RBSE Solutions Class 7 Maths Chapter 2 Fractions and Decimal Numbers Exercise 2.6

Question 1. Find:
(i) \( 0.8 \div 4 \)
(ii) \( 0.42 \div 7 \)
(iii) \( 3.96 \div 6 \)
(iv) \( 842.4 \div 4 \)
(v) \( 14.49 \div 7 \)
(vi) \( 36 \div 0.2 \)
(vii) \( 7 \div 3.5 \)
(viii) \( 0.09 \div 3 \)
Answer:
(i) To divide 0.8 by 4, we perform the division normally. \( 0.8 \div 4 = 0.2 \). When you divide a decimal number, place the decimal point in the quotient directly above the decimal point in the dividend.
(ii) To divide 0.42 by 7, we get \( 0.42 \div 7 = 0.06 \). Ensure you place the decimal point correctly in the answer.
(iii) Dividing 3.96 by 6 gives us \( 3.96 \div 6 = 0.66 \). It's like dividing 396 by 6 and then adjusting the decimal place.
(iv) When 842.4 is divided by 4, the result is \( 842.4 \div 4 = 210.6 \). This is a straightforward division problem.
(v) Dividing 14.49 by 7 results in \( 14.49 \div 7 = 2.07 \). This division involves carrying over numbers, similar to whole number division.
(vi) To divide 36 by 0.2, we first convert the divisor to a whole number by multiplying both the dividend and divisor by 10. So, \( 36 \div 0.2 = (36 \times 10) \div (0.2 \times 10) = 360 \div 2 = 180 \). Multiplying by powers of 10 makes decimal division easier.
(vii) To divide 7 by 3.5, we follow the same method: multiply both by 10. \( 7 \div 3.5 = (7 \times 10) \div (3.5 \times 10) = 70 \div 35 = 2 \). This simplifies the division greatly.
(viii) Dividing 0.09 by 3 yields \( 0.09 \div 3 = 0.03 \). The zeros after the decimal point need to be handled carefully in the quotient.
In simple words: For simple divisions, just divide the numbers and put the decimal point in the correct place. If you divide by a decimal, move the decimal point in both numbers until the divisor becomes a whole number.

🎯 Exam Tip: When dividing decimals, always make the divisor a whole number by multiplying both the dividend and divisor by the same power of 10. This makes the calculation much simpler and reduces errors.

Question 2. Find:
(i) \( 4.2 \div 10 \)
(ii) \( 98.6 \div 10 \)
(iii) \( 0.2 \div 10 \)
(iv) \( 143.2 \div 100 \)
(v) \( 86 \div 100 \)
(vi) \( 8.05 \div 100 \)
(vii) \( 44.32 \div 100 \)
(viii) \( 1.3 \div 1000 \)
(ix) \( 0.06 \div 1000 \)
Answer:
(i) When dividing by 10, move the decimal point one place to the left. So, \( 4.2 \div 10 = 0.42 \). This is a quick mental calculation.
(ii) Dividing 98.6 by 10 means moving the decimal point one place to the left. So, \( 98.6 \div 10 = 9.86 \). The value of each digit decreases by a factor of 10.
(iii) For \( 0.2 \div 10 \), move the decimal point one place left, which gives \( 0.02 \). You might need to add a zero as a placeholder.
(iv) When dividing by 100, move the decimal point two places to the left. So, \( 143.2 \div 100 = 1.432 \). This rule applies consistently.
(v) For \( 86 \div 100 \), remember 86 can be written as 86.0. Moving the decimal two places left gives \( 0.86 \). Whole numbers are treated as having a decimal at the end.
(vi) Dividing 8.05 by 100 results in \( 0.0805 \). Again, move the decimal point two places to the left.
(vii) For \( 44.32 \div 100 \), move the decimal point two places left, resulting in \( 0.4432 \). This is a simple shift.
(viii) When dividing by 1000, move the decimal point three places to the left. So, \( 1.3 \div 1000 = 0.0013 \). Add leading zeros as needed.
(ix) For \( 0.06 \div 1000 \), move the decimal point three places left. This gives \( 0.00006 \). You will need to add extra zeros to shift the decimal point correctly.
In simple words: When you divide a number by 10, 100, or 1000, just move the decimal point to the left by the number of zeros in 10, 100, or 1000. For example, dividing by 100 moves it two places left.

