Class Five Mathematics Notes: Numbers

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All Class Five Mathematics Topics

Class Five Mathematics notes for primary schools in Tanzania. Topic 1, Numbers, is free to read below: even, odd and prime numbers, factors and multiples, LCM and GCF, addition and subtraction of fractions, multiplication and division of decimals, and converting percentages, with worked examples and end-of-topic questions. The other topics are available in the Click Online Academy app.

  1. Topic 1NumbersRead below · Free
  2. Topic 2Measurement of Length, Mass and VolumeContinue in the app
  3. Topic 3Circumference and Area of CircleContinue in the app
  4. Topic 4Factors and Multiples of NumbersContinue in the app
  5. Topic 5FractionsContinue in the app
  6. Topic 6DecimalsContinue in the app
  7. Topic 7AlgebraContinue in the app
  8. Topic 8Financial MathematicsContinue in the app

Chapter One: Numbers

Mathematics • Class Five • Count, Calculate & Explore

📚 Menu

🔑 Key Terms and Concepts

Even Number
A number that is divisible by 2 (ends with 0, 2, 4, 6 or 8).
Odd Number
A number that is not divisible by 2 (ends with 1, 3, 5, 7 or 9).
Prime Number
A number that has only two factors: 1 and itself (e.g. 2, 3, 5, 7, 11).
Composite Number
A number that has more than two factors (e.g. 4, 6, 8, 9, 12).
Factor
A number that divides another number exactly (no remainder).
Multiple
The result of multiplying a number by a whole number.
LCM (Lowest Common Multiple)
The smallest number that is a multiple of two or more numbers.
GCF (Greatest Common Factor)
The largest number that divides two or more numbers exactly.
Fraction
A part of a whole (e.g. ½, ¾).
Decimal
A number with a decimal point (e.g. 0.5, 2.75).
Percentage
A number out of 100 (e.g. 25% means 25 out of 100).

🔢 Even, Odd and Prime Numbers

  • Even numbers are divisible by 2 (last digit 0, 2, 4, 6 or 8).
  • Odd numbers are not divisible by 2 (last digit 1, 3, 5, 7 or 9).
  • Prime numbers have only two factors: 1 and the number itself.
  • Composite numbers have more than two factors.
Number chart from 1 to 100 with even, odd and prime numbers shown in different colours
Figure 1: Even, odd and prime numbers on a number chart

Worked Examples

Even numbers between 10 and 20: 12, 14, 16, 18, 20
Odd numbers between 10 and 20: 11, 13, 15, 17, 19
Prime numbers less than 20: 2, 3, 5, 7, 11, 13, 17, 19
Is 15 even, odd or prime?
→ Last digit is 5 → Odd. Factors of 15: 1, 3, 15 → Composite (not prime).
2 is the only even prime number! Every other even number can be divided by 2, so it has more than two factors.

✏️ Quick Revision – Even, Odd, Prime

1. From 21, 24, 29, 35, 40 – which are even, odd and prime?

Even: 24, 40. Odd: 21, 29, 35. Prime: 29.

2. Why is 1 not a prime number?

A prime number must have exactly two factors (1 and itself). 1 has only one factor – itself.

✖️ Factors and Multiples

Factor: A number that divides another number exactly.
Multiple: The result of multiplying a number by a whole number.

A factor tree and a list of factor pairs for the number 12
Figure 2: A factor tree and factor pairs

Worked Examples

Factors of 12: 1, 2, 3, 4, 6, 12
Multiples of 6: 6, 12, 18, 24, 30, 36…
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
First five multiples of 8: 8, 16, 24, 32, 40
Every number is a multiple of itself and has 1 and itself as factors. The number 1 is a factor of every whole number!

✏️ Quick Revision – Factors & Multiples

1. List all factors of 36.

1, 2, 3, 4, 6, 9, 12, 18, 36

2. Write the first six multiples of 7.

7, 14, 21, 28, 35, 42

🔄 LCM and GCF

LCM (Lowest Common Multiple): The smallest number that is a multiple of two or more numbers.
GCF (Greatest Common Factor): The largest number that divides two or more numbers exactly.

Lists of multiples and factors of two numbers with the LCM and GCF circled
Figure 3: Finding the LCM and GCF by listing

Worked Examples

LCM of 4 and 6:
Multiples of 4: 4, 8, 12, 16, 20, 24…
Multiples of 6: 6, 12, 18, 24…
Common multiples: 12, 24… → LCM = 12
GCF of 12 and 18:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6 → GCF = 6
LCM is useful when adding fractions (common denominator). GCF helps you simplify fractions to their lowest terms!

✏️ Quick Revision – LCM & GCF

1. Find the LCM of 3 and 5.

15

2. Find the GCF of 16 and 24.

8

🍕 Addition and Subtraction of Fractions

Steps:

  1. Find the LCM of the denominators (common denominator).
  2. Convert fractions to have the common denominator.
  3. Add or subtract the numerators.
  4. Simplify if necessary.
Fraction bars showing how to add fractions that have a common denominator
Figure 4: Adding fractions using fraction bars

Worked Examples

⅔ + ⅕
LCM of 3 and 5 = 15
⅔ = 10/15, ⅕ = 3/15
10/15 + 3/15 = 13/15
¾ − ⅖
LCM of 4 and 5 = 20
¾ = 15/20, ⅖ = 8/20
15/20 − 8/20 = 7/20

Mixed Fractions

Convert mixed numbers to improper fractions first, then add or subtract.

