GSEB Class 7 Maths Solutions Chapter 2 Fractions and Decimals Exercise 2.6

Question 1. Find:
(i) 0.2 x 6
(ii) 8 x 4.6
(iii) 2.71 x 5
(iv) 20.1 x 4
(v) 0.05 x 7
(vi) 211.02 x 4
(vii) 2 x 0.86
Answer:
(i) First, multiply 2 by 6 to get 12. As there is only one number after the decimal point in 0.2, the result will also have one decimal place. So, \( 0.2 \times 6 = 1.2 \)
(ii) Multiply 8 by 46 to get 368. Since 4.6 has one digit after the decimal point, the answer will have one decimal place. Therefore, \( 8 \times 4.6 = 36.8 \)
(iii) Start by multiplying 271 by 5, which gives 1355. Because there are two digits after the decimal point in 2.71, the final product must also have two decimal places. Hence, \( 2.71 \times 5 = 13.55 \)
(iv) First, calculate 201 multiplied by 4, which equals 804. Given that 20.1 has one digit after the decimal point, the final answer will also have one decimal place. Thus, \( 20.1 \times 4 = 80.4 \)
(v) Multiply 5 by 7 to get 35. Since there are two digits after the decimal point in 0.05, the product will contain two decimal places. So, \( 0.05 \times 7 = 0.35 \)
(vi) First, multiply 21102 by 4, which totals 84408. Because 211.02 has two numbers after the decimal point, the answer should also have two decimal places. Therefore, \( 211.02 \times 4 = 844.08 \)
(vii) Multiply 2 by 86, which yields 172. Since 0.86 has two digits after the decimal point, the final outcome will also have two decimal places. Hence, \( 2 \times 0.86 = 1.72 \)
In simple words: To find these products, first ignore the decimal points and multiply the numbers. Then, count the total number of digits after the decimal point in the original number(s). Place the decimal point in your answer so that it has the same number of digits after it.

Exam Tip: Always count the number of digits after the decimal point carefully in the original numbers to correctly place the decimal point in your answer.

Question 2. Find the area of rectangle whose length is 5.7 cm and breadth 3 cm.
Answer: The given length of the rectangle is \( 5.7 \) cm, and its breadth is \( 3 \) cm. To find the area, we multiply the length by the breadth. So, Area = \( 5.7 \text{ cm} \times 3 \text{ cm} \). This calculation can be written as \( \frac{57}{10} \times 3 \text{ cm}^2 \), which results in \( 17.1 \text{ cm}^2 \).
In simple words: To get the area of a rectangle, you just multiply its length by its width. In this case, it's 5.7 cm times 3 cm, which gives 17.1 square centimeters.

Exam Tip: Always remember the formula for the area of a rectangle: Area = Length × Breadth. Also, remember to include the correct units (e.g., cm²).

Question 3. Find:
(i) 1.3 x 10
(ii) 36.8 x 10
(iii) 153.7 x 10
(iv) 168.07 x 10
(v) 31.1 x 100
(vi) 156.1 x 100
(vii) 3.62 x 100
(viii) 43.07 x 100
(ix) 0.5 x 10
(x) 0.08 x 10
(xi) 0.9 x 100
(xii) 0.03 x 1000
Answer:
(i) When multiplying by 10, which has one zero, we shift the decimal point one place to the right. Therefore, \( 1.3 \times 10 = 13 \).
(ii) Since 10 has one zero, the decimal point moves one place to the right. Thus, \( 36.8 \times 10 = 368 \).
(iii) Because 10 has a single zero, the decimal point is moved one position to the right. As a result, \( 153.7 \times 10 = 1537 \).
(iv) As 10 contains one zero, the decimal point shifts one place to the right. Hence, \( 168.07 \times 10 = 1680.7 \).
(v) Since 100 has two zeros, the decimal point is moved two positions to the right. So, \( 31.1 \times 100 = 3110.0 \).
(vi) Because 100 contains two zeros, the decimal point moves two places to the right. Therefore, \( 156.1 \times 100 = 15610 \).
(vii) As 100 has two zeros, the decimal point is shifted two positions to the right. Thus, \( 3.62 \times 100 = 362 \).
(viii) Given that 100 has two zeros, the decimal point moves two places to the right. Hence, \( 43.07 \times 100 = 4307 \).
(ix) Since 10 has one zero, the decimal point is shifted one position to the right. As a result, \( 0.5 \times 10 = 5 \).
(x) Because 10 has a single zero, the decimal point moves one place to the right. So, \( 0.08 \times 10 = 0.8 \).
(xi) Given that 100 has two zeros, the decimal point is shifted two positions to the right. Thus, \( 0.9 \times 100 = 90 \).
(xii) Since 1000 has three zeros, the decimal point moves three places to the right. Therefore, \( 0.03 \times 1000 = 30 \).
In simple words: When you multiply a decimal number by 10, 100, or 1000, you just move the decimal point to the right. The number of places you move it is equal to how many zeros are in 10, 100, or 1000.

