Exam Notes
Rational Numbers 8 Class 8 Exam Prep Revision β Grandmaster Guide
A
Ayush (Founder)
Exam Strategist
Last Updated: 2026-04-20
- Rational numbers are of the form p/q where p, q are integers and q β 0
- Equivalent rational numbers are obtained by multiplying or dividing both numerator and denominator by the same non-zero integer
- Standard form of a rational number is p/q where p, q have no common factors and q β 0
- Rational numbers can be represented on a number line
- Additive inverse of a rational number p/q is -p/q
- Multiplicative inverse of a rational number p/q is q/p
- p/q + r/s = (ps + qr)/qs
- p/q - r/s = (ps - qr)/qs
- p/q Γ r/s = pr/qs
- p/q Γ· r/s = ps/qr
πͺ€ The 5 Mistakes That Cost Marks
- Not simplifying rational numbers to their standard form
- Not finding the LCM while adding or subtracting rational numbers
- Not using the distributive property while multiplying rational numbers
- Not using the additive inverse while subtracting rational numbers
- Not checking for any common factors between numerator and denominator
βοΈ 3 Solved PYQs
- Simplify: 12/16 Step 1: Find the greatest common factor of 12 and 16, which is 4 Step 2: Divide both numerator and denominator by 4 Step 3: Simplified form is 3/4
- Add: 1/6 + 1/6 Step 1: Since denominators are the same, add the numerators Step 2: 1/6 + 1/6 = 2/6 Step 3: Simplify the fraction to its standard form Step 4: 2/6 = 1/3
- Subtract: 2/3 - 1/3 Step 1: Since denominators are the same, subtract the numerators Step 2: 2/3 - 1/3 = 1/3
π§ The One Thing Most Students Get Wrong
- Most students get confused between adding and subtracting rational numbers with different denominators
- They forget to find the LCM of the denominators and add or subtract the numerators accordingly
- For example, 1/4 + 1/6 Step 1: Find the LCM of 4 and 6, which is 12 Step 2: Convert both fractions to have a denominator of 12 Step 3: 1/4 = 3/12 and 1/6 = 2/12 Step 4: Add the fractions: 3/12 + 2/12 = 5/12
ποΈ Ayush's Note
- To compare two rational numbers, convert them to equivalent fractions with the same denominator
- To add or subtract rational numbers, find the LCM of the denominators and add or subtract the numerators accordingly
- Rational numbers can be positive, negative, or zero
- The additive inverse of a rational number is obtained by changing its sign
- The multiplicative inverse of a rational number is obtained by swapping its numerator and denominator
π Last 5 Minutes Box
- Quickly revise the formulae for adding, subtracting, multiplying, and dividing rational numbers
- Make sure to simplify rational numbers to their standard form
- Practice comparing and ordering rational numbers
- Go through the solved examples and try to solve them on your own
- Make a mental note of the common mistakes that can cost marks
π Practice MCQs
1. What is the standard form of the rational number 6/8?
A) 3/4
B) 2/3
C) 1/2
D) 3/8
Answer: A) 3/4.
2. What is the sum of 1/4 and 1/6?
A) 5/12
B) 3/12
C) 2/12
D) 1/12
Answer: A) 5/12.
3. What is the difference of 2/3 and 1/3?
A) 1/3
B) 2/3
C) 3/3
D) 4/3
Answer: A) 1/3.
4. What is the product of 2/3 and 3/4?
A) 6/12
B) 1/2
C) 1/6
D) 2/6
Answer: A) 6/12.
5. What is the quotient of 3/4 and 2/3?
A) 9/8
B) 8/9
C) 3/2
D) 2/3
Answer: A) 9/8.
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π Academic References
Content verified against peer-reviewed research:
- οΏ½Let the People RapοΏ½: Cultural Rhetorics Pedagogy and Practices U... β Journal of Basic Writing (2019) π β DOI β
- Frustration and Hope: Examining StudentsοΏ½ Emotional Responses to ... β Journal of Basic Writing (2019) β DOI β
- Editors' Column β Journal of Basic Writing (2019) β DOI β
π = Open Access article
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