What is 2/18 plus 5/21? (Answer: 22/63)

Exact Answer

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Problem: What is 2/18 plus 5/21?
Formula / Expression: 2/18 + 5/21
Final Answer: 22/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).
Working: LCD(18, 21) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 2/18 by 7, and multiply the numerator and denominator of 5/21 by 6 so both fractions share the common base 126.
Working: 2 × 7/18 × 7 = 14/126 and 5 × 6/21 × 6 = 30/126

Step 3: Add the Numerators
Now add the numerators (14 + 30 = 44) and keep the common denominator 126 unchanged.
Working: 14 + 30/126 = 44/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 44 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 44 ÷ 2/126 ÷ 2 = 22/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 63 produces a repeating decimal (approximately 0.349206, or 34.9206%).
Working: 22 ÷ 63 = 0.349206 (34.9206%)

Key Values:
- Simplified Fraction: 22/63
- Mixed Number Form: 22/63
- Decimal Value: 0.349206
- Percentage: 34.9206%

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Solved with FractionsCalc:
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2/18 + 5/21 = 22/63

Simplified Fraction

22/63

Mixed Number

Proper (22/63)

Decimal Value

0.349206

Percentage

34.9206%

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Step-by-Step Solution: 2/18 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 2/18 by 7, and multiply the numerator and denominator of 5/21 by 6 so both fractions share the common base 126.

2 × 7/18 × 7 = 14/126 and 5 × 6/21 × 6 = 30/126

Step 3

Add the Numerators

Now add the numerators (14 + 30 = 44) and keep the common denominator 126 unchanged.

14 + 30/126 = 44/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 44 and 126, which is 2. Divide both the numerator and denominator by 2.

44 ÷ 2/126 ÷ 2 = 22/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 63 produces a repeating decimal (approximately 0.349206, or 34.9206%).

22 ÷ 63 = 0.349206 (34.9206%)

Visual Representation

The diagram below illustrates 2/18 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/63`
Mixed Number Form	`22/63`
Decimal Form	`0.349206`
Percentage	`34.9206%`

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Frequently Asked Questions

What is 2/18 plus 5/21 as a fraction?

2/18 + 5/21 in simplest fraction form is 22/63.

What is 2/18 plus 5/21 as a decimal?

2/18 + 5/21 converted to a decimal is 0.349206.

What is 2/18 plus 5/21 as a percentage?

2/18 + 5/21 expressed as a percentage is 34.9206%.

Does 2/18 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.349206...) because the denominator contains prime factors other than 2 and 5.