GRADE 8
MATHEMATICS MADE EASY
Part 1: Rational Numbers & Algebraic Expressions
Student-Friendly Study Reviewer
, Table of Contents
• 1. Rational Numbers
• 2. Comparing and Ordering Rational Numbers
• 3. Operations with Rational Numbers
• 4. Laws of Exponents
• 5. Algebraic Expressions
• 6. Combining Like Terms
• 7. Evaluating Algebraic Expressions
• 8. Worked Examples
• 9. Quick Review
• 10. 20-Item Practice Quiz
• 11. Answer Key
1. Rational Numbers
A rational number is any number that can be written as a/b, where a and b are integers and b is not zero.
Examples: 3/4, −5/2, 7 = 7/1, 0 = 0/1, and 0.25 = 1/4.
Important: A denominator can never be zero. The expression 5/0 is undefined.
2. Comparing and Ordering Rational Numbers
To compare fractions, rewrite them using a common denominator. Example: 2/3 = 10/15 and 3/5 = 9/15, so
2/3 > 3/5.
For negative numbers, the number farther to the left on the number line is smaller. Example: −5 < −2.
3. Operations with Rational Numbers
Addition: With the same signs, add absolute values and keep the sign. With different signs, subtract absolute
values and keep the sign of the number with the greater absolute value.
Examples: −2/7 + (−3/7) = −5/7; 5/8 + (−2/8) = 3/8.
Subtraction: Change subtraction into addition of the opposite: a − b = a + (−b). Example: 3/4 − 1/2 = 1/4.
Multiplication: Multiply numerators and denominators. Same signs give positive; different signs give
negative. Example: 2/3 × 5/7 = 10/21.
Division: Keep the first fraction, change division to multiplication, and use the reciprocal of the second
fraction. Example: 3/5 ÷ 2/7 = 21/10.
4. Laws of Exponents
MATHEMATICS MADE EASY
Part 1: Rational Numbers & Algebraic Expressions
Student-Friendly Study Reviewer
, Table of Contents
• 1. Rational Numbers
• 2. Comparing and Ordering Rational Numbers
• 3. Operations with Rational Numbers
• 4. Laws of Exponents
• 5. Algebraic Expressions
• 6. Combining Like Terms
• 7. Evaluating Algebraic Expressions
• 8. Worked Examples
• 9. Quick Review
• 10. 20-Item Practice Quiz
• 11. Answer Key
1. Rational Numbers
A rational number is any number that can be written as a/b, where a and b are integers and b is not zero.
Examples: 3/4, −5/2, 7 = 7/1, 0 = 0/1, and 0.25 = 1/4.
Important: A denominator can never be zero. The expression 5/0 is undefined.
2. Comparing and Ordering Rational Numbers
To compare fractions, rewrite them using a common denominator. Example: 2/3 = 10/15 and 3/5 = 9/15, so
2/3 > 3/5.
For negative numbers, the number farther to the left on the number line is smaller. Example: −5 < −2.
3. Operations with Rational Numbers
Addition: With the same signs, add absolute values and keep the sign. With different signs, subtract absolute
values and keep the sign of the number with the greater absolute value.
Examples: −2/7 + (−3/7) = −5/7; 5/8 + (−2/8) = 3/8.
Subtraction: Change subtraction into addition of the opposite: a − b = a + (−b). Example: 3/4 − 1/2 = 1/4.
Multiplication: Multiply numerators and denominators. Same signs give positive; different signs give
negative. Example: 2/3 × 5/7 = 10/21.
Division: Keep the first fraction, change division to multiplication, and use the reciprocal of the second
fraction. Example: 3/5 ÷ 2/7 = 21/10.
4. Laws of Exponents
