What is 9/22 plus 3/6? (Answer: 10/11)

Exact Answer

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Problem: What is 9/22 plus 3/6?
Formula / Expression: 9/22 + 3/6
Final Answer: 10/11
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 9/22 by 3, and multiply the numerator and denominator of 3/6 by 11 so both fractions share the common base 66.
Working: 9 × 3/22 × 3 = 27/66 and 3 × 11/6 × 11 = 33/66

Step 3: Add the Numerators
Now add the numerators (27 + 33 = 60) and keep the common denominator 66 unchanged.
Working: 27 + 33/66 = 60/66

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 60 and 66, which is 6. Divide both the numerator and denominator by 6.
Working: 60 ÷ 6/66 ÷ 6 = 10/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 11 produces a repeating decimal (approximately 0.909091, or 90.9091%).
Working: 10 ÷ 11 = 0.909091 (90.9091%)

Key Values:
- Simplified Fraction: 10/11
- Mixed Number Form: 10/11
- Decimal Value: 0.909091
- Percentage: 90.9091%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-22-plus-3-6/
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9/22 + 3/6 = 10/11

Simplified Fraction

10/11

Mixed Number

Proper (10/11)

Decimal Value

0.909091

Percentage

90.9091%

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Step-by-Step Solution: 9/22 + 3/6

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 6) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

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

9 × 3/22 × 3 = 27/66 and 3 × 11/6 × 11 = 33/66

Step 3

Add the Numerators

Now add the numerators (27 + 33 = 60) and keep the common denominator 66 unchanged.

27 + 33/66 = 60/66

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 60 and 66, which is 6. Divide both the numerator and denominator by 6.

60 ÷ 6/66 ÷ 6 = 10/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 11 produces a repeating decimal (approximately 0.909091, or 90.9091%).

10 ÷ 11 = 0.909091 (90.9091%)

Visual Representation

The diagram below illustrates 9/22 plus 3/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/11`
Mixed Number Form	`10/11`
Decimal Form	`0.909091`
Percentage	`90.9091%`

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Frequently Asked Questions

What is 9/22 plus 3/6 as a fraction?

9/22 + 3/6 in simplest fraction form is 10/11.

What is 9/22 plus 3/6 as a decimal?

9/22 + 3/6 converted to a decimal is 0.909091.

What is 9/22 plus 3/6 as a percentage?

9/22 + 3/6 expressed as a percentage is 90.9091%.

Does 9/22 plus 3/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.909091...) because the denominator contains prime factors other than 2 and 5.