What is 2/14 plus 3/9? (Answer: 10/21)

Exact Answer

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Problem: What is 2/14 plus 3/9?
Formula / Expression: 2/14 + 3/9
Final Answer: 10/21
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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 2/14 by 9, and multiply the numerator and denominator of 3/9 by 14 so both fractions share the common base 126.
Working: 2 × 9/14 × 9 = 18/126 and 3 × 14/9 × 14 = 42/126

Step 3: Add the Numerators
Now add the numerators (18 + 42 = 60) and keep the common denominator 126 unchanged.
Working: 18 + 42/126 = 60/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 60 and 126, which is 6. Divide both the numerator and denominator by 6.
Working: 60 ÷ 6/126 ÷ 6 = 10/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).
Working: 10 ÷ 21 = 0.47619 (47.619%)

Key Values:
- Simplified Fraction: 10/21
- Mixed Number Form: 10/21
- Decimal Value: 0.47619
- Percentage: 47.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-14-plus-3-9/
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2/14 + 3/9 = 10/21

Simplified Fraction

10/21

Mixed Number

Proper (10/21)

Decimal Value

0.47619

Percentage

47.619%

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Step-by-Step Solution: 2/14 + 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 2/14 by 9, and multiply the numerator and denominator of 3/9 by 14 so both fractions share the common base 126.

2 × 9/14 × 9 = 18/126 and 3 × 14/9 × 14 = 42/126

Step 3

Add the Numerators

Now add the numerators (18 + 42 = 60) and keep the common denominator 126 unchanged.

18 + 42/126 = 60/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 60 and 126, which is 6. Divide both the numerator and denominator by 6.

60 ÷ 6/126 ÷ 6 = 10/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).

10 ÷ 21 = 0.47619 (47.619%)

Visual Representation

The diagram below illustrates 2/14 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/21`
Mixed Number Form	`10/21`
Decimal Form	`0.47619`
Percentage	`47.619%`

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Frequently Asked Questions

What is 2/14 plus 3/9 as a fraction?

2/14 + 3/9 in simplest fraction form is 10/21.

What is 2/14 plus 3/9 as a decimal?

2/14 + 3/9 converted to a decimal is 0.47619.

What is 2/14 plus 3/9 as a percentage?

2/14 + 3/9 expressed as a percentage is 47.619%.

Does 2/14 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.47619...) because the denominator contains prime factors other than 2 and 5.