Operations

Unit Review Sheet

Facts and Definitions

Lesson 1: Addition and Subtraction Review

• An algorithm is a step-by-step way of performing a particular task, often a calculation or problem-solving type of task.
• Adding and subtracting multi-digit decimal numbers is very similar to adding and subtracting multi-digit whole numbers.

Lesson 2: Multiplication Review

• Multiplication is repeated addition. For example, 4 × 3 means "4 groups of 3" and is the same as 3 + 3 + 3 + 3.
• The numbers being multiplied are called factors, and the answer to a multiplication problem is called the product.
• You can show multiplication using the multiplication symbol (×), the dot operator (∙), or parentheses.
• A property of something is a characteristic that applies to all instances of that thing.
• The commutative property of multiplication states that you can multiply numbers in any order. For example, 3 × 5 has the same answer as 5 × 3.
• The associative property of multiplication says that it doesn't matter how the factors are grouped in a multiplication problem. For example, the problem
  (12 × 2) × 5 can be regrouped as 12 × (2 × 5).
• The distributive property of multiplication states that multiplying the sum of two numbers by a factor is the same as multiplying both numbers by the factor and then adding the products.

Lesson 3: Division Review

• Division is the opposite of multiplication. For example, 3 × 2 = 6, and 6 ÷ 2 = 3.
• Division is repeated subtraction. In other words, 8 ÷ 4 means 8 − 4 = 4 − 4 = 0. Four can be subtracted from eight two times.
• In a division problem, the number being divided is called the dividend and the number that does the dividing is called the divisor. In the problem 6 ÷ 2 = 3, the number 6 is the dividend that is being divided by the divisor, which is 2. The answer to a division problem is called the quotient.
• If one number is divisible by another, it means that the quotient has no remainders. For example, 10 is divisible by 5 but not by 3.
• Remainders in division word problems can be interpreted in different ways. The remainder may need to be included, discarded, or used to round an answer up by 1. Using decimals and zeros can allow division to continue so that no remainder is needed.

Lesson 4: Exponents and Order of Operations

• Mathematical expression: a math sentence that includes at least two numbers and one or more operators (+,−,×,÷)
• Order of operations: a set of rules that define the order in which to complete operations when solving a mathematical expression
• An exponential expression contains two parts — a base and an exponent.
• The base of an exponential expression is a factor, and the exponent indicates how many times to use that base as a factor.
• A notation is a shorthand way of writing something. For example, 3⁴ is a shorter way to write 3 × 3 × 3 × 3.

Lesson 5: Factors and Prime Factorization

• Natural numbers are the set of counting numbers starting at 1 (1, 2, 3, etc.).
• Factors are numbers that are multiplied together to get other numbers called products.
• To factor means to break a number down into factors or to express a number as its factors.
• A prime number is a natural number greater than one that has no factors other than one and itself.
• A composite number is a natural number that is not prime. A composite number has more than one factor pair.
• The number 1 is neither prime nor composite.
• The prime factorization of a composite number is all of the prime factors that make up the number, usually written in order from least to greatest.

Lesson 6: Greatest Common Factor

• A common factor is a factor shared by two or more numbers.
• The greatest common factor (GCF) is the largest, or greatest, common factor shared by two (or more) numbers.
• The distributive property of multiplication states that multiplying the sum (or difference) of two numbers by a factor is the same as multiplying both numbers by the factor and then adding (or subtracting) the products.
• Prime factorization can be used to identify the greatest common factor of two or more numbers.

Lesson 7: Least Common Multiple

• A multiple of a natural number is the product of that number times another number.
• A common multiple is any multiple that is shared by two or more natural numbers.
• The Least Common Multiple (LCM) is the smallest, or least, common multiple shared by two or more numbers.
• The rule for finding the least common multiple of two or more numbers with prime factorization is to use each prime factor the largest number of times that it appears in either number.

Lesson 8: Unit 1 Test

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Final Project: Planning a Party

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