What is 4/14 plus 3/9? (Answer: 13/21)

Exact Answer

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Problem: What is 4/14 plus 3/9?
Formula / Expression: 4/14 + 3/9
Final Answer: 13/21
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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 3/9 by 14 so both fractions share the common base 126.
Working: 4 × 9/14 × 9 = 36/126 and 3 × 14/9 × 14 = 42/126

Step 3: Add the Numerators
Now add the numerators (36 + 42 = 78) and keep the common denominator 126 unchanged.
Working: 36 + 42/126 = 78/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 126, which is 6. Divide both the numerator and denominator by 6.
Working: 78 ÷ 6/126 ÷ 6 = 13/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).
Working: 13 ÷ 21 = 0.619048 (61.9048%)

Key Values:
- Simplified Fraction: 13/21
- Mixed Number Form: 13/21
- Decimal Value: 0.619048
- Percentage: 61.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-14-plus-3-9/
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4/14 + 3/9 = 13/21

Simplified Fraction

13/21

Mixed Number

Proper (13/21)

Decimal Value

0.619048

Percentage

61.9048%

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Step-by-Step Solution: 4/14 + 3/9

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 3/9 by 14 so both fractions share the common base 126.

4 × 9/14 × 9 = 36/126 and 3 × 14/9 × 14 = 42/126

Step 3

Add the Numerators

Now add the numerators (36 + 42 = 78) and keep the common denominator 126 unchanged.

36 + 42/126 = 78/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 126, which is 6. Divide both the numerator and denominator by 6.

78 ÷ 6/126 ÷ 6 = 13/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).

13 ÷ 21 = 0.619048 (61.9048%)

Visual Representation

The diagram below illustrates 4/14 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/21`
Mixed Number Form	`13/21`
Decimal Form	`0.619048`
Percentage	`61.9048%`

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Frequently Asked Questions

What is 4/14 plus 3/9 as a fraction?

4/14 + 3/9 in simplest fraction form is 13/21.

What is 4/14 plus 3/9 as a decimal?

4/14 + 3/9 converted to a decimal is 0.619048.

What is 4/14 plus 3/9 as a percentage?

4/14 + 3/9 expressed as a percentage is 61.9048%.

Does 4/14 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.619048...) because the denominator contains prime factors other than 2 and 5.