PRIMARY 4 MATHEMATICS LEARNING GUIDE · GUIDE 2
Fractions and decimals are two different representations of number. Primary 4 becomes difficult when students treat them as disconnected procedures instead of relationships among wholes, equal parts, sets and place values.
This guide develops improper fractions, mixed numbers, fraction of a set, fraction addition and subtraction, decimals to three decimal places, conversion between selected fractions and decimals, rounding and arithmetic. The aim is to help a learner see what the symbols mean before applying a method.
Series route: return to the Primary 4 Mathematics Learning Hub. Earlier foundation: Whole Numbers, Factors, Multiples and the Four Operations.
1. A Fraction Is a Number
The fraction 3/4 is not an instruction waiting to be completed. It is a number. It can represent three parts out of four equal parts, three quarters of a set, a quotient 3÷4, or a point on a number line.
This matters because the same fraction can be represented in several forms. Three quarters of a rectangle, 3/4 of 20 objects and the number 0.75 are connected by the same value.
Before using a fraction rule, identify the whole.
Many fraction mistakes begin because the learner loses track of what counts as one whole.
2. Proper Fractions, Improper Fractions and Mixed Numbers
A proper fraction is less than one when the numerator is smaller than the denominator. An improper fraction is at least one when the numerator is equal to or greater than the denominator. A mixed number combines a whole number and a proper fraction.
For example, 7/4 means seven quarters. Four quarters make one whole, leaving three quarters. Therefore:
7/4 = 1 3/4.
Reverse the conversion:
2 2/5 = 10/5 + 2/5 = 12/5.
The method is not a magic “multiply and add” trick. It counts how many equal fifths exist in two wholes and two additional fifths.
3. Number-Line Meaning
Place 5/4 on a number line. Since 4/4 = 1, 5/4 is one quarter beyond 1. Therefore 5/4 = 1 1/4.
Number lines help students compare fractions without relying only on numerator and denominator digits. The position of a fraction depends on the value of the whole ratio, not on which visible number is larger.
For example, 3/4 is greater than 5/8 because 3/4 = 6/8, and 6/8 > 5/8.
4. Fraction of a Set
To find 3/5 of 20, first find one fifth: 20÷5 = 4. Then take three fifths: 4×3 = 12.
This two-step interpretation reveals the structure:
whole set ÷ denominator × numerator.
The denominator tells how many equal parts the whole is divided into. The numerator tells how many of those equal parts are selected.
Reverse problem
If 3/5 of a set is 12, then one fifth is 12÷3 = 4. The whole is 4×5 = 20.
Changing the unknown tests whether the relationship is understood in both directions.
5. Equivalent Fractions Preserve Value
Equivalent fractions use different numerators and denominators to represent the same value.
1/2 = 2/4 = 3/6 = 5/10.
Multiplying numerator and denominator by the same non-zero whole number preserves the ratio between them.
This is not merely useful for simplifying. Equivalent fractions make addition, subtraction and comparison possible when denominators differ.
6. Adding Fractions With the Same Denominator
When denominators match, the size of the parts is already the same.
3/8 + 2/8 = 5/8.
We add the number of eighths. We do not add the denominators because the unit “eighth” stays unchanged.
The same idea appears in measurement: 3 cm + 2 cm = 5 cm. The unit remains centimetres. In fraction addition, the unit is the chosen part size.
7. Adding Fractions With Different Denominators
Consider 1/3 + 1/4. Thirds and quarters are different-sized parts, so they cannot be counted together directly.
Use a common denominator of 12:
1/3 = 4/12 and 1/4 = 3/12.
Therefore 1/3 + 1/4 = 7/12.
Common multiples from Guide 1 now become useful. A common denominator is not an unrelated fraction trick; it is the application of multiplicative structure.
8. Subtracting Fractions
For 5/6 − 1/4, use a common denominator of 12:
5/6 = 10/12 and 1/4 = 3/12.
10/12 − 3/12 = 7/12.
Estimate first: 5/6 is a little less than 1, and 1/4 is 0.25. The answer should be a little above one half. 7/12 is about 0.58, which is sensible.
