What is 2/14 plus 8/49? (Answer: 15/49)

Exact Answer

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Problem: What is 2/14 plus 8/49?
Formula / Expression: 2/14 + 8/49
Final Answer: 15/49
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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 8/49 by 2 so both fractions share the common base 98.
Working: 2 × 7/14 × 7 = 14/98 and 8 × 2/49 × 2 = 16/98

Step 3: Add the Numerators
Now add the numerators (14 + 16 = 30) and keep the common denominator 98 unchanged.
Working: 14 + 16/98 = 30/98

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 98, which is 2. Divide both the numerator and denominator by 2.
Working: 30 ÷ 2/98 ÷ 2 = 15/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 49 produces a repeating decimal (approximately 0.306122, or 30.6122%).
Working: 15 ÷ 49 = 0.306122 (30.6122%)

Key Values:
- Simplified Fraction: 15/49
- Mixed Number Form: 15/49
- Decimal Value: 0.306122
- Percentage: 30.6122%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-14-plus-8-49/
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2/14 + 8/49 = 15/49

Simplified Fraction

15/49

Mixed Number

Proper (15/49)

Decimal Value

0.306122

Percentage

30.6122%

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Step-by-Step Solution: 2/14 + 8/49

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 8/49 by 2 so both fractions share the common base 98.

2 × 7/14 × 7 = 14/98 and 8 × 2/49 × 2 = 16/98

Step 3

Add the Numerators

Now add the numerators (14 + 16 = 30) and keep the common denominator 98 unchanged.

14 + 16/98 = 30/98

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 30 and 98, which is 2. Divide both the numerator and denominator by 2.

30 ÷ 2/98 ÷ 2 = 15/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 49 produces a repeating decimal (approximately 0.306122, or 30.6122%).

15 ÷ 49 = 0.306122 (30.6122%)

Visual Representation

The diagram below illustrates 2/14 plus 8/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/49`
Mixed Number Form	`15/49`
Decimal Form	`0.306122`
Percentage	`30.6122%`

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Frequently Asked Questions

What is 2/14 plus 8/49 as a fraction?

2/14 + 8/49 in simplest fraction form is 15/49.

What is 2/14 plus 8/49 as a decimal?

2/14 + 8/49 converted to a decimal is 0.306122.

What is 2/14 plus 8/49 as a percentage?

2/14 + 8/49 expressed as a percentage is 30.6122%.

Does 2/14 plus 8/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.306122...) because the denominator contains prime factors other than 2 and 5.