Mathematics
Grade 5
15 min
Add, subtract, multiply, and divide whole numbers
Add, subtract, multiply, and divide whole numbers
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1
Introduction & Learning Objectives
Learning Objectives
Identify the four basic operations (addition, subtraction, multiplication, division) within a single expression.
Explain the importance of following a specific order when solving problems with multiple operations.
Correctly apply the Order of Operations (Parentheses, Multiplication/Division, Addition/Subtraction) to solve whole number expressions.
Accurately perform calculations involving mixed operations with whole numbers.
Solve multi-step word problems by setting up and evaluating expressions using the Order of Operations.
Recognize and correct common errors made when solving mixed operation problems.
Have you ever tried to follow a recipe 🍪 or build something with instructions? What happens if you do the steps out of order? In math, the order matters...
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Key Concepts & Vocabulary
TermDefinitionExample
Order of OperationsA set of rules that tells you the correct sequence to perform operations in a mathematical expression to ensure everyone gets the same answer.In '5 + 3 × 2', you multiply 3 × 2 first, then add 5, because multiplication comes before addition in the order of operations.
ExpressionA mathematical phrase that contains numbers, operations (like +, -, ×, ÷), and sometimes grouping symbols, but no equals sign.10 ÷ 2 + 3 × 4 is an expression.
Grouping SymbolsSymbols like parentheses ( ) or brackets [ ] that tell you to perform the operations inside them first.In '(5 + 3) × 2', you add 5 + 3 first because it's inside the parentheses.
Whole NumbersThe set of non-negative counting numbers: 0, 1, 2, 3, and so on, without fractions or de...
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Core Formulas
Order of Operations: Grouping Symbols
`\text{1. Grouping Symbols: } (\quad), [\quad]`
Always perform operations inside parentheses or other grouping symbols first. Think of them as a 'VIP' section of the problem.
Order of Operations: Multiplication and Division
`\text{2. Multiplication and Division: } \times, \div \quad (\text{from left to right})`
After handling grouping symbols, perform all multiplication and division operations. If both are present, work from the left side of the expression to the right.
Order of Operations: Addition and Subtraction
`\text{3. Addition and Subtraction: } +, - \quad (\text{from left to right})`
Finally, after all grouping symbols, multiplication, and division are done, perform all addition and subtraction operations. If bo...
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Challenging
Insert one pair of parentheses into the expression 6 × 4 + 10 ÷ 2 to make its value 42.
A.(6 × 4) + 10 ÷ 2
B.6 × (4 + 10) ÷ 2
C.6 × 4 + (10 ÷ 2)
D.(6 × 4 + 10) ÷ 2
Challenging
A bus has 45 seats. The bus starts empty. At the first stop, 15 people get on. At the second stop, 3 groups of 4 people get on. At the third stop, 7 people get off. How many empty seats are on the bus?
A.25
B.20
C.13
D.11
Challenging
What number must replace the blank to make the equation true? 8 × ( _ - 5) + 2 = 26
A.3
B.6
C.8
D.10
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