What is 2/7 plus 5/16? (Answer: 67/112)

Exact Answer

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Problem: What is 2/7 plus 5/16?
Formula / Expression: 2/7 + 5/16
Final Answer: 67/112
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 112
Multiply the numerator and denominator of 2/7 by 16, and multiply the numerator and denominator of 5/16 by 7 so both fractions share the common base 112.
Working: 2 × 16/7 × 16 = 32/112 and 5 × 7/16 × 7 = 35/112

Step 3: Add the Numerators
Now add the numerators (32 + 35 = 67) and keep the common denominator 112 unchanged.
Working: 32 + 35/112 = 67/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 112 is 1, confirming that 67/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 112 produces a repeating decimal (approximately 0.598214, or 59.8214%).
Working: 67 ÷ 112 = 0.598214 (59.8214%)

Key Values:
- Simplified Fraction: 67/112
- Mixed Number Form: 67/112
- Decimal Value: 0.598214
- Percentage: 59.8214%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-5-16/
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2/7 + 5/16 = 67/112

Simplified Fraction

67/112

Mixed Number

Proper (67/112)

Decimal Value

0.598214

Percentage

59.8214%

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Step-by-Step Solution: 2/7 + 5/16

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 16) = 112

Step 2

Convert to Equivalent Fractions with Common Denominator 112

Multiply the numerator and denominator of 2/7 by 16, and multiply the numerator and denominator of 5/16 by 7 so both fractions share the common base 112.

2 × 16/7 × 16 = 32/112 and 5 × 7/16 × 7 = 35/112

Step 3

Add the Numerators

Now add the numerators (32 + 35 = 67) and keep the common denominator 112 unchanged.

32 + 35/112 = 67/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 112 is 1, confirming that 67/112 cannot be reduced further—it is already in its simplest irreducible form.

67/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 112 produces a repeating decimal (approximately 0.598214, or 59.8214%).

67 ÷ 112 = 0.598214 (59.8214%)

Visual Representation

The diagram below illustrates 2/7 plus 5/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/112`
Mixed Number Form	`67/112`
Decimal Form	`0.598214`
Percentage	`59.8214%`

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Frequently Asked Questions

What is 2/7 plus 5/16 as a fraction?

2/7 + 5/16 in simplest fraction form is 67/112.

What is 2/7 plus 5/16 as a decimal?

2/7 + 5/16 converted to a decimal is 0.598214.

What is 2/7 plus 5/16 as a percentage?

2/7 + 5/16 expressed as a percentage is 59.8214%.

Does 2/7 plus 5/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.598214...) because the denominator contains prime factors other than 2 and 5.