What is 2/33 plus 11/21? (Answer: 45/77)

Exact Answer

==================================================
Problem: What is 2/33 plus 11/21?
Formula / Expression: 2/33 + 11/21
Final Answer: 45/77
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
Working: LCD(33, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 2/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.
Working: 2 × 7/33 × 7 = 14/231 and 11 × 11/21 × 11 = 121/231

Step 3: Add the Numerators
Now add the numerators (14 + 121 = 135) and keep the common denominator 231 unchanged.
Working: 14 + 121/231 = 135/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 135 ÷ 3/231 ÷ 3 = 45/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 77 produces a repeating decimal (approximately 0.584416, or 58.4416%).
Working: 45 ÷ 77 = 0.584416 (58.4416%)

Key Values:
- Simplified Fraction: 45/77
- Mixed Number Form: 45/77
- Decimal Value: 0.584416
- Percentage: 58.4416%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-11-21/
==================================================

2/33 + 11/21 = 45/77

Simplified Fraction

45/77

Mixed Number

Proper (45/77)

Decimal Value

0.584416

Percentage

58.4416%

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 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 2/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.

2 × 7/33 × 7 = 14/231 and 11 × 11/21 × 11 = 121/231

Step 3

Add the Numerators

Now add the numerators (14 + 121 = 135) and keep the common denominator 231 unchanged.

14 + 121/231 = 135/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 231, which is 3. Divide both the numerator and denominator by 3.

135 ÷ 3/231 ÷ 3 = 45/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 77 produces a repeating decimal (approximately 0.584416, or 58.4416%).

45 ÷ 77 = 0.584416 (58.4416%)

Visual Representation

The diagram below illustrates 2/33 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/77`
Mixed Number Form	`45/77`
Decimal Form	`0.584416`
Percentage	`58.4416%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/33 plus 11/21 as a fraction?

2/33 + 11/21 in simplest fraction form is 45/77.

What is 2/33 plus 11/21 as a decimal?

2/33 + 11/21 converted to a decimal is 0.584416.

What is 2/33 plus 11/21 as a percentage?

2/33 + 11/21 expressed as a percentage is 58.4416%.

Does 2/33 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.584416...) because the denominator contains prime factors other than 2 and 5.