What is 7/22 plus 2/4? (Answer: 9/11)

Exact Answer

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Problem: What is 7/22 plus 2/4?
Formula / Expression: 7/22 + 2/4
Final Answer: 9/11
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).
Working: LCD(22, 4) = 44

Step 2: Convert to Equivalent Fractions with Common Denominator 44
Multiply the numerator and denominator of 7/22 by 2, and multiply the numerator and denominator of 2/4 by 11 so both fractions share the common base 44.
Working: 7 × 2/22 × 2 = 14/44 and 2 × 11/4 × 11 = 22/44

Step 3: Add the Numerators
Now add the numerators (14 + 22 = 36) and keep the common denominator 44 unchanged.
Working: 14 + 22/44 = 36/44

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 44, which is 4. Divide both the numerator and denominator by 4.
Working: 36 ÷ 4/44 ÷ 4 = 9/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 11 produces a repeating decimal (approximately 0.818182, or 81.8182%).
Working: 9 ÷ 11 = 0.818182 (81.8182%)

Key Values:
- Simplified Fraction: 9/11
- Mixed Number Form: 9/11
- Decimal Value: 0.818182
- Percentage: 81.8182%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-22-plus-2-4/
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7/22 + 2/4 = 9/11

Simplified Fraction

9/11

Mixed Number

Proper (9/11)

Decimal Value

0.818182

Percentage

81.8182%

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Step-by-Step Solution: 7/22 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).

LCD(22, 4) = 44

Step 2

Convert to Equivalent Fractions with Common Denominator 44

Multiply the numerator and denominator of 7/22 by 2, and multiply the numerator and denominator of 2/4 by 11 so both fractions share the common base 44.

7 × 2/22 × 2 = 14/44 and 2 × 11/4 × 11 = 22/44

Step 3

Add the Numerators

Now add the numerators (14 + 22 = 36) and keep the common denominator 44 unchanged.

14 + 22/44 = 36/44

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 44, which is 4. Divide both the numerator and denominator by 4.

36 ÷ 4/44 ÷ 4 = 9/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 11 produces a repeating decimal (approximately 0.818182, or 81.8182%).

9 ÷ 11 = 0.818182 (81.8182%)

Visual Representation

The diagram below illustrates 7/22 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/11`
Mixed Number Form	`9/11`
Decimal Form	`0.818182`
Percentage	`81.8182%`

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Frequently Asked Questions

What is 7/22 plus 2/4 as a fraction?

7/22 + 2/4 in simplest fraction form is 9/11.

What is 7/22 plus 2/4 as a decimal?

7/22 + 2/4 converted to a decimal is 0.818182.

What is 7/22 plus 2/4 as a percentage?

7/22 + 2/4 expressed as a percentage is 81.8182%.

Does 7/22 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.818182...) because the denominator contains prime factors other than 2 and 5.