What is 1/3 plus 3/9? (Answer: 2/3)

Exact Answer

==================================================
Problem: What is 1/3 plus 3/9?
Formula / Expression: 1/3 + 3/9
Final Answer: 2/3
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.
Working: LCD(3, 9) = 9

Step 2: Convert to Equivalent Fractions with Common Denominator 9
Multiply the numerator and denominator of 1/3 by 3, and multiply the numerator and denominator of 3/9 by 1 so both fractions share the common base 9.
Working: 1 × 3/3 × 3 = 3/9 and 3 × 1/9 × 1 = 3/9

Step 3: Add the Numerators
Now add the numerators (3 + 3 = 6) and keep the common denominator 9 unchanged.
Working: 3 + 3/9 = 6/9

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 6 and 9, which is 3. Divide both the numerator and denominator by 3.
Working: 6 ÷ 3/9 ÷ 3 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-plus-3-9/
==================================================

1/3 + 3/9 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 1/3 + 3/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.

LCD(3, 9) = 9

Step 2

Convert to Equivalent Fractions with Common Denominator 9

Multiply the numerator and denominator of 1/3 by 3, and multiply the numerator and denominator of 3/9 by 1 so both fractions share the common base 9.

1 × 3/3 × 3 = 3/9 and 3 × 1/9 × 1 = 3/9

Step 3

Add the Numerators

Now add the numerators (3 + 3 = 6) and keep the common denominator 9 unchanged.

3 + 3/9 = 6/9

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 6 and 9, which is 3. Divide both the numerator and denominator by 3.

6 ÷ 3/9 ÷ 3 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 1/3 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/3 plus 3/9 as a fraction?

1/3 + 3/9 in simplest fraction form is 2/3.

What is 1/3 plus 3/9 as a decimal?

1/3 + 3/9 converted to a decimal is 0.666667.

What is 1/3 plus 3/9 as a percentage?

1/3 + 3/9 expressed as a percentage is 66.6667%.

Does 1/3 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.