What is 2/33 plus 2/3? (Answer: 8/11)

Exact Answer

==================================================
Problem: What is 2/33 plus 2/3?
Formula / Expression: 2/33 + 2/3
Final Answer: 8/11
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 33 is an exact multiple of 3 (3 × 11 = 33). The Least Common Denominator (LCD) is simply 33, meaning we only need to scale one fraction.
Working: LCD(33, 3) = 33

Step 2: Convert to Equivalent Fractions with Common Denominator 33
Multiply the numerator and denominator of 2/33 by 1, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.
Working: 2 × 1/33 × 1 = 2/33 and 2 × 11/3 × 11 = 22/33

Step 3: Add the Numerators
Now add the numerators (2 + 22 = 24) and keep the common denominator 33 unchanged.
Working: 2 + 22/33 = 24/33

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 33, which is 3. Divide both the numerator and denominator by 3.
Working: 24 ÷ 3/33 ÷ 3 = 8/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 11 produces a repeating decimal (approximately 0.727273, or 72.7273%).
Working: 8 ÷ 11 = 0.727273 (72.7273%)

Key Values:
- Simplified Fraction: 8/11
- Mixed Number Form: 8/11
- Decimal Value: 0.727273
- Percentage: 72.7273%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-2-3/
==================================================

2/33 + 2/3 = 8/11

Simplified Fraction

8/11

Mixed Number

Proper (8/11)

Decimal Value

0.727273

Percentage

72.7273%

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: 2/33 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 33 is an exact multiple of 3 (3 × 11 = 33). The Least Common Denominator (LCD) is simply 33, meaning we only need to scale one fraction.

LCD(33, 3) = 33

Step 2

Convert to Equivalent Fractions with Common Denominator 33

Multiply the numerator and denominator of 2/33 by 1, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.

2 × 1/33 × 1 = 2/33 and 2 × 11/3 × 11 = 22/33

Step 3

Add the Numerators

Now add the numerators (2 + 22 = 24) and keep the common denominator 33 unchanged.

2 + 22/33 = 24/33

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 33, which is 3. Divide both the numerator and denominator by 3.

24 ÷ 3/33 ÷ 3 = 8/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 11 produces a repeating decimal (approximately 0.727273, or 72.7273%).

8 ÷ 11 = 0.727273 (72.7273%)

Visual Representation

The diagram below illustrates 2/33 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/11`
Mixed Number Form	`8/11`
Decimal Form	`0.727273`
Percentage	`72.7273%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/33 plus 2/3 as a fraction?

2/33 + 2/3 in simplest fraction form is 8/11.

What is 2/33 plus 2/3 as a decimal?

2/33 + 2/3 converted to a decimal is 0.727273.

What is 2/33 plus 2/3 as a percentage?

2/33 + 2/3 expressed as a percentage is 72.7273%.

Does 2/33 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.727273...) because the denominator contains prime factors other than 2 and 5.