What is 4/29 plus 3/9? (Answer: 41/87)

Exact Answer

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Problem: What is 4/29 plus 3/9?
Formula / Expression: 4/29 + 3/9
Final Answer: 41/87
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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 4/29 by 9, and multiply the numerator and denominator of 3/9 by 29 so both fractions share the common base 261.
Working: 4 × 9/29 × 9 = 36/261 and 3 × 29/9 × 29 = 87/261

Step 3: Add the Numerators
Now add the numerators (36 + 87 = 123) and keep the common denominator 261 unchanged.
Working: 36 + 87/261 = 123/261

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 261, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/261 ÷ 3 = 41/87

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 87 produces a repeating decimal (approximately 0.471264, or 47.1264%).
Working: 41 ÷ 87 = 0.471264 (47.1264%)

Key Values:
- Simplified Fraction: 41/87
- Mixed Number Form: 41/87
- Decimal Value: 0.471264
- Percentage: 47.1264%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-29-plus-3-9/
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4/29 + 3/9 = 41/87

Simplified Fraction

41/87

Mixed Number

Proper (41/87)

Decimal Value

0.471264

Percentage

47.1264%

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Step-by-Step Solution: 4/29 + 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 4/29 by 9, and multiply the numerator and denominator of 3/9 by 29 so both fractions share the common base 261.

4 × 9/29 × 9 = 36/261 and 3 × 29/9 × 29 = 87/261

Step 3

Add the Numerators

Now add the numerators (36 + 87 = 123) and keep the common denominator 261 unchanged.

36 + 87/261 = 123/261

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 261, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/261 ÷ 3 = 41/87

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 87 produces a repeating decimal (approximately 0.471264, or 47.1264%).

41 ÷ 87 = 0.471264 (47.1264%)

Visual Representation

The diagram below illustrates 4/29 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/87`
Mixed Number Form	`41/87`
Decimal Form	`0.471264`
Percentage	`47.1264%`

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Frequently Asked Questions

What is 4/29 plus 3/9 as a fraction?

4/29 + 3/9 in simplest fraction form is 41/87.

What is 4/29 plus 3/9 as a decimal?

4/29 + 3/9 converted to a decimal is 0.471264.

What is 4/29 plus 3/9 as a percentage?

4/29 + 3/9 expressed as a percentage is 47.1264%.

Does 4/29 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.471264...) because the denominator contains prime factors other than 2 and 5.