31.45 with her. She asks her father to give the remaining money. How much money should Anju take from her father?
Answer:
Total people = 4 friends + Anju = 5 people
Cost of each ice cream cone = Rs. 17.65
Total cost = \(5 \times 17.65 = \text{Rs. } 88.25\)
Money Anju has = Rs. 31.45
Money to take from father = Total cost - Money she has
\(= 88.25 - 31.45 = \text{Rs. } 56.80\)
In simple words: Calculate total cost for 5 people, then subtract the money Anju already has.

Exam Tip: Remember to include Anju herself along with her 4 friends when calculating the total number of people.

Question 25. Mrs. Sharma received an award of Rs. 1,00,000 in a game show. She paid the bill of Rs. 15000.50 to the hospital where her mother was admitted, donated 50,000 to an orphanage and the remaining money to an N.G.O. How much money she donated to the N.G.O.? What type of lady was Mrs. Sharma:
(a) Honest
(b) Smart
(c) Kind hearted
Answer:
Total award amount = Rs. 1,00,000.00
Hospital bill = Rs. 15,000.50
Donation to orphanage = Rs. 50,000.00
Total money spent and donated = \(15000.50 + 50000.00 = \text{Rs. } 65,000.50\)
Money donated to N.G.O. = \(1,00,000.00 - 65,000.50 = \text{Rs. } 34,999.50\)
Character trait: (c) Kind hearted
In simple words: Add the hospital bill and orphanage donation, then subtract from the total award to find the N.G.O. share.

Exam Tip: Deduct all expenses and specific donations from the total amount to find the remainder.

Multiplication of Fractions

1. Fractions multiplication is similar to the multiplication of any two real numbers. Or you can say, we apply the simple method to multiply fractions here. Simply, we can write the formula for multiplication of fraction as;
The product of Fraction = Product of numerator/Product of denominator

2. To multiply fractions, simplify it first and then multiply the numerators and denominators separately.

Questions based on MULTIPLICATION OF FRACTIONS:-

Question. Find the product: (i) (3/5) × (7/11)
Solution:
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (3 × 7)/ (5 × 11)
= (21/55)

(ii) (5/8) × (4/7)
Solution:
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (5 × 4)/ (8 × 7)
= (20/56) … [÷ by 4]
= (5/14)

(iii) (4/9) × (15/16)
Solution:
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (4 × 15)/ (9 × 16)
= (60/144) … [ by 12]
= (5/12)

(iv) (2/5) × 15
Solution:
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (2 × 15)/ (5 × 1)
= (30/5) … [÷ by 5]
= 6

Question. Simplify: (i) (2/3) × (5/44) × (33/35)
Solution:
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (2×5×33)/ (3×44×35)
On simplifying we get,
= (1×1×11) / (1×22×7)
= (11/154)
= (1/14)

(ii) (12/25) × (15/28) × (35/36)
Solution:
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (12×15×35)/ (25×28×36)
On simplifying we get,
= (1×3×5) / (5×4×3)
Again simplifying we get,
= (1×1×1)/ (1×4×1)
= (1/4)

(iii) [1(4/7)] × [1(13/22)] × [1(1/15)]
Solution:
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
By Converting mixed fraction into improper fraction we get,
= (11/7) × (35/22) × (16/15)
= (11×35×16)/ (7×22×15)
On simplifying we get,
= (1×5×16) / (1×2×15)
Again simplifying we get,
= (1×1×8)/ (1×1×3)
= (8/3)
= [2(2/3)]

Question. Find : (i) (1/3) of 24
Solution:
We have:
= (1/3) of (24/1)
This can be written as,
= (24/1) × (1/3)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (24 × 1)/ (1 × 3)
= (24/3)
= 8

(ii) (3/4) of 32
Solution:
We have:
= (3/4) of (32/1)
This can be written as,
= (32/1) × (3/4)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (32 × 3)/ (1 × 4)
On simplifying we get,
= (8×3)/ (1×1)
= 24

Question. Apples are sold at ₹ [48(4/5)] per kg. What is the cost of [3(3/4)] kg of apples?
Solution:
From the question,
The cost of 1 kg of apples = [48(4/5)] = (244/5)
Therefore, the cost of [3(3/4)] kg of apples = (15/4)
Then,
= (244/5) × (15/4)
= (244 × 15) / (5 × 4)
On simplifying we get,
= (61 × 3) / (1 × 1)
= ₹ 183
Hence, the cost of [3(3/4)] kg is ₹ 183

Question. Cloth is being sold at ₹ [42(1/2)] per meter. What is the cost of [5(3/5)] meters of this cloth?
Solution:
From the question,
The cost of 1 meter of cloth = ₹ [42(1/2)] = (85/2)
Therefore, the cost of [5(3/5)] meters of cloth = (28/5)
Then,
= (85/2) × (28/5)
= (85 × 28) / (2 × 5)
On simplifying we get,
= (17 × 14) / (1 × 1)
= ₹ 238
Hence, the cost of [5(3/5)] meters of cloth is ₹ 238.

