# Fractions, Decimals, and Percentages (FDP)

Fractions, decimals, and percentages are all different ways to represent parts of a whole. Understanding how they relate and how to convert between them is key for Functional Skills Maths Level 1.

## Fractions

A fraction represents a part of a whole. It has two numbers:

• The numerator (top number) shows how many parts you have.
• The denominator (bottom number) shows how many parts make up the whole.

• Common Fractions: You should be familiar with fractions like 1/2, 1/4, 3/4, 1/3, 2/3, 1/5, 1/10.
• Finding a Fraction of a Quantity: To find a fraction of a number, divide the number by the denominator, then multiply by the numerator. For example, to find 2/3 of 30: (30 ÷ 3) × 2 = 10 × 2 = 20.
• Equivalent Fractions: These are fractions that look different but have the same value (e.g., 1/2 = 2/4). You can create equivalent fractions by multiplying or dividing both the numerator and denominator by the same number.

## Decimals

A decimal is another way to show parts of a whole, using place value. The decimal point separates whole numbers from parts of a whole.

• Place Value: The first digit after the decimal point is the tenths (e.g., 0.1), and the second is the hundredths (e.g., 0.01).
• Comparing Decimals: To compare, line up the decimal points and compare digits from left to right. For example, 0.5 is larger than 0.45.
• Adding/Subtracting Decimals: Always line up the decimal points before adding or subtracting.
• Rounding: To round a decimal to the nearest whole number, look at the first digit after the decimal point. If it's 5 or more, round up; if it's 4 or less, round down.

## Percentages

A percentage means 'out of 100'. The symbol is %.

• Common Percentages: You should know 10%, 25%, 50%, 75%, 100%.
• Finding a Percentage of a Quantity:
• To find 50%, divide by 2.
• To find 25%, divide by 4.
• To find 10%, divide by 10.
• To find other percentages, you can find 1% (divide by 100) then multiply by the percentage you need.

## Conversions

It's important to convert between FDP:

• Fraction to Decimal: Divide the numerator by the denominator (e.g., 1/2 = 1 ÷ 2 = 0.5).
• Decimal to Percentage: Multiply by 100 (e.g., 0.75 × 100 = 75%).
• Percentage to Decimal: Divide by 100 (e.g., 25% ÷ 100 = 0.25).
• Fraction to Percentage: Convert to a decimal first, then to a percentage.

Key Equivalents to Remember:

• 1/2 = 0.5 = 50%
• 1/4 = 0.25 = 25%
• 3/4 = 0.75 = 75%
• 1/10 = 0.1 = 10%

## Measures: Length, Weight, and Capacity

Understanding measures is a core skill in Functional Skills Maths. It involves knowing the correct units, how to convert between them, and how to read scales accurately. You'll need to apply these skills to solve practical problems.

## Length

Length tells us how long something is.

• Units:
• Millimetres (mm): Used for very small lengths, e.g., thickness of a coin. (1 cm = 10 mm)
• Centimetres (cm): Used for small lengths, e.g., length of a pencil, height of a book. (1 m = 100 cm)
• Metres (m): Used for medium lengths, e.g., height of a door, length of a room, fabric. (1 km = 1000 m)
• Kilometres (km): Used for long distances, e.g., distance between towns or cities.
• Tools: Rulers, tape measures.
• Conversions: To convert a larger unit to a smaller unit, you multiply. To convert a smaller unit to a larger unit, you divide. For example, to convert 2m to cm, multiply by 100: 2 x 100 = 200 cm.

## Weight (Mass)

Weight (or mass) tells us how heavy something is.

• Units:
• Grams (g): Used for light items, e.g., a bag of crisps, ingredients in a recipe.
• Kilograms (kg): Used for heavier items, e.g., a bag of sugar, a person's weight, luggage. (1 kg = 1000 g)
• Tonnes (t): Used for very heavy items, e.g., a car, a lorry, large quantities of materials. (1 t = 1000 kg)
• Tools: Kitchen scales, bathroom scales, industrial scales.
• Conversions: Similar to length, multiply to go from larger to smaller units, divide for smaller to larger. For example, to convert 500g to kg, divide by 1000: 500 ÷ 1000 = 0.5 kg.

## Capacity

Capacity tells us how much liquid a container can hold.

• Units:
• Millilitres (ml): Used for small amounts of liquid, e.g., a spoon of medicine, a can of drink.
• Litres (l): Used for larger amounts of liquid, e.g., a bottle of milk, a jug of water, petrol. (1 l = 1000 ml)
• Tools: Measuring jugs, measuring spoons.
• Conversions: For example, to convert 2.5 litres to ml, multiply by 1000: 2.5 x 1000 = 2500 ml.

## Key Skills

• Choosing appropriate units: Always select the unit that makes the most sense for the item being measured (e.g., km for a journey, g for a feather).
• Reading scales: Pay close attention to the increments (what each line represents) on a scale before reading the measurement. Scales can go up in 1s, 2s, 5s, 10s, 20s, 50s, 100s, etc.
• Calculations: Be ready to add, subtract, multiply, or divide measurements. Ensure all measurements are in the same unit before performing calculations.

