Here, we present the solutions for Fractions and Decimals, chapter 2 of the NCERT book. We have explained each problem so students with issues with this chapter can also solve it easily. Let us know if you have any issues with any questions.
Class 7 Maths Chapter 2 Exercise 2.5 Fractions and Decimals
1. Find:
(i) 0.4 ÷ 2
Step 1: Convert the division to a fraction: 0.4 ÷ 2 = 0.4/2.
Step 2: To eliminate the decimal, multiply both the numerator and denominator by 10 (shifting the decimal one place to the right). This gives us 4/20.
Step 3: Simplify the fraction: 4 ÷ 20 = 0.2.
Final Answer: 0.4 ÷ 2 = 0.2.
(ii) 0.35 ÷ 5
Step 1: Convert the division to a fraction: 0.35 ÷ 5 = 0.35/5.
Step 2: Eliminate the decimal by multiplying the numerator and denominator by 100 (shifting the decimal two places to the right). This gives us 35/500.
Step 3: Simplify the fraction: 35 ÷ 500 = 0.07.
Final Answer: 0.35 ÷ 5 = 0.07.
(iii) 2.48 ÷ 4
Step 1: Convert the division to a fraction: 2.48 ÷ 4 = 2.48/4.
Step 2: To remove the decimal, multiply both the numerator and denominator by 100 (shifting the decimal two places to the right). This results in 248/400.
Step 3: Simplify the fraction: 248 ÷ 400 = 0.62.
Final Answer: 2.48 ÷ 4 = 0.62.
(iv) 65.4 ÷ 6
Step 1: Convert the division to a fraction: 65.4 ÷ 6 = 65.4/6.
Step 2: Remove the decimal by multiplying the numerator and denominator by 10 (shifting the decimal one place to the right). This results in 654/60.
Step 3: Simplify the fraction: 654 ÷ 60 = 10.9.
Final Answer: 65.4 ÷ 6 = 10.9.
(v) 651.2 ÷ 4
Step 1: Convert the division to a fraction: 651.2 ÷ 4 = 651.2/4.
Step 2: Eliminate the decimal by multiplying both numerator and denominator by 10 (shifting the decimal one place to the right). This gives us 6512/40.
Step 3: Simplify the fraction: 6512 ÷ 40 = 162.8.
Final Answer: 651.2 ÷ 4 = 162.8.
(vi) 14.49 ÷ 7
Step 1: Convert the division to a fraction: 14.49 ÷ 7 = 14.49/7.
Step 2: Remove the decimal by multiplying both numerator and denominator by 100 (shifting the decimal two places to the right). This results in 1449/700.
Step 3: Simplify the fraction: 1449 ÷ 700 = 2.07.
Final Answer: 14.49 ÷ 7 = 2.07.
(vii) 3.96 ÷ 4
Step 1: Convert the division to a fraction: 3.96 ÷ 4 = 3.96/4.
Step 2: To remove the decimal, multiply both the numerator and denominator by 100 (shifting the decimal two places to the right). This gives us 396/400.
Step 3: Simplify the fraction: 396 ÷ 400 = 0.99.
Final Answer: 3.96 ÷ 4 = 0.99.
(viii) 0.80 ÷ 5
Step 1: Convert the division to a fraction: 0.80 ÷ 5 = 0.80/5.
Step 2: Eliminate the decimal by multiplying the numerator and denominator by 100 (shifting the decimal two places to the right). This results in 80/500.
Step 3: Simplify the fraction: 80 ÷ 500 = 0.16.
Final Answer: 0.80 ÷ 5 = 0.16.
2. Find:
(i) 4.8 ÷ 10
Step 1: Convert the division to a fraction: 4.8 ÷ 10 = 4.8/10.
Step 2: To eliminate the decimal, multiply both the numerator and denominator by 10 (shifting the decimal one place to the right). This gives us 48/100.
Step 3: Simplify the fraction: 48 ÷ 100 = 0.48.
Final Answer: 4.8 ÷ 10 = 0.48.
(ii) 52.5 ÷ 10
Step 1: Convert the division to a fraction: 52.5 ÷ 10 = 52.5/10.
Step 2: Remove the decimal by multiplying both the numerator and denominator by 10 (shifting the decimal one place to the right). This results in 525/100.
Step 3: Simplify the fraction: 525 ÷ 100 = 5.25.
Final Answer: 52.5 ÷ 10 = 5.25.
(iii) 0.7 ÷ 10
Step 1: Convert the division to a fraction: 0.7 ÷ 10 = 0.7/10.
Step 2: To remove the decimal, multiply both numerator and denominator by 10 (shifting the decimal one place to the right). This gives us 7/100.
Step 3: Simplify the fraction: 7 ÷ 100 = 0.07.
Final Answer: 0.7 ÷ 10 = 0.07.
(iv) 33.1 ÷ 10
Step 1: Convert the division to a fraction: 33.1 ÷ 10 = 33.1/10.
Step 2: Eliminate the decimal by multiplying the numerator and denominator by 10 (shifting the decimal one place to the right). This results in 331/100.
Step 3: Simplify the fraction: 331 ÷ 100 = 3.31.
Final Answer: 33.1 ÷ 10 = 3.31.
(v) 272.23 ÷ 10
Step 1: Convert the division to a fraction: 272.23 ÷ 10 = 272.23/10.
