What is 2/31 plus 2/22? (Answer: 53/341)

Exact Answer

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Problem: What is 2/31 plus 2/22?
Formula / Expression: 2/31 + 2/22
Final Answer: 53/341
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 22 = 682.
Working: LCD(31, 22) = 682

Step 2: Convert to Equivalent Fractions with Common Denominator 682
Multiply the numerator and denominator of 2/31 by 22, and multiply the numerator and denominator of 2/22 by 31 so both fractions share the common base 682.
Working: 2 × 22/31 × 22 = 44/682 and 2 × 31/22 × 31 = 62/682

Step 3: Add the Numerators
Now add the numerators (44 + 62 = 106) and keep the common denominator 682 unchanged.
Working: 44 + 62/682 = 106/682

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 682, which is 2. Divide both the numerator and denominator by 2.
Working: 106 ÷ 2/682 ÷ 2 = 53/341

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 341 produces a repeating decimal (approximately 0.155425, or 15.5425%).
Working: 53 ÷ 341 = 0.155425 (15.5425%)

Key Values:
- Simplified Fraction: 53/341
- Mixed Number Form: 53/341
- Decimal Value: 0.155425
- Percentage: 15.5425%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-31-plus-2-22/
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2/31 + 2/22 = 53/341

Simplified Fraction

53/341

Mixed Number

Proper (53/341)

Decimal Value

0.155425

Percentage

15.5425%

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Step-by-Step Solution: 2/31 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 22 = 682.

LCD(31, 22) = 682

Step 2

Convert to Equivalent Fractions with Common Denominator 682

Multiply the numerator and denominator of 2/31 by 22, and multiply the numerator and denominator of 2/22 by 31 so both fractions share the common base 682.

2 × 22/31 × 22 = 44/682 and 2 × 31/22 × 31 = 62/682

Step 3

Add the Numerators

Now add the numerators (44 + 62 = 106) and keep the common denominator 682 unchanged.

44 + 62/682 = 106/682

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 106 and 682, which is 2. Divide both the numerator and denominator by 2.

106 ÷ 2/682 ÷ 2 = 53/341

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 341 produces a repeating decimal (approximately 0.155425, or 15.5425%).

53 ÷ 341 = 0.155425 (15.5425%)

Visual Representation

The diagram below illustrates 2/31 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/341`
Mixed Number Form	`53/341`
Decimal Form	`0.155425`
Percentage	`15.5425%`

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Frequently Asked Questions

What is 2/31 plus 2/22 as a fraction?

2/31 + 2/22 in simplest fraction form is 53/341.

What is 2/31 plus 2/22 as a decimal?

2/31 + 2/22 converted to a decimal is 0.155425.

What is 2/31 plus 2/22 as a percentage?

2/31 + 2/22 expressed as a percentage is 15.5425%.

Does 2/31 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.155425...) because the denominator contains prime factors other than 2 and 5.