What is 2/19 plus 2/16? (Answer: 35/152)

Exact Answer

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Problem: What is 2/19 plus 2/16?
Formula / Expression: 2/19 + 2/16
Final Answer: 35/152
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 16 = 304.
Working: LCD(19, 16) = 304

Step 2: Convert to Equivalent Fractions with Common Denominator 304
Multiply the numerator and denominator of 2/19 by 16, and multiply the numerator and denominator of 2/16 by 19 so both fractions share the common base 304.
Working: 2 × 16/19 × 16 = 32/304 and 2 × 19/16 × 19 = 38/304

Step 3: Add the Numerators
Now add the numerators (32 + 38 = 70) and keep the common denominator 304 unchanged.
Working: 32 + 38/304 = 70/304

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 304, which is 2. Divide both the numerator and denominator by 2.
Working: 70 ÷ 2/304 ÷ 2 = 35/152

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 152 produces a repeating decimal (approximately 0.230263, or 23.0263%).
Working: 35 ÷ 152 = 0.230263 (23.0263%)

Key Values:
- Simplified Fraction: 35/152
- Mixed Number Form: 35/152
- Decimal Value: 0.230263
- Percentage: 23.0263%

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Solved with FractionsCalc:
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2/19 + 2/16 = 35/152

Simplified Fraction

35/152

Mixed Number

Proper (35/152)

Decimal Value

0.230263

Percentage

23.0263%

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Step-by-Step Solution: 2/19 + 2/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 16 = 304.

LCD(19, 16) = 304

Step 2

Convert to Equivalent Fractions with Common Denominator 304

Multiply the numerator and denominator of 2/19 by 16, and multiply the numerator and denominator of 2/16 by 19 so both fractions share the common base 304.

2 × 16/19 × 16 = 32/304 and 2 × 19/16 × 19 = 38/304

Step 3

Add the Numerators

Now add the numerators (32 + 38 = 70) and keep the common denominator 304 unchanged.

32 + 38/304 = 70/304

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 304, which is 2. Divide both the numerator and denominator by 2.

70 ÷ 2/304 ÷ 2 = 35/152

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 152 produces a repeating decimal (approximately 0.230263, or 23.0263%).

35 ÷ 152 = 0.230263 (23.0263%)

Visual Representation

The diagram below illustrates 2/19 plus 2/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/152`
Mixed Number Form	`35/152`
Decimal Form	`0.230263`
Percentage	`23.0263%`

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Frequently Asked Questions

What is 2/19 plus 2/16 as a fraction?

2/19 + 2/16 in simplest fraction form is 35/152.

What is 2/19 plus 2/16 as a decimal?

2/19 + 2/16 converted to a decimal is 0.230263.

What is 2/19 plus 2/16 as a percentage?

2/19 + 2/16 expressed as a percentage is 23.0263%.

Does 2/19 plus 2/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.230263...) because the denominator contains prime factors other than 2 and 5.