What is 1/4 plus 5/9? (Answer: 29/36)

Exact Answer

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Problem: What is 1/4 plus 5/9?
Formula / Expression: 1/4 + 5/9
Final Answer: 29/36
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 9 = 36.
Working: LCD(4, 9) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 1/4 by 9, and multiply the numerator and denominator of 5/9 by 4 so both fractions share the common base 36.
Working: 1 × 9/4 × 9 = 9/36 and 5 × 4/9 × 4 = 20/36

Step 3: Add the Numerators
Now add the numerators (9 + 20 = 29) and keep the common denominator 36 unchanged.
Working: 9 + 20/36 = 29/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 36 is 1, confirming that 29/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 36 produces a repeating decimal (approximately 0.805556, or 80.5556%).
Working: 29 ÷ 36 = 0.805556 (80.5556%)

Key Values:
- Simplified Fraction: 29/36
- Mixed Number Form: 29/36
- Decimal Value: 0.805556
- Percentage: 80.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-5-9/
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1/4 + 5/9 = 29/36

Simplified Fraction

29/36

Mixed Number

Proper (29/36)

Decimal Value

0.805556

Percentage

80.5556%

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Step-by-Step Solution: 1/4 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 9 = 36.

LCD(4, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 1/4 by 9, and multiply the numerator and denominator of 5/9 by 4 so both fractions share the common base 36.

1 × 9/4 × 9 = 9/36 and 5 × 4/9 × 4 = 20/36

Step 3

Add the Numerators

Now add the numerators (9 + 20 = 29) and keep the common denominator 36 unchanged.

9 + 20/36 = 29/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 36 is 1, confirming that 29/36 cannot be reduced further—it is already in its simplest irreducible form.

29/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 36 produces a repeating decimal (approximately 0.805556, or 80.5556%).

29 ÷ 36 = 0.805556 (80.5556%)

Visual Representation

The diagram below illustrates 1/4 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/36`
Mixed Number Form	`29/36`
Decimal Form	`0.805556`
Percentage	`80.5556%`

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Frequently Asked Questions

What is 1/4 plus 5/9 as a fraction?

1/4 + 5/9 in simplest fraction form is 29/36.

What is 1/4 plus 5/9 as a decimal?

1/4 + 5/9 converted to a decimal is 0.805556.

What is 1/4 plus 5/9 as a percentage?

1/4 + 5/9 expressed as a percentage is 80.5556%.

Does 1/4 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.805556...) because the denominator contains prime factors other than 2 and 5.