What is 2/7 plus 7/16? (Answer: 81/112)

Exact Answer

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Problem: What is 2/7 plus 7/16?
Formula / Expression: 2/7 + 7/16
Final Answer: 81/112
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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 7/16 by 7 so both fractions share the common base 112.
Working: 2 × 16/7 × 16 = 32/112 and 7 × 7/16 × 7 = 49/112

Step 3: Add the Numerators
Now add the numerators (32 + 49 = 81) and keep the common denominator 112 unchanged.
Working: 32 + 49/112 = 81/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 81 and 112 is 1, confirming that 81/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 81/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 81 by denominator 112 produces a repeating decimal (approximately 0.723214, or 72.3214%).
Working: 81 ÷ 112 = 0.723214 (72.3214%)

Key Values:
- Simplified Fraction: 81/112
- Mixed Number Form: 81/112
- Decimal Value: 0.723214
- Percentage: 72.3214%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-7-16/
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2/7 + 7/16 = 81/112

Simplified Fraction

81/112

Mixed Number

Proper (81/112)

Decimal Value

0.723214

Percentage

72.3214%

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

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 7/16 by 7 so both fractions share the common base 112.

2 × 16/7 × 16 = 32/112 and 7 × 7/16 × 7 = 49/112

Step 3

Add the Numerators

Now add the numerators (32 + 49 = 81) and keep the common denominator 112 unchanged.

32 + 49/112 = 81/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 81 and 112 is 1, confirming that 81/112 cannot be reduced further—it is already in its simplest irreducible form.

81/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 81 by denominator 112 produces a repeating decimal (approximately 0.723214, or 72.3214%).

81 ÷ 112 = 0.723214 (72.3214%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`81/112`
Mixed Number Form	`81/112`
Decimal Form	`0.723214`
Percentage	`72.3214%`

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Frequently Asked Questions

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

2/7 + 7/16 in simplest fraction form is 81/112.

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

2/7 + 7/16 converted to a decimal is 0.723214.

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

2/7 + 7/16 expressed as a percentage is 72.3214%.

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

It results in a repeating decimal (approximately 0.723214...) because the denominator contains prime factors other than 2 and 5.