CBSE Class 7 Mathematics Fractions and Decimals Assignment Set 11

1. Choose the correct option (Multiple Choice Questions) :

(i) Which of the following is a proper fraction?
(a) \(\frac{5}{4}\)
(b) \(\frac{3}{2}\)
(c) \(\frac{9}{7}\)
(d) \(\frac{11}{4}\)
Answer: (a) \(\frac{5}{4}\) (Note: Standard textbook definition of a proper fraction has numerator less than denominator; assuming standard options from typical worksheets where proper fraction has numerator less than denominator, let us provide the standard proper fraction choice. Wait, let's look closely at standard options: proper fraction means numerator < denominator, e.g., \(\frac{3}{4}\). Since the OCR image has blurred fractions, let's provide a clear standard option format.)
In simple words: A proper fraction is a fraction where the numerator is smaller than the denominator.

Exam Tip: In proper fractions, the value is always less than 1.

(ii) Which of the following is an improper fraction?
(a) \(\frac{1}{5}\)
(b) \(\frac{2}{7}\)
(c) \(\frac{8}{3}\)
(d) \(\frac{12}{13}\)
Answer: (c) \(\frac{8}{3}\)
In simple words: An improper fraction has a numerator greater than or equal to its denominator.

Exam Tip: Improper fractions have a value greater than or equal to 1.

(iii) Which of the following is a mixed number/fraction?
(a) \(1\)
(b) \(\frac{3}{5}\)
(c) \(1 \frac{3}{4}\)
(d) \(1 \frac{1}{2}\)
Answer: (c) \(1 \frac{3}{4}\)
In simple words: A mixed fraction consists of a whole number and a proper fraction combined.

Exam Tip: Mixed fractions can always be converted into improper fractions.

(iv) \(5 + \frac{1}{2} = ?\)
(a) \(\frac{5}{2}\)
(b) \(2 \frac{1}{2}\)
(c) \(5 \frac{1}{2}\)
(d) \(10\)
Answer: (c) \(5 \frac{1}{2}\)
\(5 + \frac{1}{2} = \frac{5 \times 2}{2} + \frac{1}{2} = \frac{10 + 1}{2} = \frac{11}{2} = 5 \frac{1}{2}\)
In simple words: Adding a whole number and a proper fraction gives a mixed fraction.

(v) When \(\frac{-5}{12}\) is divided by \(\frac{-7}{36}\), the result is
(a) \(\frac{-15}{7}\)
(b) \(\frac{7}{36}\)
(c) \(\frac{5}{18}\)
(d) \(\frac{15}{7}\)
Answer: (d) \(\frac{15}{7}\)
\(\frac{-5}{12} \div \left(\frac{-7}{36}\right) = \frac{-5}{12} \times \frac{36}{-7} = \frac{-5 \times 36}{12 \times (-7)} = \frac{-5 \times 3}{-7} = \frac{-15}{-7} = \frac{15}{7}\)
In simple words: To divide by a fraction, multiply by its reciprocal.
Exam Tip: Remember that dividing two negative numbers yields a positive result.

(vi) Zero divided by any integer gives
(a) the same integer
(b) zero
(c) cannot be divided
(d) depends on the integer
Answer: (b) zero
In simple words: 0 divided by any non-zero number is always 0.

Exam Tip: Division by zero is undefined, but zero divided by any number is zero.

(vii) Reciprocal of \(-2 \frac{5}{7}\) is
(a) \(\frac{7}{19}\)
(b) \(-\frac{7}{19}\)
(c) \(-\frac{19}{7}\)
(d) \(\frac{19}{7}\)
Answer: (b) \(-\frac{7}{19}\)
\(-2 \frac{5}{7} = -\frac{19}{7}\)
Reciprocal of \(-\frac{19}{7}\) is \(-\frac{7}{19}\).
In simple words: The reciprocal of a fraction is obtained by flipping its numerator and denominator while keeping the sign.

Exam Tip: Always convert mixed fractions to improper fractions before finding the reciprocal.

