What is 2/15 plus 9/22? (Answer: 179/330)

Exact Answer

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Problem: What is 2/15 plus 9/22?
Formula / Expression: 2/15 + 9/22
Final Answer: 179/330
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 22 = 330.
Working: LCD(15, 22) = 330

Step 2: Convert to Equivalent Fractions with Common Denominator 330
Multiply the numerator and denominator of 2/15 by 22, and multiply the numerator and denominator of 9/22 by 15 so both fractions share the common base 330.
Working: 2 × 22/15 × 22 = 44/330 and 9 × 15/22 × 15 = 135/330

Step 3: Add the Numerators
Now add the numerators (44 + 135 = 179) and keep the common denominator 330 unchanged.
Working: 44 + 135/330 = 179/330

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 179 and 330 is 1, confirming that 179/330 cannot be reduced further—it is already in its simplest irreducible form.
Working: 179/330

Step 5: Decimal & Percentage Representation
Dividing the numerator 179 by denominator 330 produces a repeating decimal (approximately 0.542424, or 54.2424%).
Working: 179 ÷ 330 = 0.542424 (54.2424%)

Key Values:
- Simplified Fraction: 179/330
- Mixed Number Form: 179/330
- Decimal Value: 0.542424
- Percentage: 54.2424%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-15-plus-9-22/
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2/15 + 9/22 = 179/330

Simplified Fraction

179/330

Mixed Number

Proper (179/330)

Decimal Value

0.542424

Percentage

54.2424%

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Step-by-Step Solution: 2/15 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 22 = 330.

LCD(15, 22) = 330

Step 2

Convert to Equivalent Fractions with Common Denominator 330

Multiply the numerator and denominator of 2/15 by 22, and multiply the numerator and denominator of 9/22 by 15 so both fractions share the common base 330.

2 × 22/15 × 22 = 44/330 and 9 × 15/22 × 15 = 135/330

Step 3

Add the Numerators

Now add the numerators (44 + 135 = 179) and keep the common denominator 330 unchanged.

44 + 135/330 = 179/330

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 179 and 330 is 1, confirming that 179/330 cannot be reduced further—it is already in its simplest irreducible form.

179/330

Step 5

Decimal & Percentage Representation

Dividing the numerator 179 by denominator 330 produces a repeating decimal (approximately 0.542424, or 54.2424%).

179 ÷ 330 = 0.542424 (54.2424%)

Visual Representation

The diagram below illustrates 2/15 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`179/330`
Mixed Number Form	`179/330`
Decimal Form	`0.542424`
Percentage	`54.2424%`

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Frequently Asked Questions

What is 2/15 plus 9/22 as a fraction?

2/15 + 9/22 in simplest fraction form is 179/330.

What is 2/15 plus 9/22 as a decimal?

2/15 + 9/22 converted to a decimal is 0.542424.

What is 2/15 plus 9/22 as a percentage?

2/15 + 9/22 expressed as a percentage is 54.2424%.

Does 2/15 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.542424...) because the denominator contains prime factors other than 2 and 5.