Mathematics
Grade 4 - Numbers, Fractions, and Geometry
Table of Contents
Large Numbers (to Millions)
In Grade 4, we work with much larger numbers - all the way up to millions!
Place Value Chart
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Reading Large Numbers
3,456,789
Millions
Thousands
Ones
Read as: "Three million, four hundred fifty-six thousand, seven hundred eighty-nine"
Comparing Numbers
Greater than
5,000 > 3,000
Less than
2,500 < 7,500
Equal to
4,000 = 4,000
Rounding Numbers
Rounding makes numbers easier to work with by changing them to the nearest ten, hundred, thousand, etc.
The Rounding Rule
- • If the digit to the right is 0, 1, 2, 3, or 4 → Round DOWN
- • If the digit to the right is 5, 6, 7, 8, or 9 → Round UP
Examples
| Number | Round to Nearest 10 | Round to Nearest 100 | Round to Nearest 1,000 |
|---|---|---|---|
| 3,456 | 3,460 (6 rounds up) | 3,500 (5 rounds up) | 3,000 (4 rounds down) |
| 7,823 | 7,820 (3 rounds down) | 7,800 (2 rounds down) | 8,000 (8 rounds up) |
| 45,678 | 45,680 | 45,700 | 46,000 |
Multiplication & Division
Multiplying 2-Digit Numbers
Example: 34 × 56
34
× 56
204 (34 × 6)
+ 1700 (34 × 50)
1904
Long Division
Example: 756 ÷ 6
126 ← Quotient (answer)
______
6 ) 756
- 6 ← 6 × 1 = 6
____
15 ← Bring down 5
-12 ← 6 × 2 = 12
____
36 ← Bring down 6
-36 ← 6 × 6 = 36
____
0 ← No remainder
Division Terms
Dividend
Number being divided (756)
Divisor
Number we divide by (6)
Quotient
The answer (126)
Remainder
What's left over (0)
Fraction Operations
Parts of a Fraction
Adding Fractions (Same Denominator)
2+3=5
555
Add the numerators. Keep the same denominator.
Subtracting Fractions (Same Denominator)
5−2=3
888
Subtract the numerators. Keep the same denominator.
Equivalent Fractions
Equivalent fractions have the same value but different numerators and denominators.
1/2
2/4
3/6
4/8
Types of Fractions
Proper Fraction
3/4, 2/5, 1/8
Numerator < Denominator
Improper Fraction
5/3, 7/4, 9/2
Numerator > Denominator
Mixed Number
1½, 2¾, 3⅓
Whole number + fraction
Decimals
Decimals are another way to write fractions. The decimal point separates the whole number from the fractional part.
Decimal Place Values
| Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|
| 10 | 1 | . | 0.1 (1/10) | 0.01 (1/100) |
| 2 | 5 | . | 3 | 7 |
25.37 = Twenty-five and thirty-seven hundredths
Fraction to Decimal Conversion
Comparing Decimals
Compare from left to right, digit by digit:
- • 0.5 > 0.3 (5 tenths > 3 tenths)
- • 0.45 < 0.54 (4 tenths < 5 tenths)
- • 0.70 = 0.7 (same value)
Angles
An angle is formed when two lines meet at a point. We measure angles in degrees (°).
Right Angle (90°)
Forms a perfect "L" shape
Examples: corner of a book, floor meets wall
Acute Angle (< 90°)
Smaller than a right angle
Examples: 30°, 45°, 60°, 75°
Obtuse Angle (> 90°)
Larger than a right angle
Examples: 100°, 120°, 150°
Straight Angle (180°)
Forms a straight line
Two right angles = one straight angle
Quick Reference
Perimeter & Area
Perimeter
Perimeter is the distance around a shape. Add all the sides together.
Rectangle
P = 2 × (length + width)
or P = 2L + 2W
Example: L = 8 cm, W = 5 cm
P = 2 × (8 + 5) = 2 × 13 = 26 cm
Square
P = 4 × side
Example: side = 6 cm
P = 4 × 6 = 24 cm
Area
Area is the space inside a shape. Measured in square units (cm², m²).
Rectangle
A = length × width
Example: L = 8 cm, W = 5 cm
A = 8 × 5 = 40 cm²
Square
A = side × side
Example: side = 6 cm
A = 6 × 6 = 36 cm²
Remember: Perimeter = distance around (cm, m). Area = space inside (cm², m²).
Word Problems
Use the CUBES strategy to solve word problems:
Circle the numbers
Underline the question
Box key words
Eliminate extra info
Solve and check
Practice Problems
1. A farmer has 2,456 mangoes. He sells 1,789 mangoes. How many mangoes are left?
Operation: Subtraction
Answer: 2,456 − 1,789 = 667 mangoes
2. A classroom has 6 rows of chairs with 8 chairs in each row. How many chairs in total?
Operation: Multiplication
Answer: 6 × 8 = 48 chairs
3. Maria ate 2/8 of a pizza. Juan ate 3/8 of the same pizza. How much did they eat together?
Operation: Addition of fractions
Answer: 2/8 + 3/8 = 5/8 of the pizza
4. A rectangular garden is 12 meters long and 8 meters wide. What is its area?
Operation: Area = length × width
Answer: 12 × 8 = 96 square meters