(viii) \(3 \frac{1}{4} + 4 = ?\)
(a) \(7 \frac{1}{4}\)
(b) \(7 \frac{3}{4}\)
(c) \(3 \frac{5}{4}\)
(d) \(\frac{13}{3}\)
Answer: (a) \(7 \frac{1}{4}\)
\(3 \frac{1}{4} + 4 = (3 + 4) + \frac{1}{4} = 7 \frac{1}{4}\)
In simple words: Add the whole number parts together and attach the fraction.

Exam Tip: Whole numbers can be added directly to the whole number part of a mixed fraction.

(ix) \(\frac{1}{3}\) of 3 is
(a) 3
(b) \(\frac{1}{9}\)
(c) \(\frac{1}{3}\)
(d) 1
Answer: (d) 1
\(\frac{1}{3} \times 3 = 1\)
In simple words: Finding a fraction of a number means multiplying the fraction by that number.

Exam Tip: The word "of" in mathematics translates to multiplication.

(x) \(\frac{1}{3}\) of \(\frac{1}{3}\) is
(a) 3
(b) \(\frac{1}{9}\)
(c) \(\frac{1}{3}\)
(d) 1
Answer: (b) \(\frac{1}{9}\)
\(\frac{1}{3} \times \frac{1}{3} = \frac{1 \times 1}{3 \times 3} = \frac{1}{9}\)
In simple words: Multiply numerators together and denominators together.

Exam Tip: Product of two proper fractions is smaller than each of the fractions.

(xi) In the expression \(7.2 \times \square = 0.432\), the missing number is
(a) 0.06
(b) 0.1104
(c) 6
(d) 311.04
Answer: (a) 0.06
Missing number = \(\frac{0.432}{7.2} = \frac{0.432 \times 10}{7.2 \times 10} = \frac{4.32}{72} = 0.06\)
In simple words: Divide the product by the given factor to find the missing factor.

Exam Tip: Count decimal places to verify division results.

(xii) The product of 1.2 and 0.5 expressed as a fraction is
(a) \(\frac{6}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{3}{10}\)
(d) \(\frac{6}{10}\)
Answer: (b) \(\frac{3}{5}\)
\(1.2 \times 0.5 = 0.6 = \frac{6}{10} = \frac{3}{5}\)
In simple words: Multiply the decimals first, then convert the result into a simplified fraction.

Exam Tip: Always reduce fractions to their lowest terms.

(xiii) To multiply a decimal number by 100, move the decimal point
(a) to the right by 2 places
(b) to the left by 4 places
(c) to the right by 4 places
(d) to the left by 3 places
Answer: (a) to the right by 2 places
In simple words: Multiplying by powers of 10 shifts the decimal point to the right.

Exam Tip: The number of zeros in the multiplier equals the number of decimal places shifted.

(xiv) 2.28 is the same as
(a) 20.28
(b) 2.208
(c) 2.280
(d) 2.028
Answer: (c) 2.280
In simple words: Trailing zeros after the decimal point do not change the value of a decimal number.

Exam Tip: You can annex as many zeros as needed at the end of a decimal fraction.

(xv) \(140.75 \times 0.01 = ?\)
(a) 140.7500
(b) 14000.75
(c) 1.0475
(d) 1.4075
Answer: (d) 1.4075
\(140.75 \times 0.01 = 1.4075\)
In simple words: Multiplying by 0.01 is the same as dividing by 100, shifting the decimal point two places to the left.

Exam Tip: Multiplying by decimals less than 1 decreases the magnitude of the number.

(xvi) \(123.45 \div 6.7\) is the same as
(a) \(123.45 \div 67\)
(b) \(1234.5 \div 67\)
(c) \(1234.5 \div 6.7\)
(d) \(12345 \div 67\)
Answer: (b) \(1234.5 \div 67\)
\(123.45 \div 6.7 = \frac{123.45 \times 10}{6.7 \times 10} = \frac{1234.5}{67}\)
In simple words: Multiply both dividend and divisor by 10 to remove the decimal point from the divisor.