Step 2: To remove the decimal, multiply both numerator and denominator by 100 (shifting the decimal two places to the right). This gives us 27223/1000.
Step 3: Simplify the fraction: 27223 ÷ 1000 = 27.223.
Final Answer: 27223 ÷ 1000 = 27.223
(vi) 0.56 ÷ 10:
To divide 0.56 by 10, we move the decimal point one place to the left.
This changes 0.56 to 0.056.
Thus, 0.56 ÷ 10 = 0.056.
(vii) 3.97 ÷ 10:
For 3.97 ÷ 10, we move the decimal point one place to the left, turning 3.97 into 0.397.
Therefore, 3.97 ÷ 10 = 0.397.
3. Find:
(i) 2.7 ÷ 100:
Dividing 2.7 by 100 involves moving the decimal point two places to the left, making it 0.027.
So, 2.7 ÷ 100 = 0.027.
(ii) 0.3 ÷ 100:
For 0.3 ÷ 100, the decimal point moves two places to the left, converting 0.3 into 0.003.
Hence, 0.3 ÷ 100 = 0.003.
(iii) 0.78 ÷ 100:
In the case of 0.78 ÷ 100, shifting the decimal point two places to the left results in 0.0078.
Therefore, 0.78 ÷ 100 = 0.0078.
(iv) 432.6 ÷ 100:
Dividing 432.6 by 100 moves the decimal point two places left, turning it into 4.326.
Thus, 432.6 ÷ 100 = 4.326.
(v) 23.6 ÷ 100:
For 23.6 ÷ 100, the decimal shifts two places to the left, resulting in 0.236.
Therefore, 23.6 ÷ 100 = 0.236.
(vi) 98.53 ÷ 100:
Similarly, 98.53 ÷ 100 becomes 0.9853 when the decimal point is moved two places to the left.
So, 98.53 ÷ 100 = 0.9853.
4. Find:
(i) 7.9 ÷ 1000:
To divide 7.9 by 1000, shift the decimal point three places to the left, which turns 7.9 into 0.0079.
Hence, 7.9 ÷ 1000 = 0.0079.
(ii) 26.3 ÷ 1000:
For 26.3 ÷ 1000, moving the decimal point three places left changes it to 0.0263.
Thus, 26.3 ÷ 1000 = 0.0263.
(iii) 38.53 ÷ 1000:
In 38.53 ÷ 1000, shifting the decimal three places to the left results in 0.03853.
Therefore, 38.53 ÷ 1000 = 0.03853.
(iv) 128.9 ÷ 1000:
Dividing 128.9 by 1000, we move the decimal point three places to the left, making it 0.1289.
So, 128.9 ÷ 1000 = 0.1289.
(v) 0.5 ÷ 1000:
For 0.5 ÷ 1000, shifting the decimal three places left turns it into 0.0005.
So, 0.5 ÷ 1000 = 0.0005.
5. Find:
(i) 7 ÷ 3.5:
To divide 7 by 3.5, we convert 3.5 into a whole number by multiplying it by 10, turning it into 35.
We do the same for 7, making it 70. The fraction becomes 70/35, which simplifies to 2.
Thus, 7 ÷ 3.5 = 2.
(ii) 36 ÷ 0.2:
To divide 36 by 0.2, we multiply 0.2 by 10 to get 2, and do the same with 36, turning it into 360.
The fraction is then 360/2, which equals 180.
Therefore, 36 ÷ 0.2 = 180.
(iii) 3.25 ÷ 0.5:
We convert 0.5 to 5 by multiplying by 10, and similarly convert 3.25 to 32.5.
The division 32.5 ÷ 5 equals 6.5.
Thus, 3.25 ÷ 0.5 = 6.5.
(iv) 30.94 ÷ 0.7:
Multiplying 0.7 by 10 gives 7, and doing the same for 30.94 gives 309.4.
The division 309.4 ÷ 7 equals 44.2.
Therefore, 30.94 ÷ 0.7 = 44.2.
(v) 0.5 ÷ 0.25:
Multiplying both numbers by 100 to eliminate decimals, we get 50 ÷ 25, which is 2.
Thus, 0.5 ÷ 0.25 = 2.
(vi) 7.75 ÷ 0.25:
Multiplying 0.25 by 100 converts it to 25, and 7.75 becomes 775.
The division 775 ÷ 25 equals 31.
Hence, 7.75 ÷ 0.25 = 31.
(vii) 76.5 ÷ 0.15:
By multiplying 0.15 by 100, it becomes 15, and 76.5 turns into 7650.
The division 7650 ÷ 15 equals 510.
Therefore, 76.5 ÷ 0.15 = 510.
(viii) 37.8 ÷ 1.4:
Multiplying 1.4 by 10 gives 14, and 37.8 becomes 378.
The fraction 378 ÷ 14 simplifies to 27.
Thus, 37.8 ÷ 1.4 = 27.
(ix) 2.73 ÷ 1.3:
Multiplying both 1.3 and 2.73 by 10, we get 13 and 27.3, respectively.
The division 27.3 ÷ 13 equals approximately 2.1.
Therefore, 2.73 ÷ 1.3 ≈ 2.1.
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?
Solution: Divide the total distance (43.2 km) by the petrol used (2.4 litres) to find the distance per litre.
43.2 km ÷ 2.4 litres = 18 km per litre.
Hence, the vehicle covers 18 km in one litre of petrol.
