What is 2/9 plus 10/30? (Answer: 5/9)

Exact Answer

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Problem: What is 2/9 plus 10/30?
Formula / Expression: 2/9 + 10/30
Final Answer: 5/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 9 × 30 = 270, keeping the calculation simpler).
Working: LCD(9, 30) = 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 10/30 by 3 so both fractions share the common base 90.
Working: 2 × 10/9 × 10 = 20/90 and 10 × 3/30 × 3 = 30/90

Step 3: Add the Numerators
Now add the numerators (20 + 30 = 50) and keep the common denominator 90 unchanged.
Working: 20 + 30/90 = 50/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 50 and 90, which is 10. Divide both the numerator and denominator by 10.
Working: 50 ÷ 10/90 ÷ 10 = 5/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).
Working: 5 ÷ 9 = 0.555556 (55.5556%)

Key Values:
- Simplified Fraction: 5/9
- Mixed Number Form: 5/9
- Decimal Value: 0.555556
- Percentage: 55.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-10-30/
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2/9 + 10/30 = 5/9

Simplified Fraction

5/9

Mixed Number

Proper (5/9)

Decimal Value

0.555556

Percentage

55.5556%

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Step-by-Step Solution: 2/9 + 10/30

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 9 × 30 = 270, keeping the calculation simpler).

LCD(9, 30) = 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 10/30 by 3 so both fractions share the common base 90.

2 × 10/9 × 10 = 20/90 and 10 × 3/30 × 3 = 30/90

Step 3

Add the Numerators

Now add the numerators (20 + 30 = 50) and keep the common denominator 90 unchanged.

20 + 30/90 = 50/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 50 and 90, which is 10. Divide both the numerator and denominator by 10.

50 ÷ 10/90 ÷ 10 = 5/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).

5 ÷ 9 = 0.555556 (55.5556%)

Visual Representation

The diagram below illustrates 2/9 plus 10/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/9`
Mixed Number Form	`5/9`
Decimal Form	`0.555556`
Percentage	`55.5556%`

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Frequently Asked Questions

What is 2/9 plus 10/30 as a fraction?

2/9 + 10/30 in simplest fraction form is 5/9.

What is 2/9 plus 10/30 as a decimal?

2/9 + 10/30 converted to a decimal is 0.555556.

What is 2/9 plus 10/30 as a percentage?

2/9 + 10/30 expressed as a percentage is 55.5556%.

Does 2/9 plus 10/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.555556...) because the denominator contains prime factors other than 2 and 5.