Question. A car covers a certain distance at a uniform speed of [66(2/3)] km per hour. How much distance will it cover in 9 hours?
Solution:
From the question,
The total distance covered by a car in 1 hour = [66(2/3)] km = (200/3)
Therefore, the distance covered by a car in 9 hour = (200/3) × 9
Then,
= (200/3) × (9/1)
= (200 × 9) / (3 × 1)
On simplifying we get,
= (200× 3) / (1 × 1)
= 600 km
Hence, the distance covered by a car in 9 hour is 600 km.

Question. One tin holds [12(3/4)] liters of oil. How many liters of oil can 26 such tins hold?
Solution:
From the question,
The total amount of oil in 1 tin = [12(3/4)] liters = (51/4)
Therefore, the amount of oil in 26 such tins = (51/4) × 26
Then,
= (51/4) × (26/1)
= (51 × 26) / (4 × 1)
On simplifying we get,
= (51× 13) / (2 × 1)
= (663/2)
= [331(1/2)] liters
Hence, the amount of oil in 26 such tins is [331(1/2)] liters.

Question. Find the product:
(i) 4.74 × 10
(ii) 0.45 × 10
(iii) 0.0215 × 10
Solution:
(i) Given 4.74 × 10
Here we have to do normal multiplication with shifting the decimal point by one place to the right
Therefore 4.74 × 10 = 47.4

(ii) Given 0.45 × 10
Here we have to do normal multiplication with shifting the decimal point by one place to the right
Therefore 0.45 × 10 = 4.5

(iii) Given 0.0215 × 10
Here we have to do normal multiplication with shifting the decimal point by one place to the right
Therefore 0.0215 × 10 = 0.215

Question. Find the product:
(i) 35.853 × 100
(ii) 42.5 × 100
Solution:
(i) Given 35.853 × 100
Here we have to do normal multiplication with shifting the decimal point by two places to the right
Therefore 35.853 × 100 = 3585.3

(ii) Given 42.5 × 100
Here we have to do normal multiplication with shifting the decimal point by two places to the right
Therefore 42.5 × 100 = 4250

Question. Find the product:
(i) 2.506 × 1000
(ii) 20.708 × 1000
Solution:
(i) Given 2.506 × 1000
Here we have to do normal multiplication with shifting the decimal point by three places to the right
Therefore 2.506 × 1000 = 2506

(ii) Given 20.708 × 1000
Here we have to do normal multiplication with shifting the decimal point by three places to the right
Therefore 20.708 × 1000 = 20708

Question. Find the product:
(i) 3.14 × 17
(ii) 0.745 × 12
Solution:
(i) Given 3.14 × 17
First multiply as usual without looking at the decimal point
3.14 × 17 = 578
Now mark the decimal point in the product to have one place of decimal as there in the given decimal
3.14 × 17 = 57.8

(ii) Given 0.745 × 12
First multiply as usual without looking at the decimal point
0.745 × 12 = 894
Now mark the decimal point in the product to have three places of decimal as there in the given decimal
0.745 × 12 = 8.94

Question. Find:
(i) 1.07 × 0.02
(ii) 211.9 × 1.13
Solution:
(i) Given 1.07 × 0.02
First multiply as usual without looking at the decimal point
1.07 × 0.02 = 00214
Sum of the decimals is 4
Now mark the decimal point in the product to have four places of decimal as there in the given decimal
1.07 × 0.02 = 0.0214

(ii) Given 211.9 × 1.13
First multiply as usual without looking at the decimal point
211.9 × 1.13 = 239447
Sum of the decimals is 3
Now mark the decimal point in the product to have three places of decimal as there in the given decimal
211.9 × 1.13 = 239.447

Question. Find the area of a rectangle whose length is 5.5m and breadth is 3.4m.
Solution:
Given length of rectangle = 5.5m
Breadth of rectangle = 3.4 m
Area of rectangle = length × breadth
= 5.5 × 3.4
= 18.7 m²

Question. If the cost of a book is Rs 25.57, find the cost 0f 24 such books.
Solution:
Given cost of a book is Rs 25.57
Cost of 24 books = 25.57 × 24
= Rs 618.00

Question. A car covers a distance of 14.75km in one liter of petrol. How much distance it will cover in 15.5 liters of petrol?
Solution:
Given that distance covered by car in 1 liter of petrol = 14.75 km
Distance covered by car in 15.5 liters of petrol = 14.75 × 15.5
= 228.625 km

Question. One kg of rice costs Rs 42.65. What will be the cost of 18.25 kg of rice?
Solution:
Given cost of 1kg of rice = 42.65
Cost of 18.25kg of rice = 42.65 × 18.25
= Rs 778.3625

Question. One meter of cloth costs Rs 152.50. What is the cost of 10.75 meters of cloth?
Solution:
Given that cost of 1m cloth = Rs 152.50
Cost of 10.75 m of cloth = 152.50 × 10.75
= Rs 1639.375

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 7 Maths Worksheet - Fractions and Decimals (1)