What is 3/16 plus 3/7? (Answer: 69/112)

Exact Answer

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Problem: What is 3/16 plus 3/7?
Formula / Expression: 3/16 + 3/7
Final Answer: 69/112
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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 3/16 by 7, and multiply the numerator and denominator of 3/7 by 16 so both fractions share the common base 112.
Working: 3 × 7/16 × 7 = 21/112 and 3 × 16/7 × 16 = 48/112

Step 3: Add the Numerators
Now add the numerators (21 + 48 = 69) and keep the common denominator 112 unchanged.
Working: 21 + 48/112 = 69/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 112 is 1, confirming that 69/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 112 produces a repeating decimal (approximately 0.616071, or 61.6071%).
Working: 69 ÷ 112 = 0.616071 (61.6071%)

Key Values:
- Simplified Fraction: 69/112
- Mixed Number Form: 69/112
- Decimal Value: 0.616071
- Percentage: 61.6071%

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Solved with FractionsCalc:
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3/16 + 3/7 = 69/112

Simplified Fraction

69/112

Mixed Number

Proper (69/112)

Decimal Value

0.616071

Percentage

61.6071%

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Step-by-Step Solution: 3/16 + 3/7

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 3/16 by 7, and multiply the numerator and denominator of 3/7 by 16 so both fractions share the common base 112.

3 × 7/16 × 7 = 21/112 and 3 × 16/7 × 16 = 48/112

Step 3

Add the Numerators

Now add the numerators (21 + 48 = 69) and keep the common denominator 112 unchanged.

21 + 48/112 = 69/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 112 is 1, confirming that 69/112 cannot be reduced further—it is already in its simplest irreducible form.

69/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 112 produces a repeating decimal (approximately 0.616071, or 61.6071%).

69 ÷ 112 = 0.616071 (61.6071%)

Visual Representation

The diagram below illustrates 3/16 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/112`
Mixed Number Form	`69/112`
Decimal Form	`0.616071`
Percentage	`61.6071%`

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Frequently Asked Questions

What is 3/16 plus 3/7 as a fraction?

3/16 + 3/7 in simplest fraction form is 69/112.

What is 3/16 plus 3/7 as a decimal?

3/16 + 3/7 converted to a decimal is 0.616071.

What is 3/16 plus 3/7 as a percentage?

3/16 + 3/7 expressed as a percentage is 61.6071%.

Does 3/16 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.616071...) because the denominator contains prime factors other than 2 and 5.