3½ + 2⅓
3½ = 7/2, 2⅓ = 7/3
LCM of 2 and 3 = 6
7/2 = 21/6, 7/3 = 14/6
21/6 + 14/6 = 35/6 = 5⅚
A mixed number like 3½ means 3 whole ones and half of another. Converting to an improper fraction (7/2) makes calculation easier!

✏️ Quick Revision – Fractions

1. Calculate ⅗ + ⅘

3/5 + 4/5 = 7/5 = 1⅖

2. Calculate 5¼ − 3⅔

5¼ = 21/4, 3⅔ = 11/3. LCM of 4 and 3 = 12.
21/4 = 63/12, 11/3 = 44/12.
63/12 − 44/12 = 19/12 = 1⁷⁄₁₂

🔵 Multiplication and Division of Decimals

Multiplication

Steps: Multiply as whole numbers → Count total decimal places → Place the decimal point in the product.

Place value chart showing tens, ones, tenths and hundredths with the decimal point
Figure 5: A decimal place value chart
2.4 × 0.3
24 × 3 = 72
Total decimal places = 1 + 1 = 2 → 0.72
3.25 × 1.2
325 × 12 = 3900
Total decimal places = 2 + 1 = 3 → 3.900 = 3.9

Division

Divide as whole numbers and place the decimal point carefully. Round to at most three decimal places if needed.

6.4 ÷ 4 = 1.6
7.2 ÷ 5 = 1.44
9 ÷ 8 = 1.125
When multiplying decimals, the number of decimal places in the answer equals the sum of the decimal places in the numbers you multiplied!

✏️ Quick Revision – Decimals

1. Calculate 1.5 × 0.4

0.6

2. Calculate 5.6 ÷ 7

0.8

📊 Converting Percentages

“Percent” means “out of 100”.

  • Percent → Fraction: divide by 100 and simplify.
  • Percent → Decimal: divide by 100 (move the decimal point two places left).
A hundred-square grid showing the same amount as a percentage, a fraction and a decimal
Figure 6: One amount shown as a percentage, a fraction and a decimal

Worked Examples

25% = 25/100 = ¼ = 0.25
40% = 40/100 = 2/5 = 0.4
75% = 75/100 = ¾ = 0.75
60% = 60/100 = 3/5 = 0.6
100% means the whole thing! 50% is half, 25% is a quarter, and 10% is one tenth. Percentages are everywhere – discounts, test scores, and statistics!

✏️ Quick Revision – Percentages

1. Convert 80% to a fraction and a decimal.

80/100 = 4/5 = 0.8

2. Convert 12.5% to a fraction and a decimal.

12.5/100 = 1/8 = 0.125

📝 End of Topic Questions

Test yourself! Try first, then click to see the answer.

Part A: Multiple Choice Questions

1. Which of the following is a prime number?

A. 15 B. 21 C. 17 D. 27
C. 17

2. The factors of 12 are:

A. 1, 2, 3, 4, 6, 12 B. 1, 2, 4, 8 C. 2, 4, 6 only D. 12, 24, 36
A. 1, 2, 3, 4, 6, 12

3. The LCM of 4 and 6 is:

A. 2 B. 12 C. 24 D. 6
B. 12

4. The GCF of 12 and 18 is:

A. 2 B. 3 C. 6 D. 12
C. 6

5. 25% as a fraction in simplest form is:

A. 25/100 B. ¼ C. ½ D. 2/5
B. ¼

6. 2.4 × 0.3 =

A. 0.72 B. 7.2 C. 0.072 D. 72
A. 0.72

7. An even number always ends with:

A. 1, 3, 5, 7 or 9 B. 0, 2, 4, 6 or 8 C. Only 0 D. Only 2
B. 0, 2, 4, 6 or 8

8. 6.4 ÷ 4 =

A. 1.6 B. 16 C. 0.16 D. 2.4
A. 1.6

9. 40% as a decimal is:

A. 4 B. 0.4 C. 0.04 D. 40
B. 0.4

10. Which number is composite?

A. 7 B. 11 C. 9 D. 13
C. 9 (factors: 1, 3, 9)

Part B: Calculation Questions

11. Find the LCM of 6 and 8.

24

12. Find the GCF of 20 and 30.

10

13. Calculate ⅔ + ⅕

13/15

14. Calculate 3½ + 2⅓

5⅚

15. A school has 120 pupils. ⅔ of them are girls. How many girls are there?

⅔ × 120 = 80 girls

✅ Suggested Answers & Summary

Click the buttons above to reveal answers. Always try the calculations yourself first!

Key skills: Identify even/odd/prime numbers, find factors and multiples, calculate LCM and GCF, add and subtract fractions, multiply and divide decimals, and convert percentages.

Practice every day – numbers are the language of mathematics!

Chapter One: Numbers • Class Five Mathematics

Count carefully • Calculate confidently • Enjoy the magic of numbers ✨🔢

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