What is 2/16 plus 8/49? (Answer: 113/392)

Exact Answer

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Problem: What is 2/16 plus 8/49?
Formula / Expression: 2/16 + 8/49
Final Answer: 113/392
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 49 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 49 = 784.
Working: LCD(16, 49) = 784

Step 2: Convert to Equivalent Fractions with Common Denominator 784
Multiply the numerator and denominator of 2/16 by 49, and multiply the numerator and denominator of 8/49 by 16 so both fractions share the common base 784.
Working: 2 × 49/16 × 49 = 98/784 and 8 × 16/49 × 16 = 128/784

Step 3: Add the Numerators
Now add the numerators (98 + 128 = 226) and keep the common denominator 784 unchanged.
Working: 98 + 128/784 = 226/784

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 226 and 784, which is 2. Divide both the numerator and denominator by 2.
Working: 226 ÷ 2/784 ÷ 2 = 113/392

Step 5: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 392 produces a repeating decimal (approximately 0.288265, or 28.8265%).
Working: 113 ÷ 392 = 0.288265 (28.8265%)

Key Values:
- Simplified Fraction: 113/392
- Mixed Number Form: 113/392
- Decimal Value: 0.288265
- Percentage: 28.8265%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-16-plus-8-49/
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2/16 + 8/49 = 113/392

Simplified Fraction

113/392

Mixed Number

Proper (113/392)

Decimal Value

0.288265

Percentage

28.8265%

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Step-by-Step Solution: 2/16 + 8/49

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 49 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 49 = 784.

LCD(16, 49) = 784

Step 2

Convert to Equivalent Fractions with Common Denominator 784

Multiply the numerator and denominator of 2/16 by 49, and multiply the numerator and denominator of 8/49 by 16 so both fractions share the common base 784.

2 × 49/16 × 49 = 98/784 and 8 × 16/49 × 16 = 128/784

Step 3

Add the Numerators

Now add the numerators (98 + 128 = 226) and keep the common denominator 784 unchanged.

98 + 128/784 = 226/784

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 226 and 784, which is 2. Divide both the numerator and denominator by 2.

226 ÷ 2/784 ÷ 2 = 113/392

Step 5

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 392 produces a repeating decimal (approximately 0.288265, or 28.8265%).

113 ÷ 392 = 0.288265 (28.8265%)

Visual Representation

The diagram below illustrates 2/16 plus 8/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/392`
Mixed Number Form	`113/392`
Decimal Form	`0.288265`
Percentage	`28.8265%`

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Frequently Asked Questions

What is 2/16 plus 8/49 as a fraction?

2/16 + 8/49 in simplest fraction form is 113/392.

What is 2/16 plus 8/49 as a decimal?

2/16 + 8/49 converted to a decimal is 0.288265.

What is 2/16 plus 8/49 as a percentage?

2/16 + 8/49 expressed as a percentage is 28.8265%.

Does 2/16 plus 8/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.288265...) because the denominator contains prime factors other than 2 and 5.