1
🔢 Decimals to Hundredths
Decimals represent values between whole numbers, using a decimal point to separate the whole part from the fractional part.
| Position | Name | Value |
|---|
| 3.47 | Ones | 3 × 1 = 3 |
| 3.47 | Tenths | 4 × 0.1 = 0.4 |
| 3.47 | Hundredths | 7 × 0.01 = 0.07 |
Reading decimals:
3.47 → "three and forty-seven hundredths"
0.5 → "five tenths"
0.08 → "eight hundredths"
Comparing decimals:
Compare left to right, digit by digit.
0.45 vs 0.5 → tenths: 4 < 5 → 0.5 > 0.45
1.30 vs 1.3 → they are equal (trailing zeros don't change value)
Tenths = 1st decimal place (0.1). Hundredths = 2nd decimal place (0.01). To compare: line up the decimal points!
2
➗ Proper, Improper & Equivalent Fractions
| Type | Rule | Example |
|---|
| Proper | Numerator < Denominator (less than 1 whole) | 3/5, 1/4, 7/8 |
| Improper | Numerator ≥ Denominator (1 whole or more) | 7/4, 5/3, 8/8 |
| Equivalent | Different numbers, same value | 1/2 = 2/4 = 3/6 |
Finding equivalent fractions:
Multiply (or divide) numerator AND denominator by the same number.
13
=
26
=
412
(×2, ×4)
Comparing fractions:
Find equivalent fractions with the same denominator, then compare numerators.
23
vs
34
→ common denom 12 →
812
vs
912
→
3/4 > 2/3
Equivalent fractions look different but are worth exactly the same. Multiply top AND bottom by the same number — never just one!
3
🔀 Mixed Numbers
A mixed number has a whole number part AND a fraction part. They are another way to write improper fractions.
Improper fraction → Mixed number:
Divide numerator by denominator.
Quotient = whole number. Remainder = new numerator. Keep denominator.
Example: 11/4 → 11 ÷ 4 = 2 remainder 3 → 2¾
Example: 7/2 → 7 ÷ 2 = 3 remainder 1 → 3½
Mixed number → Improper fraction:
Multiply whole number by denominator, add the numerator. Keep denominator.
Example: 2¾ → (2 × 4) + 3 = 8 + 3 = 11 → 11/4
Example: 3½ → (3 × 2) + 1 = 6 + 1 = 7 → 7/2
Mixed number → improper: "Multiply the whole by the bottom, add the top, keep the bottom."
4
↔️ Integers on a Number Line
Integers include all whole numbers AND their negatives, plus zero.
Key rules:
Numbers get bigger as you move right
Numbers get smaller as you move left
Negative numbers are always less than positive numbers
Zero is neither positive nor negative
← negative numbers
positive numbers →
| Statement | True or False? |
|---|
| -3 < -1 | ✅ TRUE (−3 is further left) |
| -5 > 2 | ❌ FALSE (negatives are always less than positives) |
| 0 > -4 | ✅ TRUE (zero is to the right of all negatives) |
On a number line: RIGHT = bigger, LEFT = smaller. −1 is always greater than −100!
5
📏 Area and Perimeter — Problem Solving
📏 Perimeter
The total distance around the outside of a shape — the sum of all sides.
Think: a fence around a garden.
⬛ Area
The amount of surface space inside a shape.
Think: painting the floor of a room.
Real-life problem solving — always follow these steps:
1. Read the problem carefully and identify what is being asked
2. Identify the shape and the measurements given
3. Choose the right formula (area or perimeter?)
4. Substitute the values and calculate
5. Write your answer with the correct unit (cm, m, cm², m²)
Example: A rectangular garden is 4.5 m long and 2.8 m wide. A fence goes around the outside. How much fencing is needed?
→ This is asking for perimeter.
P = 2 × (4.5 + 2.8) = 2 × 7.3 = 14.6 m of fencing needed.
Area uses square units (cm², m²). Perimeter uses regular units (cm, m). If the problem says "cover", "paint", or "tile" → area. If it says "fence", "walk around", "border" → perimeter!