Unit 3: Class 9 Functional Math NBF Notes New Book

Introduction

Unit 3 of the new NBF Functional Mathematics Grade 9 textbook is about Budgeting, a life skill as much as a mathematics topic.

A budget is a plan for managing income and expenses so that spending never exceeds earnings, which Islam also teaches as moderation and balance. This unit uses ratio, proportion, percentages, algebraic expressions, and simple projections to help students track money, compare deals, and adjust a budget when expenses exceed income. These notes follow the new NBF book for session 2026-27.

What You Will Learn

By the end of this unit, students will be able to:

• apply ratios and proportions to allocate income across different budget categories;
• solve real-world problems involving unit rates, such as cost per item or hourly wages;
• use algebraic expressions to model financial situations such as income and expenditure balance;
• use percent increase or decrease to track changes in income or expenses over time;
• estimate future expenses and income using simple linear projection;
• apply logical reasoning to adjust a budget when expenses exceed income.

Key Topics Explained

1. Ratio and Proportion in Budgeting

A ratio is a unit-less numerical comparison between two or more quantities of the same kind, such as the 2:1 ratio of hydrogen to oxygen in water. A proportion is the equality of two or more ratios. In budgeting, ratios and proportions are used to allocate a total budget across categories such as marketing and salaries, and to compare how a new allocation changes the ratio between two categories.

2. Unit Rates and Hourly Wages

A unit rate expresses a cost or wage per single unit, found by dividing the total cost or earnings by the total quantity or hours: unit rate = total cost ÷ total quantity. Hourly wages are the amount earned per hour of work, found the same way: wage per hour = total earnings ÷ total hours.

Once a unit rate is known, proportions are used to find the cost or earnings for any other quantity or number of hours, and unit rates are also the key tool for comparing which of two deals is better value.

3. Algebraic Expressions for Income and Expenditure

Financial situations can be modelled using algebraic expressions: if income is x, expenses are y, and savings are z, the relationship is x − y = z. This simple equation can be rearranged to find any one quantity when the other two are known, and it can be adjusted to reflect a percentage increase in income or a change in expenses.

4. Percent Increase and Decrease

Percent increase and percent decrease measure how much income or an expense has changed over time. Percent increase = (increase ÷ original value) × 100%, and percent decrease = (decrease ÷ original value) × 100%. These tools help compare changes over time, identify spending trends, and make informed financial decisions.

5. Estimating Future Expenses and Income

Simple linear projection estimates future values by extending a past trend. The method has four steps: gather historical data, identify whether the trend is increasing or decreasing, calculate the average change per period, and project that change forward to estimate a future value.

6. Adjusting a Budget with Logical Reasoning

When expenses exceed income, a deficit exists, found as deficit = expenses − income. To resolve it, expenses are separated into essential items (housing, food, utilities) and non-essential items (entertainment, hobbies).

Non-essential spending is reduced first, essential costs are optimized where possible, income may be increased, and finally the budget is adjusted to restore balance, weighing the pros and cons of each change.

Worked Examples

Example 1 (Ratio allocation): A business allocates 2/5 of its Rs. 200,000 budget for marketing and 3/10 for salaries. Find the amount for each and the amount left over.
Marketing = (2/5) × 200,000 = Rs. 80,000. Salaries = (3/10) × 200,000 = Rs. 60,000.
Left over = 200,000 − (80,000 + 60,000) = Rs. 60,000.

Example 2 (Unit rate comparison): A pack of 12 bottles of juice costs $9, how much do 20 bottles cost at the same rate?
Cost of 1 bottle = 9 ÷ 12 = $0.75. Cost of 20 bottles = 20 × 0.75 = $15.

Example 3 (Percent decrease): Rahat’s expenses decrease from $2,000 to $1,800. Find the percent decrease.
Decrease = 2,000 − 1,800 = $200. Percent decrease = (200 ÷ 2,000) × 100% = 10%.

Example 4 (Linear projection): A small industry’s income was Rs. 40,000 in 2016, Rs. 42,000 in 2017, and Rs. 44,000 in 2018. Project the income for 2019.
Average annual increase = Rs. 2,000. Projected income for 2019 = 44,000 + 2,000 = Rs. 46,000.

Example 5 (Adjusting a budget): Yahyaa’s monthly income was Rs. 160,000, with expenses totalling Rs. 140,000. If his income drops to Rs. 120,000, find the deficit he must cut.
Deficit = 140,000 − 120,000 = Rs. 20,000, which Yahyaa needs to cut from his expenses, starting with non-essential spending.

Important Formulas at a Glance

Exercises in Unit 3

Exam Tips

• Convert the given fractions or percentages to the same total budget before comparing categories.
• Always divide by the quantity, not multiply, when finding a unit rate.
• State the income–expense equation clearly before substituting numbers.
• Calculate the deficit first in budget-adjustment questions, then decide which expenses to cut.
• Check whether a question asks for percent increase or percent decrease before applying the formula.

About HSA Notes

HSA Notes is a free educational platform for secondary and higher secondary students in Pakistan. It publishes solved notes, model papers, and study material aligned with the NBF, PECTAA, PCTAA, and FBISE curricula, covering Mathematics, Physics, Chemistry, Biology, Computer Science, and English. Our solutions are written by our own team, giving students clear, original, step-by-step help.

Online Classes

Students who want guided learning can join our online classes run by Hamdard Science Academy. The classes follow the new NBF book unit by unit, so Unit 3 concepts, examples, and exercises are taught in a clear order alongside these notes. To ask about the schedule, fees, or admission, email hsanotes48@gmail.com.

Conclusion

Budgeting turns everyday financial decisions into a mathematical skill, using ratio, percentage, and simple algebra. With regular practice, students not only score well in this unit but also pick up a habit of planning their own money wisely. Free solved exercises and PDF notes are available on HSA Notes, and online classes are there if you need extra support.