What is 2/9 plus 7/30? (Answer: 41/90)

Exact Answer

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Problem: What is 2/9 plus 7/30?
Formula / Expression: 2/9 + 7/30
Final Answer: 41/90
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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 7/30 by 3 so both fractions share the common base 90.
Working: 2 × 10/9 × 10 = 20/90 and 7 × 3/30 × 3 = 21/90

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 90 unchanged.
Working: 20 + 21/90 = 41/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 90 is 1, confirming that 41/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 90 produces a repeating decimal (approximately 0.455556, or 45.5556%).
Working: 41 ÷ 90 = 0.455556 (45.5556%)

Key Values:
- Simplified Fraction: 41/90
- Mixed Number Form: 41/90
- Decimal Value: 0.455556
- Percentage: 45.5556%

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2/9 + 7/30 = 41/90

Simplified Fraction

41/90

Mixed Number

Proper (41/90)

Decimal Value

0.455556

Percentage

45.5556%

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Step-by-Step Solution: 2/9 + 7/30

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 7/30 by 3 so both fractions share the common base 90.

2 × 10/9 × 10 = 20/90 and 7 × 3/30 × 3 = 21/90

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 90 unchanged.

20 + 21/90 = 41/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 90 is 1, confirming that 41/90 cannot be reduced further—it is already in its simplest irreducible form.

41/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 90 produces a repeating decimal (approximately 0.455556, or 45.5556%).

41 ÷ 90 = 0.455556 (45.5556%)

Visual Representation

The diagram below illustrates 2/9 plus 7/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/90`
Mixed Number Form	`41/90`
Decimal Form	`0.455556`
Percentage	`45.5556%`

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Frequently Asked Questions

What is 2/9 plus 7/30 as a fraction?

2/9 + 7/30 in simplest fraction form is 41/90.

What is 2/9 plus 7/30 as a decimal?

2/9 + 7/30 converted to a decimal is 0.455556.

What is 2/9 plus 7/30 as a percentage?

2/9 + 7/30 expressed as a percentage is 45.5556%.

Does 2/9 plus 7/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.455556...) because the denominator contains prime factors other than 2 and 5.