9. Mixed Numbers in Addition and Subtraction
Suppose 1 2/3 + 2 1/6. Add the whole numbers and fraction parts:
1 + 2 = 3.
2/3 = 4/6, so 4/6 + 1/6 = 5/6.
The total is 3 5/6.
Now consider 3 1/4 − 1 3/4. One route is to convert both to improper fractions:
13/4 − 7/4 = 6/4 = 1 1/2.
Choose a representation that makes the relationship easy to control. Converting is a tool, not a requirement in every case.
10. Decimal Place Value to Three Decimal Places
Decimals extend the base-ten place-value system to values smaller than one.
In 4.372, the 3 represents 3 tenths, the 7 represents 7 hundredths and the 2 represents 2 thousandths.
Expanded form:
4.372 = 4 + 0.3 + 0.07 + 0.002.
A student who reads 4.372 as “four point three hundred seventy-two” may be seeing the digits but not the place values. Ask what each digit represents.
11. Comparing Decimals
Compare 0.6 and 0.56. Write them with equal decimal places: 0.60 and 0.56. Sixty hundredths is greater than fifty-six hundredths, so 0.6 > 0.56.
The number of digits does not determine size. Whole-number comparison habits can mislead students when applied to decimal strings.
Three-place comparison
Compare 2.305 and 2.35. Write 2.350. Since 350 thousandths is greater than 305 thousandths, 2.35 is greater.
12. Fractions and Decimals as Connected Representations
Some fractions convert easily into decimals because their denominators divide powers of ten used at this level.
3/10 = 0.3.
27/100 = 0.27.
3/4 = 75/100 = 0.75.
1/5 = 2/10 = 0.2.
The key idea is equivalent fractions. Converting a fraction to a decimal is often a place-value problem in disguise.
13. Rounding Decimals
To round 4.376 to one decimal place, identify the neighbouring tenths: 4.3 and 4.4. The midpoint is 4.35. Since 4.376 lies above the midpoint, it rounds to 4.4.
To two decimal places, 4.376 lies between 4.37 and 4.38 and is nearer 4.38. Therefore 4.38.
Rounding should be understood as choosing the nearer value on a specified place-value grid.
14. Adding and Subtracting Decimals
Place values must align.
Example: 12.45 + 3.7.
Write 3.7 as 3.70. Then:
12.45 + 3.70 = 16.15.
The decimal points align because ones are added to ones, tenths to tenths and hundredths to hundredths.
Subtraction
8.00 − 2.76 = 5.24.
Writing 8 as 8.00 makes the place-value structure visible and supports regrouping.
15. Multiplying Decimals by a One-Digit Whole Number
For 2.35×4, think of 2.35 as 235 hundredths. 235 hundredths ×4 = 940 hundredths = 9.40 = 9.4.
This place-value interpretation is more reliable than “move the decimal point” language because the decimal point has not moved arbitrarily; the numerical value has been multiplied.
16. Dividing Decimals by a One-Digit Whole Number
For 7.2÷3, think of 7.2 as 72 tenths. 72 tenths ÷3 = 24 tenths = 2.4.
Check by multiplication: 2.4×3 = 7.2.
Inverse-operation checks are especially useful in decimal calculations because misplaced place values can produce answers that still look numerically tidy.
17. Whole Number Division With a Decimal Quotient
Suppose 7 litres of juice are shared equally among 4 containers. Each container receives 7÷4 = 1.75 litres.
The quotient need not be a whole number. The division continues into tenths and hundredths because the quantity being shared is divisible into smaller equal units.
This is an important conceptual bridge between whole-number division and decimal representation.
18. Word Problems: Identify the Whole and the Unit
Example: 3/5 of the 45 pupils in a level chose a particular activity. How many pupils chose it?
One fifth of 45 is 9. Three fifths is 27. Answer: 27 pupils.
Example: A ribbon is 4.8 m long. 1.35 m is used. How much remains?
4.80 − 1.35 = 3.45 m.
Both questions require the learner to preserve a reference whole: the set of 45 pupils in the first, the original 4.8 m length in the second.
19. Fractions and Decimals in Multi-Step Problems
A tank contains 24 litres of water. 3/8 of the water is used. Then 4.5 litres are added. How much water is in the tank now?
