What is 2/19 plus 7/10? (Answer: 153/190)

Exact Answer

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Problem: What is 2/19 plus 7/10?
Formula / Expression: 2/19 + 7/10
Final Answer: 153/190
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 10 = 190.
Working: LCD(19, 10) = 190

Step 2: Convert to Equivalent Fractions with Common Denominator 190
Multiply the numerator and denominator of 2/19 by 10, and multiply the numerator and denominator of 7/10 by 19 so both fractions share the common base 190.
Working: 2 × 10/19 × 10 = 20/190 and 7 × 19/10 × 19 = 133/190

Step 3: Add the Numerators
Now add the numerators (20 + 133 = 153) and keep the common denominator 190 unchanged.
Working: 20 + 133/190 = 153/190

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 153 and 190 is 1, confirming that 153/190 cannot be reduced further—it is already in its simplest irreducible form.
Working: 153/190

Step 5: Decimal & Percentage Representation
Dividing the numerator 153 by denominator 190 produces a repeating decimal (approximately 0.805263, or 80.5263%).
Working: 153 ÷ 190 = 0.805263 (80.5263%)

Key Values:
- Simplified Fraction: 153/190
- Mixed Number Form: 153/190
- Decimal Value: 0.805263
- Percentage: 80.5263%

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Solved with FractionsCalc:
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2/19 + 7/10 = 153/190

Simplified Fraction

153/190

Mixed Number

Proper (153/190)

Decimal Value

0.805263

Percentage

80.5263%

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Step-by-Step Solution: 2/19 + 7/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 10 = 190.

LCD(19, 10) = 190

Step 2

Convert to Equivalent Fractions with Common Denominator 190

Multiply the numerator and denominator of 2/19 by 10, and multiply the numerator and denominator of 7/10 by 19 so both fractions share the common base 190.

2 × 10/19 × 10 = 20/190 and 7 × 19/10 × 19 = 133/190

Step 3

Add the Numerators

Now add the numerators (20 + 133 = 153) and keep the common denominator 190 unchanged.

20 + 133/190 = 153/190

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 153 and 190 is 1, confirming that 153/190 cannot be reduced further—it is already in its simplest irreducible form.

153/190

Step 5

Decimal & Percentage Representation

Dividing the numerator 153 by denominator 190 produces a repeating decimal (approximately 0.805263, or 80.5263%).

153 ÷ 190 = 0.805263 (80.5263%)

Visual Representation

The diagram below illustrates 2/19 plus 7/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`153/190`
Mixed Number Form	`153/190`
Decimal Form	`0.805263`
Percentage	`80.5263%`

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Frequently Asked Questions

What is 2/19 plus 7/10 as a fraction?

2/19 + 7/10 in simplest fraction form is 153/190.

What is 2/19 plus 7/10 as a decimal?

2/19 + 7/10 converted to a decimal is 0.805263.

What is 2/19 plus 7/10 as a percentage?

2/19 + 7/10 expressed as a percentage is 80.5263%.

Does 2/19 plus 7/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.805263...) because the denominator contains prime factors other than 2 and 5.