By the end of this chapter, you will be able to:
These skills will help you solve everyday problems and make precise calculations essential in your trade work.
Compiled by: Millicent Akoth
Plumbing professionals in Kenya frequently encounter measurements and quantities that require accurate arithmetic operations to ensure efficient material use, cost estimation, and system design. Mastery of whole numbers and fractions is fundamental in interpreting blueprints, mixing materials, and cutting pipes to precise lengths. This chapter develops essential skills in handling whole numbers and fractions, enabling plumbers to perform calculations necessary for daily site tasks and project planning.
Whole numbers are the set of non-negative integers including zero, used extensively in plumbing for counting items such as fittings, fixtures, or sections of pipe.
$$\text{Whole numbers} = \{0, 1, 2, 3, 4, \ldots \}$$
Example 1: A plumber counts 15 pipe connectors needed for a project. Identify the whole number.
Given: Number of connectors = 15
$$\text{Whole number} = 15$$
Answer: 15 connectors
Example 2: A water tank contains 0 liters initially before filling. Identify the whole number representing the initial volume.
Given: Initial volume = 0 liters
$$\text{Whole number} = 0$$
Answer: 0 liters
Example 3: A contractor orders 120 meters of PVC pipes in whole meter lengths. Identify the whole number of pipe sections if each section is 1 meter.
Given: Total length = 120 m, section length = 1 m
$$\text{Number of sections} = \frac{120}{1} = 120$$
Answer: 120 sections
Example 4: A plumber installs 8 taps in a hotel. Confirm if 8 is a whole number.
Given: Number of taps = 8
$$\text{Whole number} = 8$$
Answer: 8 taps
Example 5: A site manager records zero delays on a plumbing job. Identify the whole number representing delays.
Given: Delays = 0
$$\text{Whole number} = 0$$
Answer: 0 delays
Fractions represent parts of a whole, crucial for plumbers when dealing with pipe diameters, partial measurements, or material ratios.
A fraction is expressed as
$$\frac{a}{b}$$
where \(a\) is the numerator (part) and \(b\) the denominator (whole), with \(b \neq 0\).
Example 1: A plumber measures a pipe length of \(\frac{3}{4}\) meters. Identify numerator and denominator.
Given: Fraction = \(\frac{3}{4}\)
Numerator = 3, Denominator = 4
Answer: Numerator = 3, Denominator = 4
Example 2: A pipe is cut to \(\frac{5}{8}\) meters. Express this fraction as a decimal.
Given: Fraction = \(\frac{5}{8}\)
$$\frac{5}{8} = 0.625$$
Answer: 0.625 meters
Example 3: A water flow rate is \(\frac{7}{10}\) of the maximum capacity. Express as a percentage.
Given: Fraction = \(\frac{7}{10}\)
$$\frac{7}{10} \times 100 = 70\%$$
Answer: 70% flow rate
Example 4: A pipe fitting is \(\frac{2}{3}\) of a meter long. Convert to decimal meters.
Given: Fraction = \(\frac{2}{3}\)
$$\frac{2}{3} = 0.6667$$ (rounded to 4 decimal places)
Answer: 0.6667 meters
Example 5: A plumber mixes \(\frac{1}{5}\) part of additive in a compound. If total compound is 10 liters, find additive volume.
Given: Fraction = \(\frac{1}{5}\), Total volume = 10 L
$$\text{Additive volume} = \frac{1}{5} \times 10 = 2 \text{ liters}$$
Answer: 2 liters of additive
Plumbers often add, subtract, multiply, or divide fractions when calculating pipe lengths, joint sizes, or material quantities.
For fractions with the same denominator:
$$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$$
For different denominators:
$$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$
For fractions with the same denominator:
$$\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$$
For different denominators:
$$\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$$
$$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$
$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$
Example 1 (Addition Easy): Two pipe sections measure \(\frac{1}{4}\) m and \(\frac{1}{2}\) m. Find total length.
Given: \(\frac{1}{4}\) m and \(\frac{1}{2}\) m
$$\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$
Answer: \(\frac{3}{4}\) meters
Example 2 (Subtraction Medium): A pipe is 1 meter long. Cut \(\frac{3}{8}\) m off. Find remaining length.
Given: Total length = 1 m, cut length = \(\frac{3}{8}\) m
Convert 1 m to fraction: \( \frac{8}{8} \)
$$\frac{8}{8} - \frac{3}{8} = \frac{5}{8}$$
Answer: \(\frac{5}{8}\) meters
Example 3 (Multiplication Applied): A pipe diameter is \(\frac{3}{5}\) m. Find cross-sectional area assuming circular pipe with radius half diameter. Use \(A = \pi r^2\), \(\pi = 3.14\).
Given: Diameter = \(\frac{3}{5}\) m
Calculate radius:
$$r = \frac{1}{2} \times \frac{3}{5} = \frac{3}{10}$$
Calculate area:
$$A = 3.14 \times (\frac{3}{10})^2 = 3.14 \times \frac{9}{100} = \frac{28.26}{100} = 0.2826$$
Answer: 0.2826 square meters
Example 4 (Division Hard): A water tank holds \(\frac{7}{8}\) cubic meters of water. Water is divided equally into \(\frac{1}{4}\) cubic meter containers. Find number of containers.
Given: Total volume = \(\frac{7}{8}\) m³, container volume = \(\frac{1}{4}\) m³
Number of containers:
$$\frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times \frac{4}{1} = \frac{28}{8} = 3.5$$
Answer: 3.5 containers (3 full, half-filled 4th container)
Example 5 (Challenge): A plumber mixes two solutions in ratio \(\frac{2}{3}\) to \(\frac{4}{5}\) liters. Find total volume.
Given: Volumes \(\frac{2}{3}\) L and \(\frac{4}{5}\) L
Find common denominator for addition: 15
Convert fractions:
$$\frac{2}{3} = \frac{10}{15}, \quad \frac{4}{5} = \frac{12}{15}$$
Add:
$$\frac{10}{15} + \frac{12}{15} = \frac{22}{15} = 1 \frac{7}{15}$$
Answer: \(1 \frac{7}{15}\) liters
Create a free account to open more of this chapter.
Free: practical guides, quick cards, workplace scenarios and more.
Create a free accountThis chapter covered the fundamental concepts of whole numbers and fractions, including identifying whole numbers and performing basic operations with fractions such as addition, subtraction, multiplication, and division. It also explored decimals and percentages, focusing on understanding decimal values, converting between fractions, decimals, and percentages, and calculating percentage changes like discounts and increases. The chapter emphasized the importance of place value in understanding the position of digits within numbers and demonstrated how to round numbers appropriately to the nearest whole number or decimal place. Ratios and proportions were introduced to solve practical arithmetic problems involving percentages, highlighting their application in everyday calculations. Finally, the chapter explained how to express numbers in decimal form and convert them to standard form or scientific notation for easier handling of very large or very small values. Together, these topics provide a solid foundation for applying basic arithmetic in various civil engineering contexts.
A plumber measures a pipe length of 7 whole meters and cuts off \(\frac{3}{4}\) of a meter. What length of pipe remains? (2 marks)
Add \(\frac{5}{8}\) of a litre of sealant to \(\frac{1}{4}\) of a litre already in the container. What is the total volume of sealant? (2 marks)
At the start of this chapter we promised you would be able to:
Tick each one you can genuinely do.
So, are you there yet?
You're competent when you can confidently do 50% or more of what this chapter promised.
Sign in to record how you're doing.