RBSE Solutions Class 7 Maths Chapter 2 Fractions and Decimal Numbers Exercise 2.5

Rajasthan Board RBSE Class 7 Maths Chapter 2 Fractions And Decimal Numbers Ex 2.5

Question 1. Find the product of the following:
(i) \( 7 \times 5.4 \)
(ii) \( 80.1 \times 2 \)
(iii) \( 0.08 \times 5 \)
(iv) \( 3 \times 0.86 \)
(v) \( 312.05 \times 4 \)
(vi) \( 6.08 \times 8 \)
Answer:
(i) To multiply \( 7 \times 5.4 \), we can first write 5.4 as a fraction.
\( 7 \times 5.4 = 7 \times \frac{54}{10} \)
\( \implies = \frac{7 \times 54}{10} \)
\( \implies = \frac{378}{10} \)
\( \implies = 37.8 \)
(ii) To multiply \( 80.1 \times 2 \), we can write 80.1 as a fraction.
\( 80.1 \times 2 = \frac{801}{10} \times 2 \)
\( \implies = \frac{801 \times 2}{10} \)
\( \implies = \frac{1602}{10} \)
\( \implies = 160.2 \)
(iii) To multiply \( 0.08 \times 5 \), we can write 0.08 as a fraction.
\( 0.08 \times 5 = \frac{8}{100} \times 5 \)
\( \implies = \frac{8 \times 5}{100} \)
\( \implies = \frac{40}{100} \)
\( \implies = 0.4 \)
(iv) To multiply \( 3 \times 0.86 \), we can write 0.86 as a fraction.
\( 3 \times 0.86 = 3 \times \frac{86}{100} \)
\( \implies = \frac{3 \times 86}{100} \)
\( \implies = \frac{258}{100} \)
\( \implies = 2.58 \)
(v) To multiply \( 312.05 \times 4 \), we can write 312.05 as a fraction.
\( 312.05 \times 4 = \frac{31205}{100} \times 4 \)
\( \implies = \frac{31205 \times 4}{100} \)
\( \implies = \frac{124820}{100} \)
\( \implies = 1248.2 \)
(vi) To multiply \( 6.08 \times 8 \), we can write 6.08 as a fraction.
\( 6.08 \times 8 = \frac{608}{100} \times 8 \)
\( \implies = \frac{608 \times 8}{100} \)
\( \implies = \frac{4864}{100} \)
\( \implies = 48.64 \)
In simple words: To multiply a whole number by a decimal, you can change the decimal into a fraction first. Then, multiply the whole number by the top part of the fraction and divide by the bottom part. This helps keep the decimal place correct.

🎯 Exam Tip: When multiplying decimals, count the total number of decimal places in all numbers being multiplied. Your final answer should have the same total number of decimal places.

Question 2. Find the product of the following:
(i) \( 3.72 \times 10 \)
(ii) \( 0.37 \times 10 \)
(iii) \( 0.5 \times 10 \)
(iv) \( 1.08 \times 100 \)
(v) \( 73.8 \times 10 \)
(vi) \( 0.06 \times 100 \)
(vii) \( 47.03 \times 1000 \)
(viii) \( 0.03 \times 1000 \)
(ix) \( 42.7 \times 1000 \)
Answer:
(i) \( 3.72 \times 10 = 37.2 \)
(ii) \( 0.37 \times 10 = 3.7 \)
(iii) \( 0.5 \times 10 = 5 \)
(iv) \( 1.08 \times 100 = 108 \)
(v) \( 73.8 \times 10 = 738 \)
(vi) \( 0.06 \times 100 = 6 \)
(vii) \( 47.03 \times 1000 = 47030 \)
(viii) \( 0.03 \times 1000 = 30 \)
(ix) \( 42.7 \times 1000 = 42700 \). When you multiply a decimal number by 10, 100, or 1000, the decimal point moves to the right. The number of places it moves is equal to the number of zeros in 10, 100, or 1000.
In simple words: When you multiply a decimal number by 10, 100, or 1000, you just move the decimal point to the right. Move it one place for 10, two places for 100, and three places for 1000.

