What is 3/7 plus 9/19? (Answer: 120/133)

Exact Answer

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Problem: What is 3/7 plus 9/19?
Formula / Expression: 3/7 + 9/19
Final Answer: 120/133
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 133
Multiply the numerator and denominator of 3/7 by 19, and multiply the numerator and denominator of 9/19 by 7 so both fractions share the common base 133.
Working: 3 × 19/7 × 19 = 57/133 and 9 × 7/19 × 7 = 63/133

Step 3: Add the Numerators
Now add the numerators (57 + 63 = 120) and keep the common denominator 133 unchanged.
Working: 57 + 63/133 = 120/133

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 120 and 133 is 1, confirming that 120/133 cannot be reduced further—it is already in its simplest irreducible form.
Working: 120/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 120 by denominator 133 produces a repeating decimal (approximately 0.902256, or 90.2256%).
Working: 120 ÷ 133 = 0.902256 (90.2256%)

Key Values:
- Simplified Fraction: 120/133
- Mixed Number Form: 120/133
- Decimal Value: 0.902256
- Percentage: 90.2256%

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Solved with FractionsCalc:
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3/7 + 9/19 = 120/133

Simplified Fraction

120/133

Mixed Number

Proper (120/133)

Decimal Value

0.902256

Percentage

90.2256%

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Step-by-Step Solution: 3/7 + 9/19

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 19) = 133

Step 2

Convert to Equivalent Fractions with Common Denominator 133

Multiply the numerator and denominator of 3/7 by 19, and multiply the numerator and denominator of 9/19 by 7 so both fractions share the common base 133.

3 × 19/7 × 19 = 57/133 and 9 × 7/19 × 7 = 63/133

Step 3

Add the Numerators

Now add the numerators (57 + 63 = 120) and keep the common denominator 133 unchanged.

57 + 63/133 = 120/133

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 120 and 133 is 1, confirming that 120/133 cannot be reduced further—it is already in its simplest irreducible form.

120/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 120 by denominator 133 produces a repeating decimal (approximately 0.902256, or 90.2256%).

120 ÷ 133 = 0.902256 (90.2256%)

Visual Representation

The diagram below illustrates 3/7 plus 9/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`120/133`
Mixed Number Form	`120/133`
Decimal Form	`0.902256`
Percentage	`90.2256%`

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Frequently Asked Questions

What is 3/7 plus 9/19 as a fraction?

3/7 + 9/19 in simplest fraction form is 120/133.

What is 3/7 plus 9/19 as a decimal?

3/7 + 9/19 converted to a decimal is 0.902256.

What is 3/7 plus 9/19 as a percentage?

3/7 + 9/19 expressed as a percentage is 90.2256%.

Does 3/7 plus 9/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.902256...) because the denominator contains prime factors other than 2 and 5.