What is 1/16 plus 2/7? (Answer: 39/112)

Exact Answer

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Problem: What is 1/16 plus 2/7?
Formula / Expression: 1/16 + 2/7
Final Answer: 39/112
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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 1/16 by 7, and multiply the numerator and denominator of 2/7 by 16 so both fractions share the common base 112.
Working: 1 × 7/16 × 7 = 7/112 and 2 × 16/7 × 16 = 32/112

Step 3: Add the Numerators
Now add the numerators (7 + 32 = 39) and keep the common denominator 112 unchanged.
Working: 7 + 32/112 = 39/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 39 and 112 is 1, confirming that 39/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 39/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 112 produces a repeating decimal (approximately 0.348214, or 34.8214%).
Working: 39 ÷ 112 = 0.348214 (34.8214%)

Key Values:
- Simplified Fraction: 39/112
- Mixed Number Form: 39/112
- Decimal Value: 0.348214
- Percentage: 34.8214%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-16-plus-2-7/
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1/16 + 2/7 = 39/112

Simplified Fraction

39/112

Mixed Number

Proper (39/112)

Decimal Value

0.348214

Percentage

34.8214%

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Step-by-Step Solution: 1/16 + 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 1/16 by 7, and multiply the numerator and denominator of 2/7 by 16 so both fractions share the common base 112.

1 × 7/16 × 7 = 7/112 and 2 × 16/7 × 16 = 32/112

Step 3

Add the Numerators

Now add the numerators (7 + 32 = 39) and keep the common denominator 112 unchanged.

7 + 32/112 = 39/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 39 and 112 is 1, confirming that 39/112 cannot be reduced further—it is already in its simplest irreducible form.

39/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 112 produces a repeating decimal (approximately 0.348214, or 34.8214%).

39 ÷ 112 = 0.348214 (34.8214%)

Visual Representation

The diagram below illustrates 1/16 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/112`
Mixed Number Form	`39/112`
Decimal Form	`0.348214`
Percentage	`34.8214%`

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Frequently Asked Questions

What is 1/16 plus 2/7 as a fraction?

1/16 + 2/7 in simplest fraction form is 39/112.

What is 1/16 plus 2/7 as a decimal?

1/16 + 2/7 converted to a decimal is 0.348214.

What is 1/16 plus 2/7 as a percentage?

1/16 + 2/7 expressed as a percentage is 34.8214%.

Does 1/16 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.348214...) because the denominator contains prime factors other than 2 and 5.