CBSE Class 7 Mathematics Fractions Assignment Set 04

ASSIGNMENT

FRACTIONS

Question 1. Cost per litre of milk is \(17\frac{3}{4}\) litres, find the cost of \(7\frac{2}{5}\) litres of milk? [Ans: Rs \(131\frac{7}{20}\)]
Answer: Cost of 1 litre of milk = Rs \(17\frac{3}{4}\)
Convert mixed fraction into improper fraction:
\(17\frac{3}{4} = \frac{(17 \times 4) + 3}{4} = \frac{68 + 3}{4} = \frac{71}{4}\)
Quantity of milk = \(7\frac{2}{5}\) litres
Convert mixed fraction into improper fraction:
\(7\frac{2}{5} = \frac{(7 \times 5) + 2}{5} = \frac{35 + 2}{5} = \frac{37}{5}\)
Total cost = Cost per litre \(\times\) Total quantity
Total cost = \(\frac{71}{4} \times \frac{37}{5}\)
Multiply numerators and denominators:
\(\frac{71 \times 37}{4 \times 5} = \frac{2627}{20}\)
Convert improper fraction back to mixed fraction:
\(\frac{2627}{20} = 131\frac{7}{20}\)
Total cost = Rs \(131\frac{7}{20}\)
In simple words: Multiply the price of 1 litre by the total number of litres to get the total cost.

Exam Tip: Always convert mixed fractions into improper fractions before multiplying.

Question 2. Find the area of the rectangular park which is \(41\frac{2}{3}\) m long and \(18\frac{3}{5}\) m broad. [Ans: \(775 \text{ m}^2\)]
Answer: Length of the rectangular park (\(l\)) = \(41\frac{2}{3}\) m = \(\frac{125}{3}\) m
Breadth of the rectangular park (\(b\)) = \(18\frac{3}{5}\) m = \(\frac{93}{5}\) m
Area of rectangle = \(l \times b\)
Area = \(\frac{125}{3} \times \frac{93}{5}\)
Simplify by cancelling common factors:
\(\frac{125}{5} = 25\) and \(\frac{93}{3} = 31\)
Area = \(25 \times 31 = 775 \text{ m}^2\)
In simple words: Multiply the length and breadth after converting them into improper fractions.

Exam Tip: Cancel common factors in the numerator and denominator before final multiplication to simplify calculations.

Question 3. There are 45 students in a class and \(\frac{3}{5}\) of them are boys. How many girls are there in the class. [Ans: 18 girls]
Answer: Total number of students = 45
Fraction of boys = \(\frac{3}{5}\)
Number of boys = \(\frac{3}{5} \times 45\)
Number of boys = \(3 \times 9 = 27\)
Number of girls = Total students - Number of boys
Number of girls = \(45 - 27 = 18\)
In simple words: Find the number of boys first, then subtract from the total class strength to find the number of girls.

Exam Tip: Alternatively, find the fraction of girls as \(1 - \frac{3}{5} = \frac{2}{5}\), and then calculate \(\frac{2}{5} \times 45 = 18\) directly.

Question 4. Each side of a square is \(6\frac{2}{3}\) long. Find its area and perimeter. [Ans: \(44\frac{4}{9} \text{ m}^2\)]
Answer: Side of the square (\(s\)) = \(6\frac{2}{3} = \frac{20}{3}\)
Perimeter of a square = \(4 \times s\)
Perimeter = \(4 \times \frac{20}{3} = \frac{80}{3} = 26\frac{2}{3}\)
Area of a square = \(s^2\)
Area = \(\left(\frac{20}{3}\right)^2 = \frac{20}{3} \times \frac{20}{3} = \frac{400}{9} = 44\frac{4}{9} \text{ m}^2\)
In simple words: Perimeter is 4 times the side, and area is side multiplied by side.

Exam Tip: Do not confuse perimeter formulas with area formulas; perimeter uses addition/multiplication by 4, while area uses squaring.

Question 5. A carton contains 40 boxes of nails and each weighs \(3\frac{3}{4} \text{ kg}\). How much would a carton of nails weigh? [Ans: 150 kg]
Answer: Number of boxes = 40
Weight of each box = \(3\frac{3}{4} \text{ kg} = \frac{15}{4} \text{ kg}\)
Total weight = Number of boxes \(\times\) Weight of each box
Total weight = \(40 \times \frac{15}{4}\)
Simplify: \(\frac{40}{4} = 10\)
Total weight = \(10 \times 15 = 150 \text{ kg}\)
In simple words: Multiply the number of boxes by the weight of one box to get the total weight.

Exam Tip: Always include proper units (kg) in your final answer.

Question 6. John read \(\frac{5}{8}\) of a novel consisting of 288 pages. How many pages are still left to be read? [Ans: 108 pages]
Answer: Total number of pages = 288
Fraction of pages read = \(\frac{5}{8}\)
Number of pages read = \(\frac{5}{8} \times 288\)
Simplify: \(\frac{288}{8} = 36\)
Number of pages read = \(5 \times 36 = 180\)
Number of pages left to be read = Total pages - Pages read
Pages left = \(288 - 180 = 108\)
Alternatively:
Fraction of pages left = \(1 - \frac{5}{8} = \frac{3}{8}\)
Pages left = \(\frac{3}{8} \times 288 = 3 \times 36 = 108 \text{ pages}\)
In simple words: Find the remaining fraction of the book and multiply it by the total number of pages.

Exam Tip: Finding the remaining fraction first can save calculation steps and reduce errors.