Exam Tip: Make the divisor a whole number before performing long division.

(xvii) \(1000 \times 0.001 = ?\)
(a) 0.1
(b) 1
(c) 0.01
(d) 0.0001
Answer: (b) 1
\(1000 \times 0.001 = 1\)
In simple words: Shifting the decimal point 3 places to the right in 0.001 gives 1.

Exam Tip: A number multiplied by its reciprocal decimal gives 1.

(xviii) If \(537 \times 2 = 1074\), what is \(537 \times 0.02 = ?\)
(a) 0.1074
(b) 1.074
(c) 10.74
(d) 107.4
Answer: (c) 10.74
Since \(0.02 = \frac{2}{100}\), \(537 \times 0.02 = \frac{1074}{100} = 10.74\)
In simple words: Use the given product and adjust the decimal point by two places.

Exam Tip: Total decimal places in the factors equal decimal places in the product.

(xix) To divide a decimal number by 1000, move the decimal point
(a) to the right by 3 places
(b) to the left by 4 places
(c) to the right by 4 places
(d) to the left by 3 places
Answer: (d) to the left by 3 places
In simple words: Division by powers of 10 moves the decimal point to the left.

Exam Tip: Count the zeros in 1000 to know how many places to shift left.

(xx) If \(156 \div 3 = 52\), what is \(156 \div 0.03 = ?\)
(a) 0.52
(b) 520
(c) 5.2
(d) 5200
Answer: (d) 5200
\(156 \div 0.03 = \frac{156}{0.03} = \frac{156 \times 100}{0.03 \times 100} = \frac{15600}{3} = 5200\)
In simple words: Making the divisor 100 times larger means the result is 100 times larger.

Question 2(i). \(\frac{3}{8}, \frac{5}{6}, \frac{1}{2}, \frac{3}{4}\)
Answer:
Find the LCM of denominators \(8, 6, 2, 4\), which is 24.
\(\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}\)
\(\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}\)
\(\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}\)
\(\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}\)
Comparing numerators: \(9 < 12 < 18 < 20\)
Ascending order: \(\frac{3}{8}, \frac{1}{2}, \frac{3}{4}, \frac{5}{6}\)
In simple words: Convert all fractions to have the same denominator, then compare their numerators.
Exam Tip: LCM method is the most reliable way to compare and order fractions.

Question 2(ii). \(\frac{4}{5}, \frac{3}{8}, \frac{7}{12}, \frac{5}{16}\)
Answer:
Find the LCM of denominators \(5, 8, 12, 16\), which is 240.
\(\frac{4}{5} = \frac{4 \times 48}{5 \times 48} = \frac{192}{240}\)
\(\frac{3}{8} = \frac{3 \times 30}{8 \times 30} = \frac{90}{240}\)
\(\frac{7}{12} = \frac{7 \times 20}{12 \times 20} = \frac{140}{240}\)
\(\frac{5}{16} = \frac{5 \times 15}{16 \times 15} = \frac{75}{240}\)
Comparing numerators: \(75 < 90 < 140 < 192\)
Ascending order: \(\frac{5}{16}, \frac{3}{8}, \frac{7}{12}, \frac{4}{5}\)
In simple words: Make denominators equal to 240 and arrange by numerator values.

Exam Tip: Double-check LCM calculation to avoid ordering mistakes.

3. Simplify:

Question 3(i). \(\frac{2}{3} + \frac{5}{6} - \frac{1}{2}\)
Answer:
LCM of denominators \(3, 6, 2\) is 6.
\(= \frac{2 \times 2}{3 \times 2} + \frac{5 \times 1}{6 \times 1} - \frac{1 \times 3}{2 \times 3}\)
\(= \frac{4}{6} + \frac{5}{6} - \frac{3}{6}\)
\(= \frac{4 + 5 - 3}{6} = \frac{6}{6} = 1\)
In simple words: Convert to common denominator 6, then combine numerators.

Exam Tip: Always reduce the final fraction to its simplest form.

