What is 2/16 plus 2/7? (Answer: 23/56)

Exact Answer

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Problem: What is 2/16 plus 2/7?
Formula / Expression: 2/16 + 2/7
Final Answer: 23/56
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 7 = 112.
Working: LCD(16, 7) = 112

Step 2: Convert to Equivalent Fractions with Common Denominator 112
Multiply the numerator and denominator of 2/16 by 7, and multiply the numerator and denominator of 2/7 by 16 so both fractions share the common base 112.
Working: 2 × 7/16 × 7 = 14/112 and 2 × 16/7 × 16 = 32/112

Step 3: Add the Numerators
Now add the numerators (14 + 32 = 46) and keep the common denominator 112 unchanged.
Working: 14 + 32/112 = 46/112

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 112, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/112 ÷ 2 = 23/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 56 produces a repeating decimal (approximately 0.410714, or 41.0714%).
Working: 23 ÷ 56 = 0.410714 (41.0714%)

Key Values:
- Simplified Fraction: 23/56
- Mixed Number Form: 23/56
- Decimal Value: 0.410714
- Percentage: 41.0714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-16-plus-2-7/
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2/16 + 2/7 = 23/56

Simplified Fraction

23/56

Mixed Number

Proper (23/56)

Decimal Value

0.410714

Percentage

41.0714%

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Step-by-Step Solution: 2/16 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 7 = 112.

LCD(16, 7) = 112

Step 2

Convert to Equivalent Fractions with Common Denominator 112

Multiply the numerator and denominator of 2/16 by 7, and multiply the numerator and denominator of 2/7 by 16 so both fractions share the common base 112.

2 × 7/16 × 7 = 14/112 and 2 × 16/7 × 16 = 32/112

Step 3

Add the Numerators

Now add the numerators (14 + 32 = 46) and keep the common denominator 112 unchanged.

14 + 32/112 = 46/112

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 112, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/112 ÷ 2 = 23/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 56 produces a repeating decimal (approximately 0.410714, or 41.0714%).

23 ÷ 56 = 0.410714 (41.0714%)

Visual Representation

The diagram below illustrates 2/16 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/56`
Mixed Number Form	`23/56`
Decimal Form	`0.410714`
Percentage	`41.0714%`

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Frequently Asked Questions

What is 2/16 plus 2/7 as a fraction?

2/16 + 2/7 in simplest fraction form is 23/56.

What is 2/16 plus 2/7 as a decimal?

2/16 + 2/7 converted to a decimal is 0.410714.

What is 2/16 plus 2/7 as a percentage?

2/16 + 2/7 expressed as a percentage is 41.0714%.

Does 2/16 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.410714...) because the denominator contains prime factors other than 2 and 5.