First find 3/8 of 24: 24÷8×3 = 9 litres.
Water remaining: 24−9 = 15 litres.
Then add 4.5 litres: 15+4.5 = 19.5 litres.
Notice that the fraction and decimal operations are connected by the physical quantity. The route should be built from the story, not from chapter labels.
20. Estimation and Plausibility
Before accepting 5.84+2.19 = 80.3, estimate 6+2≈8. The claimed answer is impossible by scale. A decimal point has almost certainly been misplaced.
Before calculating 7/8−1/3 exactly, note that 7/8 is close to 1 and 1/3 is about one third, so the answer should be around one half. If exact working produces 13/24 ≈ 0.54, the result is plausible.
Estimation gives the learner a second perspective on the calculation.
21. Common Misconceptions
| Mistake | What went wrong | Repair |
|---|---|---|
| 7/4 is “impossible” because 7>4 | Fraction assumed to be always less than one | Use number line and seven quarters |
| 1/3+1/4=2/7 | Part sizes not preserved | Create equal-sized parts first |
| 0.56>0.6 | Whole-number digit comparison | Write 0.56 and 0.60 |
| 3/4=0.34 | Numerator/denominator copied into decimal places | Use equivalent fractions to hundredths |
| 2.35×4=8.120 | Digits multiplied without place-value regrouping | Interpret as 235 hundredths |
22. Practice Set
- Convert 11/4 to a mixed number.
- Convert 3 2/7 to an improper fraction.
- Find 5/6 of 42.
- If 4/7 of a set is 20, find the whole set.
- Calculate 2/3+1/4.
- Calculate 5/6−1/3.
- Calculate 1 3/4+2 1/2.
- Write 0.407 in expanded form.
- Arrange 0.58, 0.508, 0.805 and 0.85 in ascending order.
- Write 3/5 as a decimal.
- Write 0.75 as a fraction in simplest form.
- Round 6.284 to one decimal place.
- Round 6.284 to two decimal places.
- Calculate 8.45+3.7.
- Calculate 10−4.68.
- Calculate 2.45×6.
- Calculate 8.4÷4.
- Divide 9 by 4 and give the quotient as a decimal.
- A class has 40 pupils. 3/8 are in one group. How many pupils are in that group?
- A 12.5 m rope has 3.75 m cut off. Then another 2.4 m is cut off. How much remains?
23. Explained Answers
1. 2 3/4.
2. (3×7+2)/7 = 23/7.
3. 42÷6×5 = 35.
4. One seventh = 20÷4 = 5; whole = 5×7 = 35.
5. 8/12+3/12 = 11/12.
6. 5/6−2/6 = 1/2.
7. 1 3/4 + 2 2/4 = 4 1/4.
8. 0.4 + 0.007.
9. 0.508, 0.58, 0.805, 0.85.
10. 3/5 = 6/10 = 0.6.
11. 75/100 = 3/4.
12. 6.3.
13. 6.28.
14. 12.15.
15. 5.32.
16. 14.7.
17. 2.1.
18. 2.25.
19. 40÷8×3 = 15 pupils.
20. 12.5−3.75−2.4 = 6.35 m.
24. Teaching the First Weak Link
If a student struggles with mixed numbers, return to number lines and equal parts before drilling conversions. If addition with unlike denominators fails, check equivalent fractions and common multiples. If decimal comparison fails, return to place value and rewrite decimals with trailing zeros. If decimal multiplication fails, reinterpret the number as tenths or hundredths.
The repair should be narrower than the chapter but deeper than the error.
A strong mini-cycle is: one model, one symbolic example, one changed example, one word problem and one independent check.
25. Where This Guide Goes Next
Fraction and decimal understanding supports Primary 5 ratio and percentage. It also supports measurement, money, data and later algebraic reasoning. A student who understands the reference whole is better prepared for every future proportional problem.
Continue to Guide 3: Area, Perimeter, Angles, Symmetry and Nets.
Sources and Boundaries
Curriculum scope is referenced to the MOE Primary Mathematics Syllabus, updated October 2025. Original examples and explanations are independently written by eduKate Publishing.
Editorial control: Wintour House V1.0 · CivDJ · eduKate Publishing.
