What is 1/4 plus 6/9? (Answer: 11/12)

Exact Answer

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Problem: What is 1/4 plus 6/9?
Formula / Expression: 1/4 + 6/9
Final Answer: 11/12
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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 6/9 by 4 so both fractions share the common base 36.
Working: 1 × 9/4 × 9 = 9/36 and 6 × 4/9 × 4 = 24/36

Step 3: Add the Numerators
Now add the numerators (9 + 24 = 33) and keep the common denominator 36 unchanged.
Working: 9 + 24/36 = 33/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 36, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/36 ÷ 3 = 11/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 12 produces a repeating decimal (approximately 0.916667, or 91.6667%).
Working: 11 ÷ 12 = 0.916667 (91.6667%)

Key Values:
- Simplified Fraction: 11/12
- Mixed Number Form: 11/12
- Decimal Value: 0.916667
- Percentage: 91.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-6-9/
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1/4 + 6/9 = 11/12

Simplified Fraction

11/12

Mixed Number

Proper (11/12)

Decimal Value

0.916667

Percentage

91.6667%

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Step-by-Step Solution: 1/4 + 6/9

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 6/9 by 4 so both fractions share the common base 36.

1 × 9/4 × 9 = 9/36 and 6 × 4/9 × 4 = 24/36

Step 3

Add the Numerators

Now add the numerators (9 + 24 = 33) and keep the common denominator 36 unchanged.

9 + 24/36 = 33/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 36, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/36 ÷ 3 = 11/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 12 produces a repeating decimal (approximately 0.916667, or 91.6667%).

11 ÷ 12 = 0.916667 (91.6667%)

Visual Representation

The diagram below illustrates 1/4 plus 6/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/12`
Mixed Number Form	`11/12`
Decimal Form	`0.916667`
Percentage	`91.6667%`

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Frequently Asked Questions

What is 1/4 plus 6/9 as a fraction?

1/4 + 6/9 in simplest fraction form is 11/12.

What is 1/4 plus 6/9 as a decimal?

1/4 + 6/9 converted to a decimal is 0.916667.

What is 1/4 plus 6/9 as a percentage?

1/4 + 6/9 expressed as a percentage is 91.6667%.

Does 1/4 plus 6/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.916667...) because the denominator contains prime factors other than 2 and 5.