🎯 Exam Tip: Remember to count the number of zeros in the power of 10 (10, 100, 1000, etc.) to know how many places to shift the decimal point to the left. Add leading zeros as placeholders if needed.

Question 3.
(i) \( 1.2 \div 0.3 \)
(ii) \( 3.64 \div 0.4 \)
(iii) \( 9.6 \div 1.6 \)
(iv) \( 1.25 \div 2.5 \)
(v) \( 30.75 \div 1.5 \)
(vi) \( 4.08 \div 1.2 \)
(vii) \( 30.94 \div 0.7 \)
(viii) \( 76.5 \div 0.15 \)
(ix) \( 7.75 \div 0.25 \)
Answer:
(i) To divide 1.2 by 0.3, make the divisor a whole number by multiplying both by 10. So, \( (1.2 \times 10) \div (0.3 \times 10) = 12 \div 3 = 4 \). This simplifies the division significantly.
(ii) For \( 3.64 \div 0.4 \), multiply both by 10 to get \( 36.4 \div 4 = 9.1 \). This conversion makes the problem easier to solve.
(iii) To divide 9.6 by 1.6, multiply both by 10. \( 96 \div 16 = 6 \). This is a straightforward whole number division after the decimal shift.
(iv) For \( 1.25 \div 2.5 \), multiply both by 10 to make the divisor a whole number. \( 12.5 \div 25 = 0.5 \). Dividing a smaller number by a larger one often results in a decimal.
(v) To divide 30.75 by 1.5, multiply both by 10. \( 307.5 \div 15 = 20.5 \). This requires standard long division with a decimal in the dividend.
(vi) For \( 4.08 \div 1.2 \), multiply both by 10. \( 40.8 \div 12 = 3.4 \). Remember to place the decimal point correctly in the quotient.
(vii) To divide 30.94 by 0.7, multiply both by 10. \( 309.4 \div 7 = 44.2 \). This is a direct decimal division problem.
(viii) For \( 76.5 \div 0.15 \), multiply both by 100 to make the divisor a whole number (since 0.15 has two decimal places). \( 7650 \div 15 = 510 \). Always choose the smallest power of 10 that makes the divisor a whole number.
(ix) To divide 7.75 by 0.25, multiply both by 100. \( 775 \div 25 = 31 \). This simplifies to a simple whole number division.
In simple words: To divide by a decimal number, move the decimal point in both numbers to the right until the number you are dividing by becomes a whole number. Then, just do a normal division.

🎯 Exam Tip: Always make the divisor (the number you are dividing by) a whole number before you start dividing. Multiply both numbers by 10, 100, or 1000 depending on how many decimal places are in the divisor.

Question 4. A scooter covers a distance of 212.5 km in 5 litres of petrol. How much distance will it cover in one litre of petrol?
Answer: A scooter travels 212.5 km using 5 litres of petrol. To find the distance it covers in one litre, we need to divide the total distance by the total petrol consumed.
Distance covered in 1 litre \( = 212.5 \div 5 \)
\( = \frac{2125}{10} \div 5 \)
\( = \frac{2125}{10} \times \frac{1}{5} \)
\( = \frac{425}{10} \)
\( = 42.5 \) km.
So, the scooter will cover 42.5 km in one litre of petrol. Calculating distance per unit of fuel is a common application of division.
In simple words: To find out how far the scooter goes on just one litre of petrol, you need to divide the total distance it traveled by the total amount of petrol it used.

🎯 Exam Tip: When solving "per unit" problems, always divide the total quantity by the number of units to find the value for one unit.