🎯 Exam Tip: Remember that for every zero in the power of ten you are multiplying by (e.g., 10, 100, 1000), you shift the decimal point one place to the right.

Question 3. Find the product of the following:
(i) \( 4.2 \times 3.5 \)
(ii) \( 6.25 \times 0.5 \)
(iii) \( 1.2 \times 0.15 \)
(iv) \( 0.08 \times 0.5 \)
(v) \( 101.01 \times 0.01 \)
(vi) \( 20.05 \times 4.8 \)
Answer:
(i) To multiply \( 4.2 \times 3.5 \):
First, multiply 42 by 35 ignoring the decimal points.
\( 42 \times 35 = 1470 \)
Now, count the total number of decimal places in 4.2 (one) and 3.5 (one), which is two.
So, place the decimal point two places from the right in the product.
\( \implies 4.2 \times 3.5 = 14.70 \)
(ii) To multiply \( 6.25 \times 0.5 \):
First, multiply 625 by 5 ignoring the decimal points.
\( 625 \times 5 = 3125 \)
Now, count the total number of decimal places in 6.25 (two) and 0.5 (one), which is three.
So, place the decimal point three places from the right in the product.
\( \implies 6.25 \times 0.5 = 3.125 \)
(iii) To multiply \( 1.2 \times 0.15 \):
First, multiply 12 by 15 ignoring the decimal points.
\( 12 \times 15 = 180 \)
Now, count the total number of decimal places in 1.2 (one) and 0.15 (two), which is three.
So, place the decimal point three places from the right in the product.
\( \implies 1.2 \times 0.15 = 0.180 \)
(iv) To multiply \( 0.08 \times 0.5 \):
First, multiply 8 by 5 ignoring the decimal points.
\( 8 \times 5 = 40 \)
Now, count the total number of decimal places in 0.08 (two) and 0.5 (one), which is three.
So, place the decimal point three places from the right in the product.
\( \implies 0.08 \times 0.5 = 0.040 = 0.04 \)
(v) To multiply \( 101.01 \times 0.01 \):
First, multiply 10101 by 1 ignoring the decimal points.
\( 10101 \times 1 = 10101 \)
Now, count the total number of decimal places in 101.01 (two) and 0.01 (two), which is four.
So, place the decimal point four places from the right in the product.
\( \implies 101.01 \times 0.01 = 1.0101 \)
(vi) To multiply \( 20.05 \times 4.8 \):
First, multiply 2005 by 48 ignoring the decimal points.
\( 2005 \times 48 = 96240 \)
Now, count the total number of decimal places in 20.05 (two) and 4.8 (one), which is three.
So, place the decimal point three places from the right in the product.
\( \implies 20.05 \times 4.8 = 96.240 = 96.24 \)
In simple words: When multiplying two decimal numbers, multiply them as if they were whole numbers first. Then, count how many digits are after the decimal point in both numbers together. This total count tells you where to put the decimal point in your final answer, starting from the right.

🎯 Exam Tip: Always double-check your decimal placement. A common mistake is miscounting the total number of decimal places, which changes the value of the entire product significantly.

Question 4. Find the area of a rectangle whose length is 6.4 cm and breadth is 3.2 cm?
Answer:
Length of the rectangle \( = 6.4 \text{ cm} \)
Breadth of the rectangle \( = 3.2 \text{ cm} \)
The formula for the area of a rectangle is length multiplied by breadth.
Area of rectangle \( = \text{Length} \times \text{Breadth} \)
\( \implies = 6.4 \text{ cm} \times 3.2 \text{ cm} \)
First, multiply 64 by 32 ignoring the decimal points.
\( 64 \times 32 = 2048 \)
Since there is one decimal place in 6.4 and one in 3.2, there will be two decimal places in the product.
\( \implies = 20.48 \text{ cm}^2 \)
In simple words: To find the area of a rectangle, you just multiply its length by its breadth. Remember to count all the decimal places in your measurements to place the decimal point correctly in your final answer for the area.

