What is 2/10 plus 6/9? (Answer: 13/15)

Exact Answer

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Problem: What is 2/10 plus 6/9?
Formula / Expression: 2/10 + 6/9
Final Answer: 13/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.
Working: LCD(10, 9) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/10 by 9, and multiply the numerator and denominator of 6/9 by 10 so both fractions share the common base 90.
Working: 2 × 9/10 × 9 = 18/90 and 6 × 10/9 × 10 = 60/90

Step 3: Add the Numerators
Now add the numerators (18 + 60 = 78) and keep the common denominator 90 unchanged.
Working: 18 + 60/90 = 78/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 90, which is 6. Divide both the numerator and denominator by 6.
Working: 78 ÷ 6/90 ÷ 6 = 13/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).
Working: 13 ÷ 15 = 0.866667 (86.6667%)

Key Values:
- Simplified Fraction: 13/15
- Mixed Number Form: 13/15
- Decimal Value: 0.866667
- Percentage: 86.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-6-9/
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2/10 + 6/9 = 13/15

Simplified Fraction

13/15

Mixed Number

Proper (13/15)

Decimal Value

0.866667

Percentage

86.6667%

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Step-by-Step Solution: 2/10 + 6/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.

LCD(10, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/10 by 9, and multiply the numerator and denominator of 6/9 by 10 so both fractions share the common base 90.

2 × 9/10 × 9 = 18/90 and 6 × 10/9 × 10 = 60/90

Step 3

Add the Numerators

Now add the numerators (18 + 60 = 78) and keep the common denominator 90 unchanged.

18 + 60/90 = 78/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 90, which is 6. Divide both the numerator and denominator by 6.

78 ÷ 6/90 ÷ 6 = 13/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).

13 ÷ 15 = 0.866667 (86.6667%)

Visual Representation

The diagram below illustrates 2/10 plus 6/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/15`
Mixed Number Form	`13/15`
Decimal Form	`0.866667`
Percentage	`86.6667%`

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Frequently Asked Questions

What is 2/10 plus 6/9 as a fraction?

2/10 + 6/9 in simplest fraction form is 13/15.

What is 2/10 plus 6/9 as a decimal?

2/10 + 6/9 converted to a decimal is 0.866667.

What is 2/10 plus 6/9 as a percentage?

2/10 + 6/9 expressed as a percentage is 86.6667%.

Does 2/10 plus 6/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.866667...) because the denominator contains prime factors other than 2 and 5.