{"id":162617,"date":"2025-02-15T04:37:05","date_gmt":"2025-02-15T04:37:05","guid":{"rendered":"https:\/\/news.gyankatta.org\/?p=162617"},"modified":"2025-02-20T07:16:56","modified_gmt":"2025-02-20T07:16:56","slug":"class-8-math-rational-numbers","status":"publish","type":"post","link":"https:\/\/news.gyankatta.org\/?p=162617","title":{"rendered":"Class 8 Math Rational Numbers Notes"},"content":{"rendered":"

Rational Numbers – Class 8<\/h1>\n

Hi kids! This chapter is all about numbers called Rational Numbers<\/span>. Don’t worry, they’re not as scary as they sound!<\/p>\n

\"Rational<\/p>\n

What are Rational Numbers?<\/h2>\n

A rational number is any number that can be written as a fraction, where both the top (numerator) and bottom (denominator) are whole numbers, and the bottom number is not zero.<\/p>\n

\n

Examples: 1\/2, 3\/4, -2\/5, 7, 0, -10\/3<\/p>\n

Non-Examples: \u221a2 (square root of 2), \u03c0 (pi)<\/p>\n<\/div>\n

Think of it like sharing a pizza! If you cut a pizza into 8 slices, and you take 3, you have 3\/8 of the pizza. That’s a rational number!<\/p>\n

Properties of Rational Numbers<\/h2>\n

1. Closure Property:<\/h3>\n

When you add, subtract, multiply, or divide (except by zero) two rational numbers, the answer is always another rational number.<\/p>\n

2. Commutative Property:<\/h3>\n

You can add or multiply rational numbers in any order. The result stays the same.<\/p>\n

\n

Example: 1\/2 + 2\/3 = 2\/3 + 1\/2<\/p>\n

Example: 1\/2 * 2\/3 = 2\/3 * 1\/2<\/p>\n<\/div>\n

3. Associative Property:<\/h3>\n

When adding or multiplying three or more rational numbers, you can group them in any way you like. The result stays the same.<\/p>\n

\n

Example: (1\/2 + 1\/3) + 1\/4 = 1\/2 + (1\/3 + 1\/4)<\/p>\n

Example: (1\/2 * 1\/3) * 1\/4 = 1\/2 * (1\/3 * 1\/4)<\/p>\n<\/div>\n

4. Distributive Property:<\/h3>\n

Multiplication distributes over addition. This means a(b + c) = ab + ac<\/p>\n

\n

Example: 1\/2 * (1\/3 + 1\/4) = (1\/2 * 1\/3) + (1\/2 * 1\/4)<\/p>\n<\/div>\n

5. Identity Property:<\/h3>\n

Adding 0 to any rational number doesn’t change it. Multiplying any rational number by 1 doesn’t change it.<\/p>\n

\n

Example: 5 + 0 = 5<\/p>\n

Example: 5 * 1 = 5<\/p>\n<\/div>\n

6. Inverse Property:<\/h3>\n

Every rational number has an additive inverse (opposite) and a multiplicative inverse (reciprocal).<\/p>\n

\n

Additive inverse of 3 is -3. 3 + (-3) = 0<\/p>\n

Multiplicative inverse of 2\/3 is 3\/2. (2\/3) * (3\/2) = 1<\/p>\n<\/div>\n

Operations on Rational Numbers<\/h2>\n

1. Addition:<\/h3>\n

To add fractions with the same denominator, add the numerators. If they have different denominators, find a common denominator first.<\/p>\n

2. Subtraction:<\/h3>\n

Similar to addition, but subtract the numerators.<\/p>\n

3. Multiplication:<\/h3>\n

Multiply the numerators and multiply the denominators.<\/p>\n

4. Division:<\/h3>\n

To divide by a fraction, multiply by its reciprocal.<\/p>\n

Keep practicing, and you’ll become a rational number whiz!<\/p>\n

Rational Numbers Questions<\/h1>\n
\n

1. Which of the following is a rational number?<\/p>\n

a) \u221a3 \u00a0\u00a0\u00a0 b) 0 \u00a0\u00a0\u00a0 c) \u03c0 \u00a0\u00a0\u00a0 d) \u221a5<\/p>\n

b) 0<\/div>\n
0 can be written as 0\/1, which fits the definition of a rational number (a fraction where the denominator is not zero). Square roots of non-perfect squares (like \u221a3 and \u221a5) and pi (\u03c0) are not rational.<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

2. What is the additive inverse of -4\/7?<\/p>\n

4\/7<\/div>\n
The additive inverse of a number is its opposite. Adding a number and its additive inverse always results in 0.<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

3. What is the multiplicative inverse (reciprocal) of 5\/2?<\/p>\n

2\/5<\/div>\n
The multiplicative inverse of a number is the number you multiply it by to get 1. To find the reciprocal, simply flip the fraction.<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

4. Simplify: 2\/3 + 1\/4<\/p>\n

11\/12<\/div>\n
Find a common denominator (12). (2\/3)*(4\/4) + (1\/4)*(3\/3) = 8\/12 + 3\/12 = 11\/12<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

5. Simplify: 3\/5 – 1\/2<\/p>\n

1\/10<\/div>\n
Find a common denominator (10). (3\/5)*(2\/2) – (1\/2)*(5\/5) = 6\/10 – 5\/10 = 1\/10<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

6. Simplify: (2\/3) * (3\/4)<\/p>\n

1\/2<\/div>\n
Multiply the numerators and multiply the denominators: (2*3)\/(3*4) = 6\/12. Then simplify to 1\/2.<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

7. Simplify: (4\/5) \u00f7 (2\/3)<\/p>\n

6\/5 or 1 1\/5<\/div>\n
To divide fractions, multiply by the reciprocal of the second fraction: (4\/5) * (3\/2) = 12\/10. Simplify to 6\/5 or the mixed number 1 1\/5.<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

8. Which property is illustrated by: 2\/5 + 3\/5 = 3\/5 + 2\/5?<\/p>\n

Commutative Property of Addition<\/div>\n
The order of addition doesn’t change the result.<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

9. Which property is illustrated by: (1\/2) * (2\/3 + 1\/4) = (1\/2 * 2\/3) + (1\/2 * 1\/4)?<\/p>\n

Distributive Property<\/div>\n
Multiplication distributes over addition.<\/div>\n
<\/div>\n<\/div>\n
\n<\/div>\n
\n

10. Is -7\/8 greater than -5\/6?<\/p>\n

No<\/div>\n
To compare, find a common denominator (-24). -7\/8 becomes -21\/24 and -5\/6 becomes -20\/24. -20\/24 is greater than -21\/24. So, -5\/6 is greater than -7\/8.<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Rational Numbers – Class 8 Hi kids! This chapter is all about numbers called Rational Numbers. Don’t worry, they’re not as scary as they sound! What are Rational Numbers? 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