What is 2/18 plus 8/21? (Answer: 31/63)

Exact Answer

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Problem: What is 2/18 plus 8/21?
Formula / Expression: 2/18 + 8/21
Final Answer: 31/63
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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 8/21 by 6 so both fractions share the common base 126.
Working: 2 × 7/18 × 7 = 14/126 and 8 × 6/21 × 6 = 48/126

Step 3: Add the Numerators
Now add the numerators (14 + 48 = 62) and keep the common denominator 126 unchanged.
Working: 14 + 48/126 = 62/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/126 ÷ 2 = 31/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 63 produces a repeating decimal (approximately 0.492063, or 49.2063%).
Working: 31 ÷ 63 = 0.492063 (49.2063%)

Key Values:
- Simplified Fraction: 31/63
- Mixed Number Form: 31/63
- Decimal Value: 0.492063
- Percentage: 49.2063%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-18-plus-8-21/
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2/18 + 8/21 = 31/63

Simplified Fraction

31/63

Mixed Number

Proper (31/63)

Decimal Value

0.492063

Percentage

49.2063%

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Step-by-Step Solution: 2/18 + 8/21

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 8/21 by 6 so both fractions share the common base 126.

2 × 7/18 × 7 = 14/126 and 8 × 6/21 × 6 = 48/126

Step 3

Add the Numerators

Now add the numerators (14 + 48 = 62) and keep the common denominator 126 unchanged.

14 + 48/126 = 62/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 126, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/126 ÷ 2 = 31/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 63 produces a repeating decimal (approximately 0.492063, or 49.2063%).

31 ÷ 63 = 0.492063 (49.2063%)

Visual Representation

The diagram below illustrates 2/18 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/63`
Mixed Number Form	`31/63`
Decimal Form	`0.492063`
Percentage	`49.2063%`

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Frequently Asked Questions

What is 2/18 plus 8/21 as a fraction?

2/18 + 8/21 in simplest fraction form is 31/63.

What is 2/18 plus 8/21 as a decimal?

2/18 + 8/21 converted to a decimal is 0.492063.

What is 2/18 plus 8/21 as a percentage?

2/18 + 8/21 expressed as a percentage is 49.2063%.

Does 2/18 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.492063...) because the denominator contains prime factors other than 2 and 5.