Exam Tip: Count the number of zeros in the multiplier (10, 100, 1000, etc.) to determine how many places to shift the decimal point to the right. Adding zeros to the end of the number might be needed before shifting.

Question 4. A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?
Answer: A two-wheeler travels \( 55.3 \) km using one liter of petrol. To calculate the distance it will cover with 10 liters, we multiply \( 55.3 \) km by 10. This gives a total distance of \( 55.3 \times 10 = 553 \) km.
In simple words: If a bike goes 55.3 km with 1 liter of fuel, it will go ten times that distance with 10 liters. So, you just multiply 55.3 by 10.

Exam Tip: For problems involving scaling quantities (like distance per liter over multiple liters), direct multiplication is the appropriate operation.

Question 5. Find:
(i) 2.5 x 0.3
(ii) 0.1 x 51.7
(iii) 0.2 x 316.8
(iv) 1.3 x 3.1
(v) 0.5 x 0.05
(vi) 11.2 x 0.15
(vii) 1.07 x 0.02
(viii) 10.05 x 1.05
(ix) 101.01 x 0.01
(x) 100.01 x 1.1
Answer:
(i) First, multiply 25 by 3 to get 75. Count the total number of digits after the decimal point in both numbers (2.5 has one, 0.3 has one, so \( 1+1=2 \)). Place the decimal point two places from the right in the product. Therefore, \( 2.5 \times 0.3 = 0.75 \).
(ii) Multiply 1 by 517, which gives 517. Count the total digits after the decimal point in both numbers (0.1 has one, 51.7 has one, so \( 1+1=2 \)). Position the decimal point two places from the right in the final result. Hence, \( 0.1 \times 51.7 = 5.17 \).
(iii) Begin by multiplying 2 by 3168, yielding 6336. Sum the decimal places from both numbers (0.2 has one, 316.8 has one, so \( 1+1=2 \)). Insert the decimal point two places from the right in the product. Thus, \( 0.2 \times 316.8 = 63.36 \).
(iv) Multiply 13 by 31 to get 403. Count the total decimal places (1.3 has one, 3.1 has one, so \( 1+1=2 \)). Place the decimal point two places from the right in the product. Therefore, \( 1.3 \times 3.1 = 4.03 \).
(v) Calculate 5 times 5, which equals 25. Add up the decimal places from both numbers (0.5 has one, 0.05 has two, so \( 1+2=3 \)). Position the decimal point three places from the right in the result. Hence, \( 0.5 \times 0.05 = 0.025 \).
(vi) First, multiply 112 by 15 to obtain 1680. Count the total number of decimal places in both factors (11.2 has one, 0.15 has two, totaling \( 1+2=3 \)). Place the decimal point three places from the right in the product. So, \( 11.2 \times 0.15 = 1.680 \).
(vii) Multiply 107 by 2 to get 214. The total number of decimal places in both numbers (1.07 has two, 0.02 has two, so \( 2+2=4 \)) indicates where to place the decimal point. Position it four places from the right in the product. Therefore, \( 1.07 \times 0.02 = 0.0214 \).
(viii) Calculate 1005 multiplied by 105, which results in 105525. Count the total decimal places from both original numbers (10.05 has two, 1.05 has two, totaling \( 2+2=4 \)). Place the decimal point four places from the right in the final answer. Hence, \( 10.05 \times 1.05 = 10.5525 \).
(ix) First, multiply 10101 by 1, which gives 10101. Sum the decimal places from both numbers (101.01 has two, 0.01 has two, so \( 2+2=4 \)). Position the decimal point four places from the right in the product. Thus, \( 101.01 \times 0.01 = 1.0101 \).
(x) Multiply 10001 by 11, which equals 110011. Count the total decimal places in both factors (100.01 has two, 1.1 has one, so \( 2+1=3 \)). Place the decimal point three places from the right in the final result. Therefore, \( 100.01 \times 1.1 = 110.011 \).
In simple words: To multiply numbers with decimals, first multiply them like whole numbers, ignoring the decimal points. Then, count all the decimal places in both of the original numbers. Your final answer must have that same total number of decimal places, counting from the right.

Exam Tip: Be extra careful when counting the total number of decimal places in both factors. A common mistake is to count them from only one number or to misplace the decimal in the product.