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The Four Operations:
Addition (+):
Combining two or more numbers to find the total or sum.
Tip: line up numbers by place value and add from right to left.
Example:
478
+ 129
———
607
Practice Problem:
Add 3,215 + 4,678
Answer: 7,893
Subtraction (−)
Finding the difference between two numbers or how much one number is greater than another.
Tip: line up by place value and borrow if needed.
Example:
703
− 298
———
405
Practice Problem:
6,000−3,452
Multiplication (×)
Finding the total when you have equal groups of a number.
Example: 4×5 means “4 groups of 5”
Long Multiplication Example:
23
× 46
———
138 ← (23 × 6)
+ 920 ← (23 × 40, shift one place left)
———
1,058
Practice Problem:
Multiply 87×34
Answer: 2958
Division (÷)
Splitting a number into equal parts.
Example: 20÷5=4 → 20 split into 5 parts = 4 each.
Long Division Example:
Divide: 672 by 8:
8 ⟌ 672
8 goes into 6 → 0 times
8 into 67 → 8 × 8 = 64 → remainder 3
Bring down 2 → 32 ÷ 8 = 4
Answer = 84
Practice Problem:
Divide: 924÷7
Answer: 132
Indices:
What Are Indices?
An index (or exponent or power) tells you how many times to multiply a number by itself
2^4: 2 x 2 x 2 x 2
Here, 2 is the base, and 4 is the index.
Practical Question:
Write the value of 4^3
Answer: 4 x 4 x 4 = 64
Laws of Indices:
What is Standard Form?
Definition:
A number is written in standard form if it’s in the format:
a × 10^n where: 1 ≤a< 10 and n is an integer (can be positive or negative)
Use it to simplify very large or small numbers
Writing Large Numbers in Standard Form
Rule:
Move the decimal point to after the first non-zero digit
Count how many places you moved → that becomes the power of 10
The power is positive for large numbers
Writing Small Numbers in Standard Form
Rule:
Move the decimal after the first non-zero digit
Count the places → that becomes the power of 10
The power is negative for small numbers
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