What is 2/33 plus 2/8? (Answer: 41/132)

Exact Answer

==================================================
Problem: What is 2/33 plus 2/8?
Formula / Expression: 2/33 + 2/8
Final Answer: 41/132
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.
Working: LCD(33, 8) = 264

Step 2: Convert to Equivalent Fractions with Common Denominator 264
Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 2/8 by 33 so both fractions share the common base 264.
Working: 2 × 8/33 × 8 = 16/264 and 2 × 33/8 × 33 = 66/264

Step 3: Add the Numerators
Now add the numerators (16 + 66 = 82) and keep the common denominator 264 unchanged.
Working: 16 + 66/264 = 82/264

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 264, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/264 ÷ 2 = 41/132

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 132 produces a repeating decimal (approximately 0.310606, or 31.0606%).
Working: 41 ÷ 132 = 0.310606 (31.0606%)

Key Values:
- Simplified Fraction: 41/132
- Mixed Number Form: 41/132
- Decimal Value: 0.310606
- Percentage: 31.0606%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-2-8/
==================================================

2/33 + 2/8 = 41/132

Simplified Fraction

41/132

Mixed Number

Proper (41/132)

Decimal Value

0.310606

Percentage

31.0606%

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 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.

LCD(33, 8) = 264

Step 2

Convert to Equivalent Fractions with Common Denominator 264

Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 2/8 by 33 so both fractions share the common base 264.

2 × 8/33 × 8 = 16/264 and 2 × 33/8 × 33 = 66/264

Step 3

Add the Numerators

Now add the numerators (16 + 66 = 82) and keep the common denominator 264 unchanged.

16 + 66/264 = 82/264

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 264, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/264 ÷ 2 = 41/132

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 132 produces a repeating decimal (approximately 0.310606, or 31.0606%).

41 ÷ 132 = 0.310606 (31.0606%)

Visual Representation

The diagram below illustrates 2/33 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/132`
Mixed Number Form	`41/132`
Decimal Form	`0.310606`
Percentage	`31.0606%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/33 plus 2/8 as a fraction?

2/33 + 2/8 in simplest fraction form is 41/132.

What is 2/33 plus 2/8 as a decimal?

2/33 + 2/8 converted to a decimal is 0.310606.

What is 2/33 plus 2/8 as a percentage?

2/33 + 2/8 expressed as a percentage is 31.0606%.

Does 2/33 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.310606...) because the denominator contains prime factors other than 2 and 5.