What is 5/14 plus 4/9? (Answer: 101/126)

Exact Answer

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Problem: What is 5/14 plus 4/9?
Formula / Expression: 5/14 + 4/9
Final Answer: 101/126
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 5/14 by 9, and multiply the numerator and denominator of 4/9 by 14 so both fractions share the common base 126.
Working: 5 × 9/14 × 9 = 45/126 and 4 × 14/9 × 14 = 56/126

Step 3: Add the Numerators
Now add the numerators (45 + 56 = 101) and keep the common denominator 126 unchanged.
Working: 45 + 56/126 = 101/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 126 is 1, confirming that 101/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 126 produces a repeating decimal (approximately 0.801587, or 80.1587%).
Working: 101 ÷ 126 = 0.801587 (80.1587%)

Key Values:
- Simplified Fraction: 101/126
- Mixed Number Form: 101/126
- Decimal Value: 0.801587
- Percentage: 80.1587%

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Solved with FractionsCalc:
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5/14 + 4/9 = 101/126

Simplified Fraction

101/126

Mixed Number

Proper (101/126)

Decimal Value

0.801587

Percentage

80.1587%

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Step-by-Step Solution: 5/14 + 4/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(14, 9) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 5/14 by 9, and multiply the numerator and denominator of 4/9 by 14 so both fractions share the common base 126.

5 × 9/14 × 9 = 45/126 and 4 × 14/9 × 14 = 56/126

Step 3

Add the Numerators

Now add the numerators (45 + 56 = 101) and keep the common denominator 126 unchanged.

45 + 56/126 = 101/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 126 is 1, confirming that 101/126 cannot be reduced further—it is already in its simplest irreducible form.

101/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 126 produces a repeating decimal (approximately 0.801587, or 80.1587%).

101 ÷ 126 = 0.801587 (80.1587%)

Visual Representation

The diagram below illustrates 5/14 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/126`
Mixed Number Form	`101/126`
Decimal Form	`0.801587`
Percentage	`80.1587%`

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Frequently Asked Questions

What is 5/14 plus 4/9 as a fraction?

5/14 + 4/9 in simplest fraction form is 101/126.

What is 5/14 plus 4/9 as a decimal?

5/14 + 4/9 converted to a decimal is 0.801587.

What is 5/14 plus 4/9 as a percentage?

5/14 + 4/9 expressed as a percentage is 80.1587%.

Does 5/14 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.801587...) because the denominator contains prime factors other than 2 and 5.