What is 5/16 plus 3/7? (Answer: 83/112)

Exact Answer

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Problem: What is 5/16 plus 3/7?
Formula / Expression: 5/16 + 3/7
Final Answer: 83/112
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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 5/16 by 7, and multiply the numerator and denominator of 3/7 by 16 so both fractions share the common base 112.
Working: 5 × 7/16 × 7 = 35/112 and 3 × 16/7 × 16 = 48/112

Step 3: Add the Numerators
Now add the numerators (35 + 48 = 83) and keep the common denominator 112 unchanged.
Working: 35 + 48/112 = 83/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 112 is 1, confirming that 83/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 112 produces a repeating decimal (approximately 0.741071, or 74.1071%).
Working: 83 ÷ 112 = 0.741071 (74.1071%)

Key Values:
- Simplified Fraction: 83/112
- Mixed Number Form: 83/112
- Decimal Value: 0.741071
- Percentage: 74.1071%

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Solved with FractionsCalc:
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5/16 + 3/7 = 83/112

Simplified Fraction

83/112

Mixed Number

Proper (83/112)

Decimal Value

0.741071

Percentage

74.1071%

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Step-by-Step Solution: 5/16 + 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 5/16 by 7, and multiply the numerator and denominator of 3/7 by 16 so both fractions share the common base 112.

5 × 7/16 × 7 = 35/112 and 3 × 16/7 × 16 = 48/112

Step 3

Add the Numerators

Now add the numerators (35 + 48 = 83) and keep the common denominator 112 unchanged.

35 + 48/112 = 83/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 112 is 1, confirming that 83/112 cannot be reduced further—it is already in its simplest irreducible form.

83/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 112 produces a repeating decimal (approximately 0.741071, or 74.1071%).

83 ÷ 112 = 0.741071 (74.1071%)

Visual Representation

The diagram below illustrates 5/16 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/112`
Mixed Number Form	`83/112`
Decimal Form	`0.741071`
Percentage	`74.1071%`

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Frequently Asked Questions

What is 5/16 plus 3/7 as a fraction?

5/16 + 3/7 in simplest fraction form is 83/112.

What is 5/16 plus 3/7 as a decimal?

5/16 + 3/7 converted to a decimal is 0.741071.

What is 5/16 plus 3/7 as a percentage?

5/16 + 3/7 expressed as a percentage is 74.1071%.

Does 5/16 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.741071...) because the denominator contains prime factors other than 2 and 5.