What is 2/6 plus 9/22? (Answer: 49/66)

Exact Answer

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Problem: What is 2/6 plus 9/22?
Formula / Expression: 2/6 + 9/22
Final Answer: 49/66
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 66 (which is smaller than their product 6 × 22 = 132, keeping the calculation simpler).
Working: LCD(6, 22) = 66

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 2/6 by 11, and multiply the numerator and denominator of 9/22 by 3 so both fractions share the common base 66.
Working: 2 × 11/6 × 11 = 22/66 and 9 × 3/22 × 3 = 27/66

Step 3: Add the Numerators
Now add the numerators (22 + 27 = 49) and keep the common denominator 66 unchanged.
Working: 22 + 27/66 = 49/66

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 66 is 1, confirming that 49/66 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 66 produces a repeating decimal (approximately 0.742424, or 74.2424%).
Working: 49 ÷ 66 = 0.742424 (74.2424%)

Key Values:
- Simplified Fraction: 49/66
- Mixed Number Form: 49/66
- Decimal Value: 0.742424
- Percentage: 74.2424%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-9-22/
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2/6 + 9/22 = 49/66

Simplified Fraction

49/66

Mixed Number

Proper (49/66)

Decimal Value

0.742424

Percentage

74.2424%

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Step-by-Step Solution: 2/6 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 66 (which is smaller than their product 6 × 22 = 132, keeping the calculation simpler).

LCD(6, 22) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 2/6 by 11, and multiply the numerator and denominator of 9/22 by 3 so both fractions share the common base 66.

2 × 11/6 × 11 = 22/66 and 9 × 3/22 × 3 = 27/66

Step 3

Add the Numerators

Now add the numerators (22 + 27 = 49) and keep the common denominator 66 unchanged.

22 + 27/66 = 49/66

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 66 is 1, confirming that 49/66 cannot be reduced further—it is already in its simplest irreducible form.

49/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 66 produces a repeating decimal (approximately 0.742424, or 74.2424%).

49 ÷ 66 = 0.742424 (74.2424%)

Visual Representation

The diagram below illustrates 2/6 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/66`
Mixed Number Form	`49/66`
Decimal Form	`0.742424`
Percentage	`74.2424%`

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Frequently Asked Questions

What is 2/6 plus 9/22 as a fraction?

2/6 + 9/22 in simplest fraction form is 49/66.

What is 2/6 plus 9/22 as a decimal?

2/6 + 9/22 converted to a decimal is 0.742424.

What is 2/6 plus 9/22 as a percentage?

2/6 + 9/22 expressed as a percentage is 74.2424%.

Does 2/6 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.742424...) because the denominator contains prime factors other than 2 and 5.