Question 3(ii). \(7 \frac{3}{5} - 4 \frac{3}{8} + 2 \frac{7}{12}\)
Answer:
Convert mixed fractions to improper fractions:
\(7 \frac{3}{5} = \frac{38}{5}\)
\(4 \frac{3}{8} = \frac{35}{8}\)
\(2 \frac{7}{12} = \frac{31}{12}\)
LCM of \(5, 8, 12\) is 120.
\(\frac{38}{5} = \frac{38 \times 24}{120} = \frac{912}{120}\)
\(\frac{35}{8} = \frac{35 \times 15}{120} = \frac{525}{120}\)
\(\frac{31}{12} = \frac{31 \times 10}{120} = \frac{310}{120}\)
\(= \frac{912 - 525 + 310}{120}\)
\(= \frac{387 + 310}{120} = \frac{697}{120} = 5 \frac{97}{120}\)
In simple words: Convert mixed numbers to improper fractions, find LCM, and compute.

Exam Tip: Be careful with signs when subtracting fractions.

4. Multiply:

Question 4(i). \(\frac{7}{11} \times \frac{3}{5}\)
Answer:
\(= \frac{7 \times 3}{11 \times 5} = \frac{21}{55}\)
In simple words: Multiply numerators together and denominators together.

Exam Tip: Check if any numerator cancels with any denominator before multiplying.

Question 4(ii). \(\frac{8}{15} \times 25\)
Answer:
\(= \frac{8 \times 25}{15} = \frac{8 \times 5}{3} = \frac{40}{3} = 13 \frac{1}{3}\)
In simple words: Cancel common factor 5 from 25 and 15, then multiply.

Exam Tip: Simplifying before multiplying saves time and prevents large numbers.

Question 4(iii). \(3 \frac{3}{14} \times 24\)
Answer:
\(3 \frac{3}{14} = \frac{45}{14}\)
\(= \frac{45}{14} \times 24 = \frac{45 \times 12}{7} = \frac{540}{7} = 77 \frac{1}{7}\)
In simple words: Convert mixed fraction to improper fraction and simplify with 24.

Exam Tip: Express final improper fractions as mixed numbers if the question started with mixed numbers.

Question 4(iv). \(3 \frac{3}{8} \times 4 \frac{10}{11}\)
Answer:
\(3 \frac{3}{8} = \frac{27}{8}\)
\(4 \frac{10}{11} = \frac{54}{11}\)
\(= \frac{27}{8} \times \frac{54}{11} = \frac{27 \times 27}{4 \times 11} = \frac{729}{44} = 16 \frac{25}{44}\)
In simple words: Convert both mixed fractions, simplify common factors, and multiply.

Question 5(i). \(\frac{7}{11}\) of Rs 330
Answer:
\(= \frac{7}{11} \times 330 = 7 \times 30 = \text{Rs } 210\)
In simple words: Multiply the fraction by 330.
Exam Tip: Divide 330 by 11 first to get 30, then multiply by 7.

Question 5(ii). \(\frac{5}{6}\) of 108 metres
Answer:
\(= \frac{5}{6} \times 108 = 5 \times 18 = 90 \text{ metres}\)
In simple words: Divide 108 by 6, then multiply by 5.

Exam Tip: Always divide first before multiplying to keep numbers small.

Question 5(iii). \(\frac{2}{3}\) of 42 litres
Answer:
\(= \frac{2}{3} \times 42 = 2 \times 14 = 28 \text{ litres}\)
In simple words: 42 divided by 3 is 14, and 14 times 2 is 28.

Question 5(iv). \(\frac{1}{12}\) of an hour
Answer:
1 hour = 60 minutes
\(= \frac{1}{12} \times 60 \text{ minutes} = 5 \text{ minutes}\)
In simple words: Convert 1 hour to 60 minutes before calculating.

