Chapter 1
English Language Arts
Course: Fundamental Subjects Content Knowledge 5511
Subject: Fundamental Subjects Content Knowledge5511
Chapter: Mathematics
1. Compute using rational numbers
Rational numbers are all numbers that can be expressed as a ratio of two integers, a/b, where b ≠ 0. They include positive and negative whole numbers, fractions, terminating decimals such as 0.25, and repeating decimals such as 0.666…. Rational numbers can be represented on the number line, unlike irrational numbers such as π or √2, which cannot be expressed as fractions.
Operations with rational numbers follow arithmetic rules:
- Addition and subtraction: Fractions must share a common denominator. For example, 5/12 + 7/18 requires finding the least common denominator (36). Rewriting as 15/36 + 14/36 = 29/36 ensures accuracy. With mixed numbers, conversion to improper fractions helps simplify steps.
- Multiplication: Multiply numerators and denominators directly. Simplification before multiplying reduces error. For instance, (6/14) × (7/9) = (3/7) × (7/9) = 21/63 = 1/3.
- Division: Division is handled by multiplying by the reciprocal of the divisor. For example, (8/9) ÷ (16/27) = (8/9) × (27/16) = 216/144 = 3/2. Recognizing division by zero as undefined is critical.
- Operations with decimals: Terminating or repeating decimals can be converted to fractions. Example: 0.125 = 125/1000 = 1/8.