- "Multiplication (often denoted by the cross symbol ×, by the mid-line dot operator ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic..."
The process of repeated addition, or of combining groups of equal size.
Multiplication basics: Understanding the concept of multiplication, multiplication tables or times tables, and basic multiplication facts.
Multiplication properties: Commutative property of multiplication, associative property of multiplication, and distributive property of multiplication.
Multiplication strategies: Repeated addition, skip counting, array model, area model, partial products, and lattice multiplication.
Multiplication with single-digit numbers: Multi-digit multiplication with single-digit numbers, using the standard algorithm or long multiplication method.
Multiplication with multiple-digit numbers: Multi-digit multiplication with multi-digit numbers, using the standard algorithm or long multiplication method.
Multiplying by powers of ten: Multiplying decimal numbers by powers of ten, and multiplying whole numbers by powers of ten.
Estimation: Estimating products using rounding, front-end estimation, and compatible numbers.
Word problems: Multiplication word problems involving real-world situations.
Mental math: Multiplication facts and strategies for doing mental multiplication.
Order of operations: Understanding the order in which operations should be performed when solving multiplication problems.
Factoring: Factoring numbers and using prime factorization to find the greatest common factor (GCF) and the least common multiple (LCM).
Base ten blocks: Using base ten blocks as a visual aid for understanding multiplication.
Fractions and decimals: Multiplying fractions, mixed numbers, and decimals.
Multiplication using manipulatives: Using manipulatives such as counters, blocks, and tiles to explore multiplication concepts.
Grouping: Understanding multiplication as grouping and using groupings to solve multiplication problems.
Exponents: Multiplying numbers by exponents, and understanding the relationship between multiplication and exponents.
Multiplication with negatives: Multiplying positive and negative numbers, and understanding the rules for multiplying with negatives.
Prime numbers: Identifying prime numbers and using them to solve multiplication problems.
Multiplication games and activities: Engaging in fun activities and games to practice multiplication skills.
Scalar multiplication: Multiplying a scalar by each element in a vector or matrix.
Matrix multiplication: Multiplying two matrices with the same number of rows and columns to yield a new matrix.
Cross multiplication: Multiplying the numerator of one fraction by the denominator of another and vice versa.
Dot multiplication: Also recognized as scalar product, multiplying two vectors to obtain a scalar quantity.
Partial product multiplication: A method of multiplying two or more numbers by breaking them into smaller, easier-to-multiply parts.
Lattice multiplication: A method for multiplying multi-digit numbers inspired by the techniques used by ancient Babylonians.
Multiplying by distribution: Also known as the FOIL method, multiplying two binomials together.
Long multiplication: The most commonly known and the traditional method of multiplying large numbers by hand.
Russian Peasant multiplication: A trick to multiplying two numbers that involves doubling one number and halving the other in a process that is repeated until the halved number is one.
Polynomial multiplication: Multiplying two or more polynomials together to create a new polynomial.
Vector multiplication: The umbrella term used for all kinds of multiplication among three-dimensional vectors.
Boolean multiplication: A logical operation that operates on binary values, often used in digital logic design.
- "The result of a multiplication operation is called a product."
- "The multiplication of whole numbers may be thought of as repeated addition..."
- "Both numbers can be referred to as factors."
- "For example, 4 multiplied by 3, often written as 3 × 4 and spoken as '3 times 4', can be calculated by adding 3 copies of 4 together..."
- "Here, 3 (the multiplier) and 4 (the multiplicand) are the factors, and 12 is the product."
- "One of the main properties of multiplication is the commutative property, which states in this case that adding 3 copies of 4 gives the same result as adding 4 copies of 3..."
- "Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have some given lengths."
- "Multiplication is also defined for other types of numbers, such as complex numbers, and for more abstract constructs, like matrices. For some of these more abstract constructs, the order in which the operands are multiplied together matters."
- "The inverse operation of multiplication is division."
- "For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4."
- "The division of a number other than 0 by itself equals 1."
- "A listing of the many different kinds of products used in mathematics is given in Product (mathematics)."