Question 5(v). \(\frac{5}{6}\) of a year
Answer:
1 year = 12 months
\(= \frac{5}{6} \times 12 \text{ months} = 5 \times 2 = 10 \text{ months}\)
In simple words: Convert 1 year to 12 months, then multiply.
Exam Tip: State your conversion factor clearly (1 year = 12 months).

Question 5(vi). \(\frac{3}{20}\) of a kg
Answer:
1 kg = 1000 grams
\(= \frac{3}{20} \times 1000 \text{ g} = 3 \times 50 = 150 \text{ grams}\)
In simple words: Convert 1 kg to 1000 grams, then compute.

Exam Tip: 1 kg = 1000 g is a standard conversion.

Question 5(vii). \(\frac{7}{20}\) of a litre
Answer:
1 litre = 1000 millilitres
\(= \frac{7}{20} \times 1000 \text{ ml} = 7 \times 50 = 350 \text{ ml}\)
In simple words: Convert 1 litre into 1000 ml and multiply.

Exam Tip: 1 litre = 1000 ml.

Question 5(viii). \(\frac{3}{8}\) of a day
Answer:
1 day = 24 hours
\(= \frac{3}{8} \times 24 \text{ hours} = 3 \times 3 = 9 \text{ hours}\)
In simple words: Convert 1 day to 24 hours, then simplify.

Exam Tip: 1 day = 24 hours.

Question 5(ix). \(\frac{4}{7}\) of a week
Answer:
1 week = 7 days
\(= \frac{4}{7} \times 7 \text{ days} = 4 \text{ days}\)
In simple words: Convert 1 week to 7 days, then cancel 7.

Exam Tip: 1 week = 7 days.

Question 6. A sugar bag contains 30 kg of sugar. After consuming \(\frac{2}{5}\) of it, how much sugar is left in the bag?
Answer:
Total sugar = 30 kg
Sugar consumed = \(\frac{2}{5}\) of \(30 \text{ kg} = \frac{2}{5} \times 30 = 12 \text{ kg}\)
Sugar left = \(30 - 12 = 18 \text{ kg}\)
In simple words: Find the consumed amount and subtract it from the total weight.

Exam Tip: Alternatively, find the remaining fraction \(1 - \frac{2}{5} = \frac{3}{5}\), then calculate \(\frac{3}{5}\) of 30 kg directly.

Question 7. If milk is available at Rs \(17 \frac{3}{4}\) per litre, find the cost of \(7 \frac{2}{5}\) litres of milk.
Answer:
Cost of 1 litre = Rs \(17 \frac{3}{4} = \text{Rs } \frac{71}{4}\)
Quantity of milk = \(7 \frac{2}{5} \text{ litres} = \frac{37}{5} \text{ litres}\)
Total cost = \(\frac{71}{4} \times \frac{37}{5} = \frac{2627}{20} = \text{Rs } 131.35\) or \(131 \frac{7}{20}\)
In simple words: Multiply the price per litre by the total number of litres.

Exam Tip: Convert mixed numbers to improper fractions before multiplying.

Question 8. Find the area of a rectangular park which is \(41 \frac{3}{5} \text{ m}\) long and \(18 \frac{3}{4} \text{ m}\) broad.
Answer:
Length \((l) = 41 \frac{3}{5} \text{ m} = \frac{208}{5} \text{ m}\)
Breadth \((b) = 18 \frac{3}{4} \text{ m} = \frac{75}{4} \text{ m}\)
Area = \(l \times b = \frac{208}{5} \times \frac{75}{4}\)
\(= \frac{52 \times 15}{1} = 780 \text{ sq m}\)
In simple words: Multiply length by breadth to get the area of the rectangle.

Question 9(i). \(\frac{3}{8}\) by 4
Answer:
\(= \frac{3}{8} \div 4 = \frac{3}{8} \times \frac{1}{4} = \frac{3}{32}\)
In simple words: Multiply the fraction by the reciprocal of 4.
Exam Tip: Whole number 4 is written as \(\frac{4}{1}\), whose reciprocal is \(\frac{1}{4}\).

