What is 1/4 plus 8/9? (Answer: 41/36)

Exact Answer

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Problem: What is 1/4 plus 8/9?
Formula / Expression: 1/4 + 8/9
Final Answer: 1 5/36 (41/36)
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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 8/9 by 4 so both fractions share the common base 36.
Working: 1 × 9/4 × 9 = 9/36 and 8 × 4/9 × 4 = 32/36

Step 3: Add the Numerators
Now add the numerators (9 + 32 = 41) and keep the common denominator 36 unchanged.
Working: 9 + 32/36 = 41/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 36 is 1, confirming that 41/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/36

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (41) is greater than the denominator (36), divide 41 by 36: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/36.
Working: 41/36 = 1 5/36

Step 6: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 36 produces a repeating decimal (approximately 1.138889, or 113.8889%).
Working: 41 ÷ 36 = 1.138889 (113.8889%)

Key Values:
- Simplified Fraction: 41/36
- Mixed Number Form: 1 5/36
- Decimal Value: 1.138889
- Percentage: 113.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-8-9/
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1/4 + 8/9 = 41/36

Simplified Fraction

41/36

Mixed Number

1 5/36

Decimal Value

1.138889

Percentage

113.8889%

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Step-by-Step Solution: 1/4 + 8/9

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 8/9 by 4 so both fractions share the common base 36.

1 × 9/4 × 9 = 9/36 and 8 × 4/9 × 4 = 32/36

Step 3

Add the Numerators

Now add the numerators (9 + 32 = 41) and keep the common denominator 36 unchanged.

9 + 32/36 = 41/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 36 is 1, confirming that 41/36 cannot be reduced further—it is already in its simplest irreducible form.

41/36

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (41) is greater than the denominator (36), divide 41 by 36: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/36.

41/36 = 15/36

Step 6

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 36 produces a repeating decimal (approximately 1.138889, or 113.8889%).

41 ÷ 36 = 1.138889 (113.8889%)

Visual Representation

The diagram below illustrates 1/4 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/36`
Mixed Number Form	`1 5/36`
Decimal Form	`1.138889`
Percentage	`113.8889%`

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Frequently Asked Questions

What is 1/4 plus 8/9 as a fraction?

1/4 + 8/9 in simplest fraction form is 41/36 (or 1 5/36 as a mixed number).

What is 1/4 plus 8/9 as a decimal?

1/4 + 8/9 converted to a decimal is 1.138889.

What is 1/4 plus 8/9 as a percentage?

1/4 + 8/9 expressed as a percentage is 113.8889%.

How do you write 1/4 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 41/36 can be written as the mixed number 1 5/36.

Does 1/4 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.138889...) because the denominator contains prime factors other than 2 and 5.