What is 3/16 plus 10/13? (Answer: 199/208)

Exact Answer

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Problem: What is 3/16 plus 10/13?
Formula / Expression: 3/16 + 10/13
Final Answer: 199/208
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 13 = 208.
Working: LCD(16, 13) = 208

Step 2: Convert to Equivalent Fractions with Common Denominator 208
Multiply the numerator and denominator of 3/16 by 13, and multiply the numerator and denominator of 10/13 by 16 so both fractions share the common base 208.
Working: 3 × 13/16 × 13 = 39/208 and 10 × 16/13 × 16 = 160/208

Step 3: Add the Numerators
Now add the numerators (39 + 160 = 199) and keep the common denominator 208 unchanged.
Working: 39 + 160/208 = 199/208

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 199 and 208 is 1, confirming that 199/208 cannot be reduced further—it is already in its simplest irreducible form.
Working: 199/208

Step 5: Decimal & Percentage Representation
Dividing the numerator 199 by denominator 208 produces a repeating decimal (approximately 0.956731, or 95.6731%).
Working: 199 ÷ 208 = 0.956731 (95.6731%)

Key Values:
- Simplified Fraction: 199/208
- Mixed Number Form: 199/208
- Decimal Value: 0.956731
- Percentage: 95.6731%

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3/16 + 10/13 = 199/208

Simplified Fraction

199/208

Mixed Number

Proper (199/208)

Decimal Value

0.956731

Percentage

95.6731%

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Step-by-Step Solution: 3/16 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 13 = 208.

LCD(16, 13) = 208

Step 2

Convert to Equivalent Fractions with Common Denominator 208

Multiply the numerator and denominator of 3/16 by 13, and multiply the numerator and denominator of 10/13 by 16 so both fractions share the common base 208.

3 × 13/16 × 13 = 39/208 and 10 × 16/13 × 16 = 160/208

Step 3

Add the Numerators

Now add the numerators (39 + 160 = 199) and keep the common denominator 208 unchanged.

39 + 160/208 = 199/208

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 199 and 208 is 1, confirming that 199/208 cannot be reduced further—it is already in its simplest irreducible form.

199/208

Step 5

Decimal & Percentage Representation

Dividing the numerator 199 by denominator 208 produces a repeating decimal (approximately 0.956731, or 95.6731%).

199 ÷ 208 = 0.956731 (95.6731%)

Visual Representation

The diagram below illustrates 3/16 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`199/208`
Mixed Number Form	`199/208`
Decimal Form	`0.956731`
Percentage	`95.6731%`

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Frequently Asked Questions

What is 3/16 plus 10/13 as a fraction?

3/16 + 10/13 in simplest fraction form is 199/208.

What is 3/16 plus 10/13 as a decimal?

3/16 + 10/13 converted to a decimal is 0.956731.

What is 3/16 plus 10/13 as a percentage?

3/16 + 10/13 expressed as a percentage is 95.6731%.

Does 3/16 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.956731...) because the denominator contains prime factors other than 2 and 5.