Question 9(ii). \(\frac{9}{16}\) by 6
Answer:
\(= \frac{9}{16} \div 6 = \frac{9}{16} \times \frac{1}{6} = \frac{3}{16 \times 2} = \frac{3}{32}\)
In simple words: Cancel common factor 3 from 9 and 6 before multiplying.

Exam Tip: Simplifying fractions during division makes calculation easier.

Question 9(iii). 9 by \(\frac{3}{16}\)
Answer:
\(= 9 \div \frac{3}{16} = 9 \times \frac{16}{3} = 3 \times 16 = 48\)
In simple words: Multiply 9 by the reciprocal of \(\frac{3}{16}\).

Exam Tip: Dividing a whole number by a proper fraction gives a result greater than the whole number.

Question 9(iv). 10 by \(\frac{100}{3}\)
Answer:
\(= 10 \div \frac{100}{3} = 10 \times \frac{3}{100} = \frac{3}{10}\)
In simple words: Multiply 10 by \(\frac{3}{100}\) and simplify.

Exam Tip: Cancel zeros between numerator and denominator.

Question 9(v). \(\frac{3}{10} \div \frac{10}{3}\)
Answer:
\(= \frac{3}{10} \times \frac{3}{10} = \frac{9}{100}\)
In simple words: Multiply the first fraction by the reciprocal of the second.

Exam Tip: Check if cross-cancellation is possible; here it is not.

Question 9(vi). \(4 \frac{4}{5} \div \frac{3}{5}\)
Answer:
\(4 \frac{4}{5} = \frac{24}{5}\)
\(= \frac{24}{5} \div \frac{3}{5} = \frac{24}{5} \times \frac{5}{3} = \frac{24}{3} = 8\)
In simple words: Convert mixed fraction to improper fraction, then multiply by the reciprocal.

Exam Tip: 5 in numerator and denominator cancel out directly.

Question 9(vii). \(5 \frac{5}{7} \div 1 \frac{1}{10}\)
Answer:
\(5 \frac{5}{7} = \frac{40}{7}\)
\(1 \frac{1}{10} = \frac{11}{10}\)
\(= \frac{40}{7} \div \frac{11}{10} = \frac{40}{7} \times \frac{10}{11} = \frac{400}{77} = 5 \frac{15}{77}\)
In simple words: Convert both to improper fractions and multiply by the reciprocal of the divisor.

Exam Tip: Ensure proper conversion of mixed numbers before division.

Question 9(viii). \(4 \div 2 \frac{2}{5}\)
Answer:
\(2 \frac{2}{5} = \frac{12}{5}\)
\(= 4 \div \frac{12}{5} = 4 \times \frac{5}{12} = \frac{5}{3} = 1 \frac{2}{3}\)
In simple words: Write 4 as \(\frac{4}{1}\) and multiply by the reciprocal of \(\frac{12}{5}\).

Exam Tip: Cancel 4 and 12 to get 3 in the denominator.

Question 10. A wire of length \(12 \frac{3}{5} \text{ m}\) is cut into 10 pieces of equal length. Find the length of each piece.
Answer:
Total length of wire = \(12 \frac{3}{5} \text{ m} = \frac{63}{5} \text{ m}\)
Number of pieces = 10
Length of each piece = \(\frac{63}{5} \div 10 = \frac{63}{5} \times \frac{1}{10} = \frac{63}{50} = 1 \frac{13}{50} \text{ m}\)
In simple words: Divide the total length by the number of equal pieces.

Exam Tip: Division by a whole number is equivalent to multiplying by its reciprocal.

Question 11. In a charity show Rs 6496 were collected by selling some tickets. If the price of each ticket was Rs \(50 \frac{3}{4}\), how many tickets were sold?
Answer:
Total collection = Rs 6496
Price of each ticket = Rs \(50 \frac{3}{4} = \text{Rs } \frac{203}{4}\)
Number of tickets sold = \(6496 \div \frac{203}{4} = 6496 \times \frac{4}{203}\)
Since \(6496 \div 203 = 32\):
Number of tickets = \(32 \times 4 = 128\)
In simple words: Divide total money collected by the price of one ticket.

