What is 2/16 plus 4/7? (Answer: 39/56)

Exact Answer

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Problem: What is 2/16 plus 4/7?
Formula / Expression: 2/16 + 4/7
Final Answer: 39/56
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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 4/7 by 16 so both fractions share the common base 112.
Working: 2 × 7/16 × 7 = 14/112 and 4 × 16/7 × 16 = 64/112

Step 3: Add the Numerators
Now add the numerators (14 + 64 = 78) and keep the common denominator 112 unchanged.
Working: 14 + 64/112 = 78/112

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 112, which is 2. Divide both the numerator and denominator by 2.
Working: 78 ÷ 2/112 ÷ 2 = 39/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 56 produces a repeating decimal (approximately 0.696429, or 69.6429%).
Working: 39 ÷ 56 = 0.696429 (69.6429%)

Key Values:
- Simplified Fraction: 39/56
- Mixed Number Form: 39/56
- Decimal Value: 0.696429
- Percentage: 69.6429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-16-plus-4-7/
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2/16 + 4/7 = 39/56

Simplified Fraction

39/56

Mixed Number

Proper (39/56)

Decimal Value

0.696429

Percentage

69.6429%

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Step-by-Step Solution: 2/16 + 4/7

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 4/7 by 16 so both fractions share the common base 112.

2 × 7/16 × 7 = 14/112 and 4 × 16/7 × 16 = 64/112

Step 3

Add the Numerators

Now add the numerators (14 + 64 = 78) and keep the common denominator 112 unchanged.

14 + 64/112 = 78/112

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 112, which is 2. Divide both the numerator and denominator by 2.

78 ÷ 2/112 ÷ 2 = 39/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 56 produces a repeating decimal (approximately 0.696429, or 69.6429%).

39 ÷ 56 = 0.696429 (69.6429%)

Visual Representation

The diagram below illustrates 2/16 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/56`
Mixed Number Form	`39/56`
Decimal Form	`0.696429`
Percentage	`69.6429%`

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Frequently Asked Questions

What is 2/16 plus 4/7 as a fraction?

2/16 + 4/7 in simplest fraction form is 39/56.

What is 2/16 plus 4/7 as a decimal?

2/16 + 4/7 converted to a decimal is 0.696429.

What is 2/16 plus 4/7 as a percentage?

2/16 + 4/7 expressed as a percentage is 69.6429%.

Does 2/16 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.696429...) because the denominator contains prime factors other than 2 and 5.