## Shape, Space, Area and Perimeter

This topic is all about understanding 2D and 3D shapes, measuring their boundaries and surfaces, and how they relate to space. It's crucial for everyday tasks like decorating, DIY, and packaging.

## 2D and 3D Shapes

• 2D Shapes (Two-Dimensional): These are flat shapes you can draw on paper. They only have length and width. Examples include squares, rectangles, triangles, and circles. They have no thickness.
• 3D Shapes (Three-Dimensional): These are solid objects that take up space. They have length, width, and height (or depth). Examples include cubes, cuboids, cylinders, and spheres.
• Key parts of 3D shapes:
• Faces: The flat surfaces of a 3D shape (e.g., a cube has 6 square faces).
• Edges: Where two faces meet (e.g., a cube has 12 edges).
• Vertices: The corners where edges meet (e.g., a cube has 8 vertices).

## Perimeter

• The perimeter is the total distance around the outside edge of a 2D shape. Think of it as the length of a fence needed to go around a garden or the trim around a picture frame.
• How to calculate: To find the perimeter, you simply add up the lengths of all the sides of the shape.
• For a rectangle or square: You can add all four sides, or use the formula: Perimeter = 2 x (length + width).
• *Example*: A rectangular garden is 10 metres long and 5 metres wide. Its perimeter is 10 + 5 + 10 + 5 = 30 metres, or 2 x (10 + 5) = 2 x 15 = 30 metres.
• Units: Perimeter is measured in linear units like centimetres (cm), metres (m), or kilometres (km).

## Area

• The area is the amount of surface a 2D shape covers. Think of it as the amount of carpet needed to cover a floor or paint needed for a wall.
• How to calculate for rectangles and squares: Multiply the length by the width.
• Formula: Area = length x width.
• *Example*: A rectangular room is 4 metres long and 3 metres wide. Its area is 4 x 3 = 12 square metres.
• Estimating Area: For irregular shapes, you might be asked to estimate the area by counting the number of whole and half squares it covers on a grid.
• Units: Area is measured in square units like square centimetres (cm²), square metres (m²), or square kilometres (km²). The little '2' means 'squared' and indicates two dimensions are being multiplied.

## Symmetry

• Line symmetry occurs when a shape can be folded exactly in half, and both halves match perfectly. The fold line is called the line of symmetry. Some shapes have many lines of symmetry, others have none.
• *Example*: A square has four lines of symmetry. A rectangle has two.

## Nets of 3D Shapes

• A net is a 2D shape that can be cut out and folded along its edges to form a 3D shape. Understanding nets helps you visualise 3D objects from 2D plans.
• *Example*: A net for a cube is a flat pattern of six squares that can be folded up to make a cube.

## Space

• Understanding 'space' at Level 1 often involves comparing the size or capacity of different 3D objects, or visualising how objects fit together. For instance, determining which container holds more or identifying the correct net for a given 3D shape. It's about how much room something takes up or how much it can hold.

## Handling Data: Tables, Charts and Averages

Handling data is about collecting, organising, representing, and interpreting information. It helps us make sense of numbers and facts in everyday life. For your Functional Skills Maths Level 1 exam, you need to be confident with tables, different types of charts, and calculating averages.

## Tables

A table organises data into rows and columns. Each row and column usually has a heading that tells you what information it contains.

• Reading a table: Start by looking at the main title to understand the overall topic. Then, read the column headings and row labels carefully.
• Extracting information: To find specific data, locate the correct row and column and see where they intersect. For example, finding the price of an item in a specific size from a price list.

## Charts

Charts are visual ways to represent data, making it easier to understand trends and comparisons.

• Bar Charts: Use rectangular bars to show quantities. The height or length of each bar represents a value.
• Always check the axis labels (what each axis represents) and the scale (the numbers along the axis) to read the values accurately.
• Pictograms: Use pictures or symbols to represent data.
• A key is essential for a pictogram. The key tells you what each picture or symbol stands for (e.g., one car symbol = 10 cars). You might need to count half or quarter symbols.
• Pie Charts: Circular charts divided into sectors (slices).
• Each sector represents a proportion or fraction of a whole. The larger the sector, the larger the proportion it represents. You'll need to interpret what each slice means in relation to the whole.

## Averages

Averages are single values that summarise a set of data.

• Mean: The most common average. To calculate the mean, add up all the values in the data set and then divide the total by the number of values.
• *Formula:* (Sum of all values) / (Number of values)
• Median: The middle value in a data set when the values are arranged in order (from smallest to largest or largest to smallest).
• If there's an odd number of values, the median is the single middle value.
• If there's an even number of values, the median is the average of the two middle values.
• Mode: The value that appears most frequently in a data set.
• A data set can have one mode, more than one mode (bimodal, multimodal), or no mode if all values appear with the same frequency.
• Range: Not an average, but a measure of spread. It tells you the difference between the highest and lowest values in a data set.
• *Formula:* Highest value - Lowest value

Practice reading different types of data representations and calculating these key statistics to prepare for your exam.