Exam Tip: Perform long division carefully when dividing large numbers.

12. Find the product:

Question 12(i). \(2.506 \times 1000\)
Answer:
\(= 2506\)
In simple words: Shift the decimal point 3 places to the right.

Exam Tip: Multiplying by 1000 moves the decimal three places to the right.

Question 12(ii). \(100 \times 0.005\)
Answer:
\(= 0.5\)
In simple words: Shift the decimal point 2 places to the right.

Exam Tip: 100 has two zeros, so move the decimal point two places right.

Question 12(iii). \(3.4 \times 17\)
Answer:
\(34 \times 17 = 578\)
Since there is 1 decimal place: \(57.8\)
In simple words: Multiply ignoring the decimal, then place the decimal point after 1 digit from the right.

Exam Tip: Count total decimal places in the factors.

Question 12(iv). \(0.745 \times 12\)
Answer:
\(745 \times 12 = 8940\)
Since there are 3 decimal places: \(8.940 = 8.94\)
In simple words: Multiply as whole numbers and put the decimal point 3 places from the right.

Exam Tip: Drop trailing zeros at the end of a decimal if needed.

Question 12(v). \(1.07 \times 0.02\)
Answer:
\(107 \times 2 = 214\)
Total decimal places = \(2 + 2 = 4\)
\(= 0.0214\)
In simple words: Multiply 107 and 2, then place the decimal 4 digits from the right.

Question 12(vi). \(211.9 \times 1.13\)
Answer:
\(2119 \times 113 = 239447\)
Total decimal places = \(1 + 2 = 3\)
\(= 239.447\)
In simple words: Multiply 2119 by 113 and adjust the decimal point by 3 places.
Exam Tip: Double-check multiplication columns.

Question 12(vii). \(10.05 \times 1.05\)
Answer:
\(1005 \times 105 = 105525\)
Total decimal places = \(2 + 2 = 4\)
\(= 10.5525\)
In simple words: Multiply the numbers and place the decimal after 4 digits.

Exam Tip: Count decimal digits carefully.

Question 12(viii). \(13.01 \times 5.01\)
Answer:
\(1301 \times 501 = 651801\)
Total decimal places = \(2 + 2 = 4\)
\(= 65.1801\)
In simple words: Multiply 1301 and 501, then insert the decimal point 4 places from the right.

Exam Tip: Verify by estimation (\(13 \times 5 \approx 65\)).

Question 13. If the cost of a book is Rs 25.75, find the cost of 24 such books.
Answer:
Cost of 1 book = Rs 25.75
Cost of 24 books = \(25.75 \times 24 = \text{Rs } 618.00\)
In simple words: Multiply the cost of one book by the total number of books.

Exam Tip: Put the currency symbol in the final answer.

Question 14. One metre of cloth costs Rs 152.50. What is the cost of 10.75 metres of cloth?
Answer:
Cost of 1 m cloth = Rs 152.50
Cost of 10.75 m cloth = \(152.50 \times 10.75\)
\(15250 \times 1075 = 16393750\)
Total decimal places = \(2 + 2 = 4\)
\(= \text{Rs } 1639.375\) or Rs 1639.38
In simple words: Multiply price per metre by the total length of cloth.

Exam Tip: Round currency to two decimal places if required.

15. Divide:

Question 15(i). 142.45 by 10
Answer:
\(= 14.245\)
In simple words: Shift the decimal point one place to the left when dividing by 10.

Exam Tip: Division by 10 shifts the decimal point one place left.

Question 15(ii). 144 by 15
Answer:
\(= \frac{144}{15} = \frac{48}{5} = 9.6\)
In simple words: Divide 144 by 15 to get 9.6.

Exam Tip: Simplify the fraction first by dividing numerator and denominator by 3.

Question 15(iii). 217.44 by 18
Answer:
\(217.44 \div 18 = 12.08\)
In simple words: Perform long division of 217.44 by 18.

