A fraction represents a part of a whole or a part of a group.
Numerator → tells how many parts we have.
Denominator → tells how many equal parts the whole is divided into.
3
5
In 3/5, 3 is the numerator and 5 is the denominator.
3 out of 5 equal parts are shaded.
Proper Fraction
Numerator is smaller than denominator.
3/7
Improper Fraction
Numerator is equal to or greater than denominator.
9/5
Mixed Number
A whole number together with a proper fraction.
2 1/3
Equivalent Fractions
Fractions having the same value.
1/2 = 2/4 = 3/6
⚖️
3. Comparing Fractions
When denominators are the same, compare the numerators.
Example: 3/8 < 5/8 because 3 < 5.
When denominators are different, convert them to equivalent fractions with a common denominator.
Example:
1/2 = 3/6
2/3 = 4/6
Therefore, 1/2 < 2/3.
Same denominator:
Add the numerators and keep the denominator.
2/7 + 3/7 = 5/7
Different denominators:
Find a common denominator first.
1/2 + 1/3
= 3/6 + 2/6
= 5/6
➖
5. Subtracting Fractions
Example:
5/8 − 2/8 = 3/8
For different denominators, first make the denominators equal.
3/4 − 1/2
= 3/4 − 2/4
= 1/4
✖️
6. Multiplying Fractions
Multiply numerator by numerator and denominator by denominator.
2/3 × 4/5 = 8/15
Keep – Change – Flip
2/3 ÷ 4/5
= 2/3 × 5/4
= 10/12 = 5/6
💡 Workbook Tip: Always simplify your final answer whenever possible.
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A turn describes how far an object or direction
rotates around a fixed point.
An angle can be understood as the amount of
turn from one direction to another.
Imagine standing in one direction. If you rotate your body,
the amount you rotate is a turn.
Example:
If you face north and turn to face east,
you have made a quarter turn.
🧭
2. Directions and Turns
Quarter Turn
Quarter turn = 90°
North → East is a quarter turn clockwise.
Half Turn
Half turn = 180°
North → South is a half turn.
Three-Quarter Turn
¾ turn = 270°
Three quarter turns make 270°.
Full Turn
Full turn = 360°
A full turn brings you back to your starting direction.
¼ turn
90°
½ turn
180°
¾ turn
270°
1 full turn
360°
Important:
One full turn is 360°. Therefore:
1 quarter = 360 ÷ 4 = 90°
1 half = 360 ÷ 2 = 180°
3 quarters = 3 × 90 = 270°
↩️
4. Clockwise and Anticlockwise
Clockwise ↻
Clockwise is the direction in which the hands
of a clock normally move.
Anticlockwise ↺
Anticlockwise means turning in the opposite
direction to the hands of a clock.
Example 1:
A student faces North and makes a quarter turn clockwise.
Which direction does the student face?
North → East
Answer: East
Example 2:
A car makes a half turn.
How many degrees has it turned?
Half turn = 180°
Answer: 180°
Example 3:
A robot makes three quarter turns.
How many degrees has it turned?
3 × 90° = 270°
Answer: 270°
💡 Remember:
Quarter → 90°
Half → 180°
Three-quarter → 270°
Full → 360°
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1. What is Measurement?
Measurement tells us how much of something there is.
We use standard units so that everyone can measure and compare things
in the same way.
Weight tells us how heavy an object is.
Capacity tells us how much liquid a container can hold.
We use units such as kilograms (kg),
grams (g), and milligrams (mg)
to measure weight.
kg
Kilogram
Used for heavier objects.
1 kg = 1000 g g
Gram
Used for lighter objects.
1000 g = 1 kg mg
Milligram
Used for very small weights.
1000 mg = 1 g Important conversions:
1 kilogram = 1000 grams
1 gram = 1000 milligrams
1 kilogram = 1,000,000 milligrams
Capacity is the amount of liquid that a container
can hold.
L
Litre
Used for larger amounts of liquid.
1 L = 1000 mL mL
Millilitre
Used for smaller amounts of liquid.
1000 mL = 1 L
A container can be partly full or completely full.
Important conversion:
1 litre = 1000 millilitres
2 litres = 2000 millilitres
½ litre = 500 millilitres
🧠
4. Choosing the Correct Unit
🏫 School Bag
A school bag is relatively heavy.
Best unit: kilograms (kg) ✏️ Pencil
A pencil is light.
Best unit: grams (g) 💧 Water Bottle
A bottle contains a measurable amount of liquid.
Best unit: litres (L) or millilitres (mL) 🥄 Medicine Spoon
A small amount of liquid is measured.
Best unit: millilitres (mL) kg → g
Multiply by 1000.
4 kg = 4 × 1000 = 4000 g
g → kg
Divide by 1000.
5000 g = 5000 ÷ 1000 = 5 kg
L → mL
Multiply by 1000.
3 L = 3000 mL
mL → L
Divide by 1000.
4000 mL = 4 L
🧮
6. Solved Word Problems
Example 1:
A bag weighs 3 kg. How many grams is this?
3 × 1000 = 3000 g
Example 2:
A bottle contains 2 L of water.
How many millilitres is this?
2 × 1000 = 2000 mL
Example 3:
A packet weighs 2500 g.
Express its weight in kilograms.
2500 ÷ 1000 = 2.5 kg
💡 Remember:
kg → g = × 1000
g → kg = ÷ 1000
L → mL = × 1000
mL → L = ÷ 1000
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