GSEB Class 7 Maths Solutions Chapter 2 Fractions and Decimals Exercise 2.7

Question 1. Find:
(i) \( 0.4 \div 2 \)
(ii) \( 0.35 \div 5 \)
(iii) \( 2.48 \div 4 \)
(iv) \( 65.4 \div 6 \)
(v) \( 651.2 \div 4 \)
(vi) \( 14.49 \div 7 \)
(vii) \( 3.96 \div 4 \)
(viii) \( 0.80 \div 5 \)
Answer:
(i) \( 0.4 \div 2 \)
Since \( 4 \div 2 = 2 \), and the given decimal number has one digit after the decimal point.
Thus, place the decimal point in the quotient so that there is one digit to its right.
Therefore, \( 0.4 \div 2 = 0.2 \)

(ii) \( 0.35 \div 5 \)
Since \( 35 \div 5 = 7 \), and the given decimal number has two digits after the decimal point.
Thus, place the decimal point in the quotient so that there are two digits to its right.
Therefore, \( 0.35 \div 5 = 0.07 \)

(iii) \( 2.48 \div 4 \)
Since \( 248 \div 4 = 62 \), and the given decimal number has two digits after the decimal point.
Thus, place the decimal point in the quotient so that there are two digits to its right.
Therefore, \( 2.48 \div 4 = 0.62 \)

(iv) \( 65.4 \div 6 \)
Since \( 654 \div 6 = 109 \), and the given decimal number has one digit after the decimal point.
Thus, place the decimal point in the quotient so that there is one digit to its right.
Therefore, \( 65.4 \div 6 = 10.9 \)

(v) \( 651.2 \div 4 \)
Since \( 6512 \div 4 = 1628 \), and the given decimal number has one digit after the decimal point.
Thus, place the decimal point in the quotient so that there is one digit to its right.
Therefore, \( 651.2 \div 4 = 162.8 \)

(vi) \( 14.49 \div 7 \)
Since \( 1449 \div 7 = 207 \), and the given decimal number has two digits after the decimal point.
Thus, place the decimal point in the quotient so that there are two digits to its right.
Therefore, \( 14.49 \div 7 = 2.07 \)

(vii) \( 3.96 \div 4 \)
Since \( 396 \div 4 = 99 \), and the given decimal number has two digits after the decimal point.
Thus, place the decimal point in the quotient so that there are two digits to its right.
Therefore, \( 3.96 \div 4 = 0.99 \)

(viii) \( 0.80 \div 5 \)
Since \( 80 \div 5 = 16 \), and the given decimal number has two digits after the decimal point.
Thus, place the decimal point in the quotient so that there are two digits to its right.
Therefore, \( 0.80 \div 5 = 0.16 \)
In simple words: To divide a decimal number by a whole number, first divide them as if they were both whole numbers. Then, count how many digits are after the decimal point in the original number. Place the decimal point in your answer so that the same number of digits are after it.

Exam Tip: Remember to align the decimal point in the quotient directly above the decimal point in the dividend when performing long division for decimals.

Question 2. Find:
(i) \( 4.8 \div 10 \)
(ii) \( 52.5 \div 10 \)
(iii) \( 0.7 \div 10 \)
(iv) \( 33.1 \div 10 \)
(v) \( 272.23 \div 10 \)
(vi) \( 0.56 \div 10 \)
(vii) \( 3.97 \div 10 \)
Answer:
(i) \( 4.8 \div 10 \)
Because there is one zero in 10, the decimal point in the quotient moves to the left by one place.
Therefore, \( 4.8 \div 10 = 0.48 \)

(ii) \( 52.5 \div 10 \)
Because there is one zero in 10, the decimal point in the quotient moves to the left by one place.
Therefore, \( 52.5 \div 10 = 5.25 \)

(iii) \( 0.7 \div 10 \)
Because there is one zero in 10, the decimal point in the quotient moves to the left by one place.
Therefore, \( 0.7 \div 10 = 0.07 \)

(iv) \( 33.1 \div 10 \)
Because there is one zero in 10, the decimal point in the quotient moves to the left by one place.
Therefore, \( 33.1 \div 10 = 3.31 \)

