What is 2/14 plus 9/49? (Answer: 16/49)

Exact Answer

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Problem: What is 2/14 plus 9/49?
Formula / Expression: 2/14 + 9/49
Final Answer: 16/49
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 49 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 98 (which is smaller than their product 14 × 49 = 686, keeping the calculation simpler).
Working: LCD(14, 49) = 98

Step 2: Convert to Equivalent Fractions with Common Denominator 98
Multiply the numerator and denominator of 2/14 by 7, and multiply the numerator and denominator of 9/49 by 2 so both fractions share the common base 98.
Working: 2 × 7/14 × 7 = 14/98 and 9 × 2/49 × 2 = 18/98

Step 3: Add the Numerators
Now add the numerators (14 + 18 = 32) and keep the common denominator 98 unchanged.
Working: 14 + 18/98 = 32/98

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 98, which is 2. Divide both the numerator and denominator by 2.
Working: 32 ÷ 2/98 ÷ 2 = 16/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 49 produces a repeating decimal (approximately 0.326531, or 32.6531%).
Working: 16 ÷ 49 = 0.326531 (32.6531%)

Key Values:
- Simplified Fraction: 16/49
- Mixed Number Form: 16/49
- Decimal Value: 0.326531
- Percentage: 32.6531%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-14-plus-9-49/
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2/14 + 9/49 = 16/49

Simplified Fraction

16/49

Mixed Number

Proper (16/49)

Decimal Value

0.326531

Percentage

32.6531%

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Step-by-Step Solution: 2/14 + 9/49

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 49 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 98 (which is smaller than their product 14 × 49 = 686, keeping the calculation simpler).

LCD(14, 49) = 98

Step 2

Convert to Equivalent Fractions with Common Denominator 98

Multiply the numerator and denominator of 2/14 by 7, and multiply the numerator and denominator of 9/49 by 2 so both fractions share the common base 98.

2 × 7/14 × 7 = 14/98 and 9 × 2/49 × 2 = 18/98

Step 3

Add the Numerators

Now add the numerators (14 + 18 = 32) and keep the common denominator 98 unchanged.

14 + 18/98 = 32/98

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 98, which is 2. Divide both the numerator and denominator by 2.

32 ÷ 2/98 ÷ 2 = 16/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 49 produces a repeating decimal (approximately 0.326531, or 32.6531%).

16 ÷ 49 = 0.326531 (32.6531%)

Visual Representation

The diagram below illustrates 2/14 plus 9/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/49`
Mixed Number Form	`16/49`
Decimal Form	`0.326531`
Percentage	`32.6531%`

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Frequently Asked Questions

What is 2/14 plus 9/49 as a fraction?

2/14 + 9/49 in simplest fraction form is 16/49.

What is 2/14 plus 9/49 as a decimal?

2/14 + 9/49 converted to a decimal is 0.326531.

What is 2/14 plus 9/49 as a percentage?

2/14 + 9/49 expressed as a percentage is 32.6531%.

Does 2/14 plus 9/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.326531...) because the denominator contains prime factors other than 2 and 5.