What is 4/14 plus 4/9? (Answer: 46/63)

Exact Answer

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Problem: What is 4/14 plus 4/9?
Formula / Expression: 4/14 + 4/9
Final Answer: 46/63
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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 4/14 by 9, and multiply the numerator and denominator of 4/9 by 14 so both fractions share the common base 126.
Working: 4 × 9/14 × 9 = 36/126 and 4 × 14/9 × 14 = 56/126

Step 3: Add the Numerators
Now add the numerators (36 + 56 = 92) and keep the common denominator 126 unchanged.
Working: 36 + 56/126 = 92/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 92 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 92 ÷ 2/126 ÷ 2 = 46/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 63 produces a repeating decimal (approximately 0.730159, or 73.0159%).
Working: 46 ÷ 63 = 0.730159 (73.0159%)

Key Values:
- Simplified Fraction: 46/63
- Mixed Number Form: 46/63
- Decimal Value: 0.730159
- Percentage: 73.0159%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-14-plus-4-9/
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4/14 + 4/9 = 46/63

Simplified Fraction

46/63

Mixed Number

Proper (46/63)

Decimal Value

0.730159

Percentage

73.0159%

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Step-by-Step Solution: 4/14 + 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 4/14 by 9, and multiply the numerator and denominator of 4/9 by 14 so both fractions share the common base 126.

4 × 9/14 × 9 = 36/126 and 4 × 14/9 × 14 = 56/126

Step 3

Add the Numerators

Now add the numerators (36 + 56 = 92) and keep the common denominator 126 unchanged.

36 + 56/126 = 92/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 92 and 126, which is 2. Divide both the numerator and denominator by 2.

92 ÷ 2/126 ÷ 2 = 46/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 63 produces a repeating decimal (approximately 0.730159, or 73.0159%).

46 ÷ 63 = 0.730159 (73.0159%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/63`
Mixed Number Form	`46/63`
Decimal Form	`0.730159`
Percentage	`73.0159%`

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Frequently Asked Questions

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

4/14 + 4/9 in simplest fraction form is 46/63.

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

4/14 + 4/9 converted to a decimal is 0.730159.

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

4/14 + 4/9 expressed as a percentage is 73.0159%.

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

It results in a repeating decimal (approximately 0.730159...) because the denominator contains prime factors other than 2 and 5.