Question 5. Find the average distance of the houses of Gopal, Narayan, and Krishna, given they are 1.5 km, 0.7 km, and 1.4 km away respectively.
Answer: The distances to the houses of Gopal, Narayan, and Krishna are 1.5 km, 0.7 km, and 1.4 km, respectively. To find the average distance, we add all the distances and then divide by the number of houses. Finding an average helps understand a typical value for a group of numbers.
Average distance \( = \frac{\text{Total distance}}{\text{Number of distances}} \)
Average distance \( = \frac{1.5 \text{ km} + 0.7 \text{ km} + 1.4 \text{ km}}{3} \)
Average distance \( = \frac{3.6 \text{ km}}{3} \)
Average distance \( = 1.2 \text{ km} \)
In simple words: Add up all the distances given and then divide by how many distances there are. This will tell you the average, or typical, distance.

🎯 Exam Tip: The formula for average is sum of all values divided by the count of values. Ensure all values are in the same units before adding them up.

Question 6. A car travels 891 km distance within 2.2 hours. Find the distance covered by car in 1 hour.
Answer: A car covers 891 km in 2.2 hours. To find the distance covered in 1 hour, we must divide the total distance by the total time taken. This calculation gives us the car's speed.
Distance covered in 1 hour \( = 891 \div 2.2 \) km
\( = \frac{891}{2.2} \)
To simplify, multiply the numerator and denominator by 10:
\( = \frac{891 \times 10}{2.2 \times 10} \)
\( = \frac{8910}{22} \)
\( = 40.5 \) km
So, the car covers 40.5 km in 1 hour.
In simple words: If you know how far a car travels in a certain time, you can find out how far it travels in one hour by dividing the total distance by the total hours.

🎯 Exam Tip: When calculating speed or distance covered per hour, divide the total distance by the total time. Remember to handle decimal divisors by converting them to whole numbers.

Question 7. Find the area of the square whose perimeter is 44.08 m.
Answer: The perimeter of the square is given as 44.08 m. To find the area, we first need to calculate the length of one side of the square. A square has four equal sides.
Perimeter of a square \( = 4 \times \text{side} \)
So, side of square \( = \frac{\text{Perimeter}}{4} \)
side of square \( = \frac{44.08}{4} \)
side of square \( = 11.02 \) m
Now, we can find the area. The area of a square is calculated by multiplying its side length by itself. Knowing the side length is crucial for both perimeter and area calculations.
Area of square \( = \text{side} \times \text{side} \)
Area of square \( = 11.02 \text{ m} \times 11.02 \text{ m} \)
Area of square \( = 121.4404 \text{ sq m} \)
In simple words: First, divide the perimeter of the square by 4 to find the length of one side. Then, multiply that side length by itself to get the area of the square.

🎯 Exam Tip: Remember the formulas for a square: Perimeter \( = 4 \times \text{side} \) and Area \( = \text{side} \times \text{side} \). Always find the side length first if only the perimeter is given and you need the area.

Question 8. If the area of a rectangle is 93.6 m² and its breadth is 3.6 m, find its length and perimeter.
Answer: The area of a rectangle is 93.6 m² and its breadth is 3.6 m. We know that the area of a rectangle is given by length multiplied by breadth. This relationship helps us find the unknown length.
Area of rectangle \( = \text{length} \times \text{breadth} \)
\( 93.6 = \text{length} \times 3.6 \)
So, length \( = 93.6 \div 3.6 \)
\( = \frac{936}{10} \div \frac{36}{10} \)
\( = \frac{936}{10} \times \frac{10}{36} \)
\( = \frac{936}{36} \)
\( = 26 \) m
Now that we have the length, we can calculate the perimeter of the rectangle. The perimeter is the total distance around the rectangle.
Perimeter of rectangle \( = 2 \times (\text{length} + \text{breadth}) \)
\( = 2 \times (26 + 3.6) \)
\( = 2 \times 29.6 \)
\( = 59.2 \) m
So, the length of the rectangle is 26 m and its perimeter is 59.2 m.
In simple words: First, divide the area by the breadth to find the length of the rectangle. Then, add the length and breadth and multiply by 2 to find the perimeter.

🎯 Exam Tip: Remember the formulas for a rectangle: Area \( = \text{length} \times \text{breadth} \) and Perimeter \( = 2 \times (\text{length} + \text{breadth}) \). Always perform division to find an unknown dimension when area is given.