What is 9/22 plus 3/7? (Answer: 129/154)

Exact Answer

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Problem: What is 9/22 plus 3/7?
Formula / Expression: 9/22 + 3/7
Final Answer: 129/154
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 154
Multiply the numerator and denominator of 9/22 by 7, and multiply the numerator and denominator of 3/7 by 22 so both fractions share the common base 154.
Working: 9 × 7/22 × 7 = 63/154 and 3 × 22/7 × 22 = 66/154

Step 3: Add the Numerators
Now add the numerators (63 + 66 = 129) and keep the common denominator 154 unchanged.
Working: 63 + 66/154 = 129/154

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 129 and 154 is 1, confirming that 129/154 cannot be reduced further—it is already in its simplest irreducible form.
Working: 129/154

Step 5: Decimal & Percentage Representation
Dividing the numerator 129 by denominator 154 produces a repeating decimal (approximately 0.837662, or 83.7662%).
Working: 129 ÷ 154 = 0.837662 (83.7662%)

Key Values:
- Simplified Fraction: 129/154
- Mixed Number Form: 129/154
- Decimal Value: 0.837662
- Percentage: 83.7662%

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Solved with FractionsCalc:
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9/22 + 3/7 = 129/154

Simplified Fraction

129/154

Mixed Number

Proper (129/154)

Decimal Value

0.837662

Percentage

83.7662%

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Step-by-Step Solution: 9/22 + 3/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 7) = 154

Step 2

Convert to Equivalent Fractions with Common Denominator 154

Multiply the numerator and denominator of 9/22 by 7, and multiply the numerator and denominator of 3/7 by 22 so both fractions share the common base 154.

9 × 7/22 × 7 = 63/154 and 3 × 22/7 × 22 = 66/154

Step 3

Add the Numerators

Now add the numerators (63 + 66 = 129) and keep the common denominator 154 unchanged.

63 + 66/154 = 129/154

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 129 and 154 is 1, confirming that 129/154 cannot be reduced further—it is already in its simplest irreducible form.

129/154

Step 5

Decimal & Percentage Representation

Dividing the numerator 129 by denominator 154 produces a repeating decimal (approximately 0.837662, or 83.7662%).

129 ÷ 154 = 0.837662 (83.7662%)

Visual Representation

The diagram below illustrates 9/22 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`129/154`
Mixed Number Form	`129/154`
Decimal Form	`0.837662`
Percentage	`83.7662%`

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Frequently Asked Questions

What is 9/22 plus 3/7 as a fraction?

9/22 + 3/7 in simplest fraction form is 129/154.

What is 9/22 plus 3/7 as a decimal?

9/22 + 3/7 converted to a decimal is 0.837662.

What is 9/22 plus 3/7 as a percentage?

9/22 + 3/7 expressed as a percentage is 83.7662%.

Does 9/22 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.837662...) because the denominator contains prime factors other than 2 and 5.