Number System & Expressions

Interactive study guide — Reveal Math Unit 6 · Standards 6.NS & 6.EE

6.1 — Dividing Fractions

Use the Keep-Change-Flip method to divide fractions by fractions and whole numbers. Always convert mixed numbers to improper fractions first.

Keep-Change-Flip

To divide fractions: Keep the first fraction, Change the division sign to multiplication, Flip the second fraction (write its reciprocal).

Example: 2/3 ÷ 1/4
Keep 2/3 → Change to × → Flip 1/4 to 4/1
2/3 × 4/1 = 8/3 = 2 2/3
Whole numbers: 5 ÷ 1/2
Write 5 as 5/1 → Keep 5/1 × Flip 2/1 = 10/1 = 10

Mixed Numbers

Convert mixed numbers to improper fractions before dividing.

Example: 1 1/2 ÷ 3/4
Convert: 1 1/2 = 3/2
3/2 × 4/3 = 12/6 = 2

Practice

3/4 ÷ 1/2 = ?

3/8
3/2 (or 1 1/2)
2/3

6 ÷ 1/3 = ?

18
2
6/3

2/5 ÷ 4/5 = ?

8/25
2
1/2
Score
0/3

6.3 — Exponents

Understand base and exponent, evaluate whole-number exponents, and write repeated multiplication using exponential notation.

Base & Exponent

In the expression bn, the base (b) is the number being multiplied and the exponent (n) tells how many times to multiply it.

Example: 24 = 2 × 2 × 2 × 2 = 16
Example: 53 = 5 × 5 × 5 = 125

Special Cases

Any number to the 1st power is itself: 71 = 7
Any number to the 0th power is 1: 90 = 1

Writing as exponents: 3 × 3 × 3 × 3 × 3 = 35

Practice

What is 34?

12
64
81

Write 7 × 7 × 7 using an exponent.

73
37
7 × 3

What is 100?

0
1
10
Score
0/3

6.4 — Order of Operations (PEMDAS)

Follow the correct order: Parentheses, Exponents, Multiply/Divide (left to right), Add/Subtract (left to right).

PEMDAS

P — Parentheses first
E — Exponents next
M / D — Multiply and Divide, left to right
A / S — Add and Subtract, left to right

Example: 3 + 4 × 2
Multiply first: 4 × 2 = 8
Then add: 3 + 8 = 11 (not 14!)
Example: (6 + 2) × 32
Parentheses: 8 × 32
Exponent: 8 × 9
Multiply: 72
Tip: Multiplication and division are done left to right — not "multiplication before division." Same for addition and subtraction.

Practice

8 + 2 × 5 = ?

50
18
15

(3 + 5)2 = ?

64
34
16

12 ÷ 4 + 2 × 3 = ?

15
3
9
Score
0/3

6.5 — Algebraic Expressions

Write expressions from verbal descriptions, evaluate them by substituting values, and apply the distributive property.

Writing Expressions

Translate words into math. "5 more than a number" → x + 5. "Twice a number" → 2x.

Evaluating Expressions

Substitute the given value for the variable, then simplify.

Example: Evaluate 3x + 7 when x = 4
3(4) + 7 = 12 + 7 = 19

Distributive Property

a(b + c) = ab + ac — multiply the outside term by each term inside the parentheses.

Example: 3(x + 2) = 3 · x + 3 · 2 = 3x + 6
Example: 5(2y − 4) = 10y − 20

Practice

Evaluate 2x + 3 when x = 5.

13
10
16

Apply the distributive property: 4(x + 3) = ?

4x + 3
x + 12
4x + 12

Which expression means "6 less than a number n"?

6 − n
n − 6
6n
Score
0/3

6.6–6.7 — Like Terms, Factors & Multiples

Combine like terms, find the Greatest Common Factor (GCF) and Least Common Multiple (LCM), and use divisibility rules.

Combining Like Terms

Like terms have the same variable and exponent. Add or subtract their coefficients.

Example: 3x + 5x = 8x
7y − 2y = 5y
4x + 3y → cannot combine (different variables)

Greatest Common Factor (GCF)

The GCF is the largest number that divides evenly into two or more numbers.

Example: GCF of 12 and 18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
GCF = 6

Least Common Multiple (LCM)

The LCM is the smallest number that is a multiple of two or more numbers.

Example: LCM of 4 and 6
Multiples of 4: 4, 8, 12, 16, 20…
Multiples of 6: 6, 12, 18, 24…
LCM = 12

Practice

Simplify: 6x + 2x

8x
12x
62x

What is the GCF of 24 and 36?

6
12
72

What is the LCM of 3 and 5?

1
8
15
Score
0/3

Vocabulary

Tap a card to reveal the definition.

Fraction
A number that represents part of a whole, written as a/b where b is not zero.
Numerator
The top number in a fraction; it tells how many parts you have.
Denominator
The bottom number in a fraction; it tells how many equal parts the whole is divided into.
Reciprocal
The flipped version of a fraction. The reciprocal of a/b is b/a. Example: reciprocal of 3/4 is 4/3.
Exponent
A small number written above and to the right of a base that tells how many times to multiply the base by itself.
Base
The number that is being multiplied when using an exponent. In 53, the base is 5.
Power
An expression with a base and an exponent, such as 24 (read "2 to the fourth power").
Order of Operations
The set of rules (PEMDAS) that tells the order in which to evaluate a math expression.
PEMDAS
Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
Variable
A letter or symbol that represents an unknown number. Example: x, y, n.
Expression
A combination of numbers, variables, and operations (no equal sign). Example: 3x + 5.
Coefficient
The number in front of a variable. In 7x, the coefficient is 7.
Term
A single number, variable, or number multiplied by a variable. In 3x + 5, the terms are 3x and 5.
Like Terms
Terms with the same variable raised to the same power. 4x and 9x are like terms; 4x and 4y are not.
Distributive Property
a(b + c) = ab + ac. Multiply the factor outside the parentheses by each term inside.
GCF
Greatest Common Factor — the largest number that divides evenly into two or more numbers.
LCM
Least Common Multiple — the smallest number that is a multiple of two or more numbers.