(v) \( 272.23 \div 10 \)
Because there is one zero in 10, the decimal point in the quotient moves to the left by one place.
Therefore, \( 272.23 \div 10 = 27.223 \)

(vi) \( 0.56 \div 10 \)
Because there is one zero in 10, the decimal point in the quotient moves to the left by one place.
Therefore, \( 0.56 \div 10 = 0.056 \)

(vii) \( 3.97 \div 10 \)
Because there is one zero in 10, the decimal point in the quotient moves to the left by one place.
Therefore, \( 3.97 \div 10 = 0.397 \)
In simple words: When you divide a decimal number by 10, you simply shift the decimal point one position to the left. This makes the number smaller, as you are splitting it into ten parts.

Exam Tip: For division by powers of 10, count the number of zeros in the divisor (e.g., 10, 100, 1000) and move the decimal point to the left by that many places.

Question 3. Find:
(i) \( 2.7 \div 100 \)
(ii) \( 0.3 \div 100 \)
(iii) \( 0.78 \div 100 \)
(iv) \( 432.6 \div 100 \)
(v) \( 23.6 \div 100 \)
(vi) \( 98.53 \div 100 \)
Answer:
(i) \( 2.7 \div 100 \)
Since there are two zeros in 100, the decimal point in the quotient is shifted to the left by two places.
Therefore, \( 2.7 \div 100 = 0.027 \)

(ii) \( 0.3 \div 100 \)
Since there are two zeros in 100, the decimal point in the quotient is shifted to the left by two places.
Therefore, \( 0.3 \div 100 = 0.003 \)

(iii) \( 0.78 \div 100 \)
Since there are two zeros in 100, the decimal point in the quotient is shifted to the left by two places.
Therefore, \( 0.78 \div 100 = 0.0078 \)

(iv) \( 432.6 \div 100 \)
Since there are two zeros in 100, the decimal point in the quotient is shifted to the left by two places.
Therefore, \( 432.6 \div 100 = 4.326 \)

(v) \( 23.6 \div 100 \)
Since there are two zeros in 100, the decimal point in the quotient is shifted to the left by two places.
Therefore, \( 23.6 \div 100 = 0.236 \)

(vi) \( 98.53 \div 100 \)
Since there are two zeros in 100, the decimal point in the quotient is shifted to the left by two places.
Therefore, \( 98.53 \div 100 = 0.9853 \)
In simple words: When you divide a decimal number by 100, you move the decimal point two places to the left. This is because you are dividing the number into 100 equal parts, making it significantly smaller.

Exam Tip: Be careful to add leading zeros if necessary when shifting the decimal point to ensure the correct number of decimal places.

Question 4. Find:
(i) \( 7.9 \div 1000 \)
(ii) \( 26.3 \div 1000 \)
(iii) \( 38.53 \div 1000 \)
(iv) \( 128.9 \div 1000 \)
(v) \( 0.5 \div 1000 \)
Answer:
(i) \( 7.9 \div 1000 \)
Since there are three zeros in 1000, the decimal point in the quotient is shifted to the left by 3 places.
Therefore, \( 7.9 \div 1000 = 0.0079 \)

(ii) \( 26.3 \div 1000 \)
Since there are three zeros in 1000, the decimal point in the quotient is shifted to the left by 3 places.
Therefore, \( 26.3 \div 1000 = 0.0263 \)

(iii) \( 38.53 \div 1000 \)
Since there are three zeros in 1000, the decimal point in the quotient is shifted to the left by 3 places.
Therefore, \( 38.53 \div 1000 = 0.03853 \)

(iv) \( 128.9 \div 1000 \)
Since there are three zeros in 1000, the decimal point in the quotient is shifted to the left by 3 places.
Therefore, \( 128.9 \div 1000 = 0.1289 \)

(v) \( 0.5 \div 1000 \)
Since there are three zeros in 1000, the decimal point in the quotient is shifted to the left by 3 places.
Therefore, \( 0.5 \div 1000 = 0.0005 \)
In simple words: Dividing a decimal by 1000 means moving the decimal point three spots to the left. This makes the number much smaller, as you're breaking it into a thousand pieces.

Exam Tip: Always double-check the number of zeros in the divisor to ensure you move the decimal point the correct number of places.

