What is 3/22 plus 1/2? (Answer: 7/11)

Exact Answer

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Problem: What is 3/22 plus 1/2?
Formula / Expression: 3/22 + 1/2
Final Answer: 7/11
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 22 is an exact multiple of 2 (2 × 11 = 22). The Least Common Denominator (LCD) is simply 22, meaning we only need to scale one fraction.
Working: LCD(22, 2) = 22

Step 2: Convert to Equivalent Fractions with Common Denominator 22
Multiply the numerator and denominator of 3/22 by 1, and multiply the numerator and denominator of 1/2 by 11 so both fractions share the common base 22.
Working: 3 × 1/22 × 1 = 3/22 and 1 × 11/2 × 11 = 11/22

Step 3: Add the Numerators
Now add the numerators (3 + 11 = 14) and keep the common denominator 22 unchanged.
Working: 3 + 11/22 = 14/22

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 22, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/22 ÷ 2 = 7/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 11 produces a repeating decimal (approximately 0.636364, or 63.6364%).
Working: 7 ÷ 11 = 0.636364 (63.6364%)

Key Values:
- Simplified Fraction: 7/11
- Mixed Number Form: 7/11
- Decimal Value: 0.636364
- Percentage: 63.6364%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-22-plus-1-2/
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3/22 + 1/2 = 7/11

Simplified Fraction

7/11

Mixed Number

Proper (7/11)

Decimal Value

0.636364

Percentage

63.6364%

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Step-by-Step Solution: 3/22 + 1/2

Step 1

Find the Least Common Denominator (LCD)

Notice that 22 is an exact multiple of 2 (2 × 11 = 22). The Least Common Denominator (LCD) is simply 22, meaning we only need to scale one fraction.

LCD(22, 2) = 22

Step 2

Convert to Equivalent Fractions with Common Denominator 22

Multiply the numerator and denominator of 3/22 by 1, and multiply the numerator and denominator of 1/2 by 11 so both fractions share the common base 22.

3 × 1/22 × 1 = 3/22 and 1 × 11/2 × 11 = 11/22

Step 3

Add the Numerators

Now add the numerators (3 + 11 = 14) and keep the common denominator 22 unchanged.

3 + 11/22 = 14/22

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 22, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/22 ÷ 2 = 7/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 11 produces a repeating decimal (approximately 0.636364, or 63.6364%).

7 ÷ 11 = 0.636364 (63.6364%)

Visual Representation

The diagram below illustrates 3/22 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/11`
Mixed Number Form	`7/11`
Decimal Form	`0.636364`
Percentage	`63.6364%`

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Frequently Asked Questions

What is 3/22 plus 1/2 as a fraction?

3/22 + 1/2 in simplest fraction form is 7/11.

What is 3/22 plus 1/2 as a decimal?

3/22 + 1/2 converted to a decimal is 0.636364.

What is 3/22 plus 1/2 as a percentage?

3/22 + 1/2 expressed as a percentage is 63.6364%.

Does 3/22 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.636364...) because the denominator contains prime factors other than 2 and 5.