What is 3/29 plus 3/9? (Answer: 38/87)

Exact Answer

==================================================
Problem: What is 3/29 plus 3/9?
Formula / Expression: 3/29 + 3/9
Final Answer: 38/87
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 9 = 261.
Working: LCD(29, 9) = 261

Step 2: Convert to Equivalent Fractions with Common Denominator 261
Multiply the numerator and denominator of 3/29 by 9, and multiply the numerator and denominator of 3/9 by 29 so both fractions share the common base 261.
Working: 3 × 9/29 × 9 = 27/261 and 3 × 29/9 × 29 = 87/261

Step 3: Add the Numerators
Now add the numerators (27 + 87 = 114) and keep the common denominator 261 unchanged.
Working: 27 + 87/261 = 114/261

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 261, which is 3. Divide both the numerator and denominator by 3.
Working: 114 ÷ 3/261 ÷ 3 = 38/87

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 87 produces a repeating decimal (approximately 0.436782, or 43.6782%).
Working: 38 ÷ 87 = 0.436782 (43.6782%)

Key Values:
- Simplified Fraction: 38/87
- Mixed Number Form: 38/87
- Decimal Value: 0.436782
- Percentage: 43.6782%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-29-plus-3-9/
==================================================

3/29 + 3/9 = 38/87

Simplified Fraction

38/87

Mixed Number

Proper (38/87)

Decimal Value

0.436782

Percentage

43.6782%

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: 3/29 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 9 = 261.

LCD(29, 9) = 261

Step 2

Convert to Equivalent Fractions with Common Denominator 261

Multiply the numerator and denominator of 3/29 by 9, and multiply the numerator and denominator of 3/9 by 29 so both fractions share the common base 261.

3 × 9/29 × 9 = 27/261 and 3 × 29/9 × 29 = 87/261

Step 3

Add the Numerators

Now add the numerators (27 + 87 = 114) and keep the common denominator 261 unchanged.

27 + 87/261 = 114/261

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 261, which is 3. Divide both the numerator and denominator by 3.

114 ÷ 3/261 ÷ 3 = 38/87

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 87 produces a repeating decimal (approximately 0.436782, or 43.6782%).

38 ÷ 87 = 0.436782 (43.6782%)

Visual Representation

The diagram below illustrates 3/29 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/87`
Mixed Number Form	`38/87`
Decimal Form	`0.436782`
Percentage	`43.6782%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/29 plus 3/9 as a fraction?

3/29 + 3/9 in simplest fraction form is 38/87.

What is 3/29 plus 3/9 as a decimal?

3/29 + 3/9 converted to a decimal is 0.436782.

What is 3/29 plus 3/9 as a percentage?

3/29 + 3/9 expressed as a percentage is 43.6782%.

Does 3/29 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.436782...) because the denominator contains prime factors other than 2 and 5.