Question 5. Find:
(i) \( 7 \div 3.5 \)
(ii) \( 36 \div 0.2 \)
(iii) \( 3.25 \div 0.5 \)
(iv) \( 30.94 \div 0.7 \)
(v) \( 0.5 \div 0.25 \)
(vi) \( 7.75 \div 0.25 \)
(vii) \( 76.5 \div 0.15 \)
(viii) \( 37.8 \div 1.4 \)
(ix) \( 2.73 \div 1.3 \)
Answer:
(i) \( 7 \div 3.5 \)
\( 7 \div 3.5 = \frac{7}{1} \div \frac{35}{10} = \frac{7}{1} \times \frac{10}{35} = \frac{1 \times 10}{1 \times 5} = \frac{10}{5} = 2 \)

(ii) \( 36 \div 0.2 \)
\( 36 \div 0.2 = \frac{36}{1} \div \frac{2}{10} = \frac{36}{1} \times \frac{10}{2} = \frac{18 \times 10}{1 \times 1} = 180 \)

(iii) \( 3.25 \div 0.5 \)
\( 3.25 \div 0.5 = \frac{325}{100} \div \frac{5}{10} = \frac{325}{100} \times \frac{10}{5} = \frac{65 \times 1}{10 \times 1} = \frac{65}{10} = 6.5 \)

(iv) \( 30.94 \div 0.7 \)
\( 30.94 \div 0.7 = \frac{3094}{100} \div \frac{7}{10} = \frac{3094}{100} \times \frac{10}{7} = \frac{442 \times 1}{10 \times 1} = \frac{442}{10} = 44.2 \)

(v) \( 0.5 \div 0.25 \)
\( 0.5 \div 0.25 = \frac{5}{10} \div \frac{25}{100} = \frac{5}{10} \times \frac{100}{25} = \frac{1 \times 10}{1 \times 5} = \frac{10}{5} = 2 \)

(vi) \( 7.75 \div 0.25 \)
\( 7.75 \div 0.25 = \frac{775}{100} \div \frac{25}{100} = \frac{775}{100} \times \frac{100}{25} = \frac{775}{25} = 31 \)

(vii) \( 76.5 \div 0.15 \)
\( 76.5 \div 0.15 = \frac{765}{10} \div \frac{15}{100} = \frac{765}{10} \times \frac{100}{15} = \frac{51 \times 10}{1 \times 1} = 510 \)

(viii) \( 37.8 \div 1.4 \)
\( 37.8 \div 1.4 = \frac{378}{10} \div \frac{14}{10} = \frac{378}{10} \times \frac{10}{14} = \frac{27 \times 1}{1 \times 1} = 27 \)

(ix) \( 2.73 \div 1.3 \)
\( 2.73 \div 1.3 = \frac{273}{100} \div \frac{13}{10} = \frac{273}{100} \times \frac{10}{13} = \frac{21 \times 1}{10 \times 1} = \frac{21}{10} = 2.1 \)
In simple words: When dividing by a decimal, the easiest way is to change the divisor into a whole number first. You do this by multiplying both the divisor and the number being divided (dividend) by a power of 10 until the divisor no longer has a decimal. Then, perform the division as you normally would.

Exam Tip: To avoid errors when dividing decimals, always convert the divisor into a whole number by multiplying both the divisor and the dividend by the same power of 10. For example, to divide by 0.25, multiply both numbers by 100.

Question 6. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre of petrol?
Answer:
Total distance covered \( = 43.2 \) km
Quantity of petrol used \( = 2.4 \) litres
Therefore, distance covered in one litre petrol \( = \frac{\text{Total distance covered}}{\text{Total quantity of petrol}} \)
\( = \frac{43.2}{2.4} \) km
We can also write this as:
\( = \frac{432}{10} \div \frac{24}{10} \) km
\( = \frac{432}{10} \times \frac{10}{24} \) km
\( = \frac{18 \times 1}{1 \times 1} \) km
\( = 18 \) km
In simple words: To find out how much distance the vehicle travels on one liter of petrol, we simply divide the total distance covered by the total amount of petrol consumed.

Exam Tip: When solving word problems involving division of decimals, clearly identify the total amount and the rate to set up the division correctly. Converting decimals to fractions can simplify the calculation.