What is 5/9 plus 9/14? (Answer: 151/126)

Exact Answer

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Problem: What is 5/9 plus 9/14?
Formula / Expression: 5/9 + 9/14
Final Answer: 1 25/126 (151/126)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 14 = 126.
Working: LCD(9, 14) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 5/9 by 14, and multiply the numerator and denominator of 9/14 by 9 so both fractions share the common base 126.
Working: 5 × 14/9 × 14 = 70/126 and 9 × 9/14 × 9 = 81/126

Step 3: Add the Numerators
Now add the numerators (70 + 81 = 151) and keep the common denominator 126 unchanged.
Working: 70 + 81/126 = 151/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 151 and 126 is 1, confirming that 151/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 151/126

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (151) is greater than the denominator (126), divide 151 by 126: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/126.
Working: 151/126 = 1 25/126

Step 6: Decimal & Percentage Representation
Dividing the numerator 151 by denominator 126 produces a repeating decimal (approximately 1.198413, or 119.8413%).
Working: 151 ÷ 126 = 1.198413 (119.8413%)

Key Values:
- Simplified Fraction: 151/126
- Mixed Number Form: 1 25/126
- Decimal Value: 1.198413
- Percentage: 119.8413%

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Solved with FractionsCalc:
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5/9 + 9/14 = 151/126

Simplified Fraction

151/126

Mixed Number

1 25/126

Decimal Value

1.198413

Percentage

119.8413%

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Step-by-Step Solution: 5/9 + 9/14

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 14 = 126.

LCD(9, 14) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 5/9 by 14, and multiply the numerator and denominator of 9/14 by 9 so both fractions share the common base 126.

5 × 14/9 × 14 = 70/126 and 9 × 9/14 × 9 = 81/126

Step 3

Add the Numerators

Now add the numerators (70 + 81 = 151) and keep the common denominator 126 unchanged.

70 + 81/126 = 151/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 151 and 126 is 1, confirming that 151/126 cannot be reduced further—it is already in its simplest irreducible form.

151/126

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (151) is greater than the denominator (126), divide 151 by 126: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/126.

151/126 = 125/126

Step 6

Decimal & Percentage Representation

Dividing the numerator 151 by denominator 126 produces a repeating decimal (approximately 1.198413, or 119.8413%).

151 ÷ 126 = 1.198413 (119.8413%)

Visual Representation

The diagram below illustrates 5/9 plus 9/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`151/126`
Mixed Number Form	`1 25/126`
Decimal Form	`1.198413`
Percentage	`119.8413%`

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Frequently Asked Questions

What is 5/9 plus 9/14 as a fraction?

5/9 + 9/14 in simplest fraction form is 151/126 (or 1 25/126 as a mixed number).

What is 5/9 plus 9/14 as a decimal?

5/9 + 9/14 converted to a decimal is 1.198413.

What is 5/9 plus 9/14 as a percentage?

5/9 + 9/14 expressed as a percentage is 119.8413%.

How do you write 5/9 plus 9/14 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 151/126 can be written as the mixed number 1 25/126.

Does 5/9 plus 9/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.198413...) because the denominator contains prime factors other than 2 and 5.