Functional Skills Mathematics

Number

# Understanding numbers and the number system

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Understanding numbers and the number system

Understanding Numbers and the Number System

Basics of Numeracy

**Place value**is the value of each digit in a number based on its position. For example, in the number 231, the 2 is in the hundreds position.**Positive numbers**are greater than zero, while**negative numbers**are less than zero. Zero is neither positive nor negative.**Fractions**represent parts of a whole. They are made of a numerator (top) and a denominator (bottom). Simplify fractions where possible.**Decimals**are another way to represent fractions and percentages. Understand how to convert between fractions, decimals and percentages.**Percentages**are fractions out of 100. They are often used to represent proportions and comparisons.

Operations

**Addition**is the process of combining numbers. The result is called the sum.**Subtraction**is finding the difference between two numbers. The result is known as the difference.**Multiplication**is the process of repeated addition. The result is called the product.**Division**is the process of distributing a set of numbers equally. The answer is known as the quotient.

Complexity of Numbers

**Square numbers**result from multiplying a number by itself.**Square roots**are the inverse operation of squaring a number.**Cubed numbers**are figures that arise from multiplying a number by itself twice.- The
**cube root**is the reverse operation of cubing a number. **Prime numbers**are numbers that have only two distinct positive divisors: 1 and itself. The first few prime numbers are: 2, 3, 5, 7, 11, and 13.**Composite numbers**are numbers that have more than two distinct positive divisors.

Number Types

**Integers**are whole numbers, both positive and negative, including zero.**Rational numbers**are numbers that can be written as a ratio of two integers. All integers, fractions, and decimals (that aren't repeating or never-ending) are examples of rational numbers.**Irrational numbers**are numbers that cannot be expressed as a ratio of two integers. They are non-repeating, non-terminating decimals.**Real numbers**comprise all rational and irrational numbers. In essence, real numbers include every number that exists on the number line.

Number Sequences

- Identify
**arithmetic sequences**, which have a constant difference between numbers. - Identify
**geometric sequences**, where each term after the first is found by multiplying the previous term by a fixed, non-zero number. - Recognise
**Fibonacci sequences**, where each number is the sum of the two preceding ones. - Calculate the
**nth term**of an arithmetic sequence.