What is 2/9 plus 6/10? (Answer: 37/45)

Exact Answer

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Problem: What is 2/9 plus 6/10?
Formula / Expression: 2/9 + 6/10
Final Answer: 37/45
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/9 by 10, and multiply the numerator and denominator of 6/10 by 9 so both fractions share the common base 90.
Working: 2 × 10/9 × 10 = 20/90 and 6 × 9/10 × 9 = 54/90

Step 3: Add the Numerators
Now add the numerators (20 + 54 = 74) and keep the common denominator 90 unchanged.
Working: 20 + 54/90 = 74/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/90 ÷ 2 = 37/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 45 produces a repeating decimal (approximately 0.822222, or 82.2222%).
Working: 37 ÷ 45 = 0.822222 (82.2222%)

Key Values:
- Simplified Fraction: 37/45
- Mixed Number Form: 37/45
- Decimal Value: 0.822222
- Percentage: 82.2222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-6-10/
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2/9 + 6/10 = 37/45

Simplified Fraction

37/45

Mixed Number

Proper (37/45)

Decimal Value

0.822222

Percentage

82.2222%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

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

2 × 10/9 × 10 = 20/90 and 6 × 9/10 × 9 = 54/90

Step 3

Add the Numerators

Now add the numerators (20 + 54 = 74) and keep the common denominator 90 unchanged.

20 + 54/90 = 74/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 90, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/90 ÷ 2 = 37/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 45 produces a repeating decimal (approximately 0.822222, or 82.2222%).

37 ÷ 45 = 0.822222 (82.2222%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/45`
Mixed Number Form	`37/45`
Decimal Form	`0.822222`
Percentage	`82.2222%`

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Frequently Asked Questions

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

2/9 + 6/10 in simplest fraction form is 37/45.

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

2/9 + 6/10 converted to a decimal is 0.822222.

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

2/9 + 6/10 expressed as a percentage is 82.2222%.

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

It results in a repeating decimal (approximately 0.822222...) because the denominator contains prime factors other than 2 and 5.