🎯 Exam Tip: Always include the correct units for area, which are square units (like \( \text{cm}^2 \)), to earn full marks. Don't forget to put the decimal in the final answer.

Question 5. If a car covers 25.17 km in 1 litre of petrol, how much distance will it cover in 10.5 litres of petrol?
Answer:
Distance covered by the car in 1 litre of petrol \( = 25.17 \text{ km} \)
To find the distance covered in 10.5 litres of petrol, we multiply the distance covered per litre by 10.5.
Distance covered in 10.5 litres of petrol \( = 25.17 \times 10.5 \text{ km} \)
First, multiply 2517 by 105 ignoring the decimal points.
\( 2517 \times 105 = 264285 \)
Since there are two decimal places in 25.17 and one in 10.5, there will be a total of three decimal places in the product.
\( \implies = 264.285 \text{ km} \)
In simple words: To figure out how far the car goes with more petrol, you multiply the distance it covers with one litre by the total number of litres. This tells you the total distance travelled.

🎯 Exam Tip: In word problems involving multiplication, ensure you identify the correct values to multiply. Always label your final answer with appropriate units like 'km' for distance.

Question 6. Prakash sells 2.500 kg of ghee to Raju every month. How much ghee would Prakash have sold to Raju in 10 months?
Answer:
Quantity of ghee sold in one month \( = 2.500 \text{ kg} \)
To find the total quantity sold in 10 months, we multiply the monthly quantity by the number of months.
Quantity sold in 10 months \( = 10 \times 2.500 \text{ kg} \)
When multiplying by 10, the decimal point moves one place to the right.
\( \implies = 25.00 \text{ kg} \)
In simple words: If someone sells a certain amount of something each month, to find out the total sold over several months, you multiply the monthly amount by the number of months.

🎯 Exam Tip: Pay attention to units in word problems. Here, the unit is kilograms (kg). Also, recall the rule for multiplying decimals by powers of 10 for quick calculations.

Question 7. One side of an equilateral triangle is 4.5 cm. Find its perimeter.
Answer:
Length of one side of an equilateral triangle \( = 4.5 \text{ cm} \)
An equilateral triangle has three sides of equal length. So, its perimeter is three times the length of one side.
Perimeter of an equilateral triangle \( = 3 \times \text{length of one side} \)
\( \implies = 3 \times 4.5 \text{ cm} \)
First, multiply 3 by 45 ignoring the decimal point.
\( 3 \times 45 = 135 \)
Since there is one decimal place in 4.5, there will be one decimal place in the product.
\( \implies = 13.5 \text{ cm} \)
In simple words: For a triangle where all three sides are the same length, called an equilateral triangle, you can find its perimeter by multiplying the length of one side by three.

🎯 Exam Tip: Remember the properties of different triangles, like an equilateral triangle having all sides equal. This helps in applying the correct formula for perimeter.

Question 8. Dipika buys a box of tomatoes at the wholesale rate of Rs 16.50 per kg from the vegetable market. If the tomatoes weigh 22.5 kg then how much money will Dipika pay to the wholesaler?
Answer:
Price of 1 kg tomato \( = \text{Rs } 16.50 \)
Weight of the tomatoes \( = 22.5 \text{ kg} \)
To find the total money Dipika will pay, we multiply the price per kg by the total weight of the tomatoes.
Total money to be paid \( = 16.50 \times 22.5 \)
First, multiply 1650 by 225 ignoring the decimal points.
\( 1650 \times 225 = 371250 \)
Since there are two decimal places in 16.50 and one in 22.5, there will be a total of three decimal places in the product.
\( \implies = \text{Rs } 371.250 = \text{Rs } 371.25 \)
In simple words: To calculate the total cost, you multiply the price for one unit (like one kilogram) by the total number of units you are buying.

🎯 Exam Tip: In money-related problems, ensure your final answer is rounded to two decimal places (for paise or cents) if necessary, even if your calculation gives more. Remember to include the currency symbol (Rs).