What is 2/7 plus 9/22? (Answer: 107/154)

Exact Answer

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Problem: What is 2/7 plus 9/22?
Formula / Expression: 2/7 + 9/22
Final Answer: 107/154
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.
Working: LCD(7, 22) = 154

Step 2: Convert to Equivalent Fractions with Common Denominator 154
Multiply the numerator and denominator of 2/7 by 22, and multiply the numerator and denominator of 9/22 by 7 so both fractions share the common base 154.
Working: 2 × 22/7 × 22 = 44/154 and 9 × 7/22 × 7 = 63/154

Step 3: Add the Numerators
Now add the numerators (44 + 63 = 107) and keep the common denominator 154 unchanged.
Working: 44 + 63/154 = 107/154

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 154 is 1, confirming that 107/154 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/154

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 154 produces a repeating decimal (approximately 0.694805, or 69.4805%).
Working: 107 ÷ 154 = 0.694805 (69.4805%)

Key Values:
- Simplified Fraction: 107/154
- Mixed Number Form: 107/154
- Decimal Value: 0.694805
- Percentage: 69.4805%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-9-22/
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2/7 + 9/22 = 107/154

Simplified Fraction

107/154

Mixed Number

Proper (107/154)

Decimal Value

0.694805

Percentage

69.4805%

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Step-by-Step Solution: 2/7 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.

LCD(7, 22) = 154

Step 2

Convert to Equivalent Fractions with Common Denominator 154

Multiply the numerator and denominator of 2/7 by 22, and multiply the numerator and denominator of 9/22 by 7 so both fractions share the common base 154.

2 × 22/7 × 22 = 44/154 and 9 × 7/22 × 7 = 63/154

Step 3

Add the Numerators

Now add the numerators (44 + 63 = 107) and keep the common denominator 154 unchanged.

44 + 63/154 = 107/154

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 154 is 1, confirming that 107/154 cannot be reduced further—it is already in its simplest irreducible form.

107/154

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 154 produces a repeating decimal (approximately 0.694805, or 69.4805%).

107 ÷ 154 = 0.694805 (69.4805%)

Visual Representation

The diagram below illustrates 2/7 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/154`
Mixed Number Form	`107/154`
Decimal Form	`0.694805`
Percentage	`69.4805%`

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Frequently Asked Questions

What is 2/7 plus 9/22 as a fraction?

2/7 + 9/22 in simplest fraction form is 107/154.

What is 2/7 plus 9/22 as a decimal?

2/7 + 9/22 converted to a decimal is 0.694805.

What is 2/7 plus 9/22 as a percentage?

2/7 + 9/22 expressed as a percentage is 69.4805%.

Does 2/7 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.694805...) because the denominator contains prime factors other than 2 and 5.