Exam Tip: Place the decimal point in the quotient directly above the decimal in the dividend.

Question 15(iv). 0.192 by 12
Answer:
\(0.192 \div 12 = 0.016\)
In simple words: Divide 192 by 12 to get 16, then adjust decimal places.

Exam Tip: Be careful with leading zeros in the quotient.

Question 15(v). 40.32 by 9.6
Answer:
\(\frac{40.32}{9.6} = \frac{403.2}{96} = 4.2\)
In simple words: Multiply both numbers by 10 to make the divisor a whole number, then divide.

Exam Tip: Always make the divisor a whole number before dividing decimals.

Question 15(vi). 0.768 by 1.6
Answer:
\(\frac{0.768}{1.6} = \frac{7.68}{16} = 0.48\)
In simple words: Multiply numerator and denominator by 10, then divide 7.68 by 16.

Exam Tip: Check division steps with multiplication.

Question 15(vii). 76 by 0.019
Answer:
\(\frac{76}{0.019} = \frac{76 \times 1000}{0.019 \times 1000} = \frac{76000}{19} = 4000\)
In simple words: Multiply both by 1000 to eliminate the decimal in the divisor.

Question 15(viii). 7 by 0.014
Answer:
\(\frac{7}{0.014} = \frac{7000}{14} = 500\)
In simple words: Multiply both numbers by 1000, then divide 7000 by 14.
Exam Tip: \(70 \div 14 = 5\), hence 500.

Question 16. The total weight of some bags of wheat is 1743 kg. If each bag weighs 49.8 kg, how many bags are there?
Answer:
Total weight = 1743 kg
Weight of each bag = 49.8 kg
Number of bags = \(\frac{1743}{49.8} = \frac{17430}{498} = 35\)
In simple words: Divide total weight by the weight of a single bag.

Exam Tip: Remove the decimal point by multiplying numerator and denominator by 10.

Question 17. Each side of a polygon is 2.5 cm in length. The perimeter of the polygon is 12.5 cm. How many sides does the polygon have?
Answer:
Perimeter = 12.5 cm
Length of each side = 2.5 cm
Number of sides = \(\frac{12.5}{2.5} = \frac{125}{25} = 5\)
In simple words: Divide the total perimeter by the length of one side.

Exam Tip: A polygon with 5 sides is a pentagon.

Question 18. The product of two decimals is 42.987. If one of them is 12.46, find the other.
Answer:
Product = 42.987
Given decimal = 12.46
Other decimal = \(\frac{42.987}{12.46} = \frac{42.987 \times 100}{12.46 \times 100} = \frac{4298.7}{1246} = 3.45\)
In simple words: Divide the product by the known decimal to find the other number.

Exam Tip: Equalize decimal places before division.

Question 19. In the repeating decimal \(0.1276988\dots\), which digit is in the 5267th place to right of the decimal point?
Answer:
Assuming the repeating block has a specific length (let's denote repeating digits or examine pattern length). In standard textbook problems of this type, let us assume a 6-digit repeating block (e.g., 127698 or similar):
Divide position 5267 by the period length (say 6):
\(5267 \div 6 = 877\) with a remainder of 5.
The 5th digit in the repeating block will be the answer.
In simple words: Divide the position number by the number of repeating digits and look at the remainder.

Exam Tip: The remainder corresponds directly to the position within the repeating cycle (remainder 0 means the last digit of the block).

Question 20. A sports team received Rs 9,58,394 as prize money. This money was split among 29 players and the coach. If the players got one share each and the coach got 0.875 shares, how much would one share be worth?
Answer:
Number of players = 29
Coach's share = 0.875 shares
Total shares = \(29 + 0.875 = 29.875\) shares
Total prize money = Rs 9,58,394
Value of one share = \(\frac{958394}{29.875} = \frac{958394000}{29875} = \text{Rs } 32,080.133 \dots\) (or Rs 32,080)
In simple words: Divide the total prize money by the total number of shares distributed.

Exam Tip: Add player shares and coach share to find the total denominator for division.