What is 1/19 plus 2/7? (Answer: 45/133)

Exact Answer

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Problem: What is 1/19 plus 2/7?
Formula / Expression: 1/19 + 2/7
Final Answer: 45/133
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 7 = 133.
Working: LCD(19, 7) = 133

Step 2: Convert to Equivalent Fractions with Common Denominator 133
Multiply the numerator and denominator of 1/19 by 7, and multiply the numerator and denominator of 2/7 by 19 so both fractions share the common base 133.
Working: 1 × 7/19 × 7 = 7/133 and 2 × 19/7 × 19 = 38/133

Step 3: Add the Numerators
Now add the numerators (7 + 38 = 45) and keep the common denominator 133 unchanged.
Working: 7 + 38/133 = 45/133

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 45 and 133 is 1, confirming that 45/133 cannot be reduced further—it is already in its simplest irreducible form.
Working: 45/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 133 produces a repeating decimal (approximately 0.338346, or 33.8346%).
Working: 45 ÷ 133 = 0.338346 (33.8346%)

Key Values:
- Simplified Fraction: 45/133
- Mixed Number Form: 45/133
- Decimal Value: 0.338346
- Percentage: 33.8346%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-19-plus-2-7/
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1/19 + 2/7 = 45/133

Simplified Fraction

45/133

Mixed Number

Proper (45/133)

Decimal Value

0.338346

Percentage

33.8346%

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Step-by-Step Solution: 1/19 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 7 = 133.

LCD(19, 7) = 133

Step 2

Convert to Equivalent Fractions with Common Denominator 133

Multiply the numerator and denominator of 1/19 by 7, and multiply the numerator and denominator of 2/7 by 19 so both fractions share the common base 133.

1 × 7/19 × 7 = 7/133 and 2 × 19/7 × 19 = 38/133

Step 3

Add the Numerators

Now add the numerators (7 + 38 = 45) and keep the common denominator 133 unchanged.

7 + 38/133 = 45/133

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 45 and 133 is 1, confirming that 45/133 cannot be reduced further—it is already in its simplest irreducible form.

45/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 133 produces a repeating decimal (approximately 0.338346, or 33.8346%).

45 ÷ 133 = 0.338346 (33.8346%)

Visual Representation

The diagram below illustrates 1/19 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/133`
Mixed Number Form	`45/133`
Decimal Form	`0.338346`
Percentage	`33.8346%`

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Frequently Asked Questions

What is 1/19 plus 2/7 as a fraction?

1/19 + 2/7 in simplest fraction form is 45/133.

What is 1/19 plus 2/7 as a decimal?

1/19 + 2/7 converted to a decimal is 0.338346.

What is 1/19 plus 2/7 as a percentage?

1/19 + 2/7 expressed as a percentage is 33.8346%.

Does 1/19 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.338346...) because the denominator contains prime factors other than 2 and 5.