Social Arithmetic, Lines, and Angles Lesson

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Updated: Apr 15, 2025

Lesson

Lesson Overview

Social Arithmetic: Understanding Profit and Loss
Profit and Loss Percentages
Finding Cost Price or Selling Price Using Percentages
Interest on Bank Savings
Understanding Lines in Geometry
Types of Angles
Naming and Reading Angles
Angle Relationships in Diagrams
Solving for Unknown Angles

Mathematics helps us understand not just numbers, but also the world around us. It helps us make smart decisions, measure objects, and solve real-life problems. This lesson focuses on three important topics:

Social Arithmetic – solving problems related to money, profit, loss, and interest
Lines and Rays – understanding the basic building blocks of geometry
Angles – learning about different types of angles and how they relate to each other

Let's begin with social arithmetic, where math meets money.

Social arithmetic involves real-life situations where we buy, sell, save, or borrow money. One of the most common topics is profit and loss.

Key Terms:

Cost Price (C.P.) – The price at which something is bought
Selling Price (S.P.) – The price at which something is sold

If S.P. is greater than C.P., it's a profit.
If S.P. is less than C.P., it's a loss.

Example 1:

C.P. = Rp50,000
S.P. = Rp55,000
Profit = S.P. − C.P. = 55,000 − 50,000 = Rp5,000

Example 2:

C.P. = Rp40,000
S.P. = Rp35,000
Loss = C.P. − S.P. = 40,000 − 35,000 = Rp5,000

Understanding this difference helps you solve business or shopping-related problems.

Profit and Loss Percentages

Sometimes, we express profit or loss as a percentage. This shows how big the gain or loss is compared to the original price.

Formulas:

Profit % = (Profit ÷ C.P.) × 100
Loss % = (Loss ÷ C.P.) × 100

Example:

C.P. = Rp2,000,000
S.P. = Rp2,200,000
Profit = 200,000
Profit % = (200,000 ÷ 2,000,000) × 100 = 10%

Always use the cost price as the base when calculating percentages.

Finding Cost Price or Selling Price Using Percentages

If you know the profit or loss percent, you can find either C.P. or S.P.

Finding Cost Price:

C.P. = S.P. ÷ (1 + Profit % ÷ 100)

Example:

S.P. = Rp2,200,000
Profit = 10%
C.P. = 2,200,000 ÷ (1 + 10/100) = 2,200,000 ÷ 1.1 = Rp2,000,000

Use similar logic for losses by subtracting the loss percent instead.

Bulk Sale Calculations

Sometimes, you're asked to find the selling price for multiple items.

Example:

C.P. of 1 bread = Rp5,000
Profit = 15%
S.P. = 5,000 + (15% of 5,000) = 5,750
Selling price for 100 loaves = 100 × 5,750 = Rp575,000

Multiply the selling price of one item by the number of items to find the total.

Interest on Bank Savings

When you save money in a bank, it earns interest. Interest is a small amount paid by the bank to you for keeping your money there.

Simple Interest Formula:

Interest = (P × R × T) ÷ 100

Where:

P = principal (starting amount)
R = rate of interest per year
T = time in years

Example:

P = Rp2,000,000
R = 8%
T = 0.75 years (9 months)
Interest = (2,000,000 × 8 × 0.75) ÷ 100 = Rp120,000
Total amount = P + Interest = Rp2,120,000

This formula is used in savings, loans, and interest-based math problems.

Understanding Lines in Geometry

Geometry begins with understanding lines. Let's learn the three types of straight paths used in math.

Line

Extends forever in both directions
Has no endpoints
Drawn with arrows on both sides

Line Segment

Has two endpoints
Fixed length
A part of a line

Ray

Has one endpoint
Extends infinitely in one direction

These basic definitions help describe sides of shapes and the formation of angles.

Types of Angles

Angles are made when two rays or lines meet at a point (called the vertex). We measure angles in degrees (°).

Common Angles:

Angle Type	Measure	Description
Acute Angle	Less than 90°	Sharp, small angle
Right Angle	Exactly 90°	Makes a square corner
Obtuse Angle	More than 90°	Open wider than a right angle
Straight Angle	Exactly 180°	A flat line

Use protractors or given diagrams to identify the correct angle type.

Take This Quiz:

Lines And Angles Quiz Questions And Answers

Naming and Reading Angles

Angles are often written as ∠ABC, where the middle letter is the vertex (the point where the angle forms).

For example:

In ∠XYZ, Y is the vertex.

When you see a diagram, look for:

Where the angle opens
Which lines or rays form the sides of the angle

Understanding angle notation helps in measuring, comparing, and naming angles accurately.

Angle Relationships in Diagrams

Angles can have relationships based on how they appear in a diagram, especially when lines cross or when a transversal cuts across parallel lines.