# Multiply and Divide Fractions & Mixed Numbers

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**Featured Multiply and Dividing Fractions & Mixed Numbers Vocabulary Words**

**Common Denominator** – A common denominator is the least common multiple of the denominators of two or more fractions. It is necessary for adding or subtracting fractions with different denominators.

**Composite Number** – A composite number is a positive integer that has more than two distinct positive divisors. In other words, it is not a prime number.

**Denominator** – In a fraction, the denominator is the bottom number that represents the total number of equal parts into which a whole is divided. It indicates the size or value of each part.

**Divide** – Division is a mathematical operation that separates a quantity into equal parts or groups. When dividing fractions or mixed numbers, it involves finding how many times one quantity fits into another.

**Dividend** – In division, the dividend is the number being divided by another number. It represents the total quantity or value that is being divided into equal parts.

**Divisible** – A number is divisible by another number if it can be divided evenly without leaving a remainder. For example, 15 is divisible by 3 because 15 can be divided into 3 equal parts.

**Divisor** – In division, the divisor is the number by which another number is divided. It represents the number of parts into which the dividend is being divided.

**Fraction** – A fraction is a numerical quantity representing a part of a whole, expressed as one integer divided by another integer, or as a decimal or percentage. Fractions are used in mathematical operations to represent proportional relationships.

**Greatest Common Divisor (GCD)** – The greatest common divisor (GCD) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. It is also known as the greatest common factor (GCF).

**Improper Fraction** – An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. It can be converted into a mixed number by dividing the numerator by the denominator.

**Integer** – An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal parts. Integers are used in arithmetic operations, including fraction multiplication and division, and represent counts or quantities.

**Lowest Common Denominator (LCD) **– The lowest common denominator (LCD) of two or more fractions is the smallest common multiple of their denominators. It is necessary for adding and subtracting fractions with different denominators.

**Mixed Number** – A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than one and less than a whole.

**Multiple** – A multiple of a number is the product of that number and an integer. For example, multiples of 3 include 3, 6, 9, 12, and so on.

**Multiply** – Multiplication is a mathematical operation that combines two or more numbers to find their total or product. When multiplying fractions or mixed numbers, it involves finding the product of their numerators and denominators.

**Numerator** – In a fraction, the numerator is the top number that represents the number of equal parts being considered. It indicates the size or value of each part.

**Prime Factorization** – Prime factorization is the process of expressing a composite number as a product of prime numbers. It is used to find the prime factors of a number and is essential for simplifying fractions.

**Prime Number** – A prime number is a positive integer greater than 1 that has exactly two distinct positive divisors – 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.

**Product** – The product is the result of multiplying two or more numbers together in a multiplication operation. It represents the total or combined value obtained by the multiplication process.

**Proper Fraction** – A proper fraction is a fraction in which the numerator is less than the denominator. It represents a quantity that is less than one.

**Quotient **– In division, the quotient is the result obtained by dividing one number (the dividend) by another number (the divisor). It represents the number of equal parts or groups into which the dividend is divided.

**Reciprocal** – The reciprocal of a fraction is another fraction obtained by interchanging the numerator and the denominator. When multiplied together, a fraction and its reciprocal result in a product of 1.

**Simplify** – To simplify a fraction means to reduce it to its simplest form by dividing both the numerator and the denominator by their greatest common divisor. It results in a fraction with the smallest possible numerator and denominator.

**Whole Number** – A whole number is a non-negative integer, including zero, that does not have any fractional or decimal parts. Whole numbers are used in arithmetic operations and represent counts or quantities.

**Zero** – Zero is the integer that represents the absence of quantity or value. It serves as the neutral element in multiplication and division operations, where multiplying or dividing by zero yields zero as the result.