Numerical Expressions and Patterns

Grade 5 · Math · Study Guide

Learn to write and evaluate numerical expressions and identify rules in number patterns.

A numerical expression is a mathematical phrase that contains numbers and operation symbols but no equals sign. For example, 3 + 4 x 2 is a numerical expression. To evaluate an expression means to find its value.

The order of operations tells us in what order to evaluate expressions. The rules are: (1) evaluate expressions inside parentheses first, (2) then multiply and divide from left to right, (3) then add and subtract from left to right. This is often remembered with the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

For example, 3 + 4 x 2 = 3 + 8 = 11 (multiply first). But (3 + 4) x 2 = 7 x 2 = 14 (parentheses first).

A number pattern is a sequence of numbers that follows a rule. To find the rule, look at how each term changes from one to the next. For example, in the pattern 2, 4, 6, 8, the rule is add 2. In the pattern 3, 6, 12, 24, the rule is multiply by 2.

Once you know a rule, you can extend the pattern, predict future terms, and even write the rule as a mathematical expression.

Key terms

Numerical expression
A combination of numbers and operation symbols that names a value but has no equals sign
Evaluate
To find the value of an expression by performing all the operations
Order of operations
The agreed-upon rules for which operations to perform first: parentheses, then multiply/divide, then add/subtract
PEMDAS
A memory aid for order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Number pattern
A sequence of numbers that follows a repeating or growing rule
Term
Each number in a sequence or pattern

Flashcards

Order of operations: first step
Evaluate what is inside parentheses first
Order of operations: second step
Multiply and divide in order from left to right
Order of operations: third step
Add and subtract in order from left to right
Evaluate: 2 + 3 x 5
17; multiply first: 3 x 5 = 15, then add 2: 2 + 15 = 17
Evaluate: (2 + 3) x 5
25; parentheses first: 2 + 3 = 5, then multiply: 5 x 5 = 25
Pattern rule: 1, 3, 9, 27
Multiply by 3 each time
Pattern rule: 100, 90, 80, 70
Subtract 10 each time

Questions

  1. What is the value of the expression 5 + 3 x 4?

    1. 32
    2. 17
    3. 20
    4. 12
    Show answer

    Answer: 17

    Order of operations: multiply before adding. 3 x 4 = 12, then 5 + 12 = 17.

  2. What is the value of (6 + 2) x 3?

    Show answer

    Answer: 24

    Parentheses first: 6 + 2 = 8, then 8 x 3 = 24.

  3. In the expression 4 x 3 + 2, you should add 3 + 2 first before multiplying.

    Show answer

    Answer: False

    According to the order of operations, you multiply before you add. So 4 x 3 = 12 first, then 12 + 2 = 14.

  4. What is the rule for the pattern: 5, 10, 15, 20, 25?

    1. Add 4
    2. Add 5
    3. Multiply by 2
    4. Multiply by 5
    Show answer

    Answer: Add 5

    Each term increases by 5: 5, 10, 15, 20, 25. The rule is add 5.

  5. The next number in the pattern 3, 6, 12, 24 is ___.

    Show answer

    Answer: 48

    Each term is multiplied by 2: 3, 6, 12, 24, 48. The rule is multiply by 2, so 24 x 2 = 48.

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