What is 2/18 plus 9/21? (Answer: 34/63)

Exact Answer

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Problem: What is 2/18 plus 9/21?
Formula / Expression: 2/18 + 9/21
Final Answer: 34/63
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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 9/21 by 6 so both fractions share the common base 126.
Working: 2 × 7/18 × 7 = 14/126 and 9 × 6/21 × 6 = 54/126

Step 3: Add the Numerators
Now add the numerators (14 + 54 = 68) and keep the common denominator 126 unchanged.
Working: 14 + 54/126 = 68/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 68 ÷ 2/126 ÷ 2 = 34/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 63 produces a repeating decimal (approximately 0.539683, or 53.9683%).
Working: 34 ÷ 63 = 0.539683 (53.9683%)

Key Values:
- Simplified Fraction: 34/63
- Mixed Number Form: 34/63
- Decimal Value: 0.539683
- Percentage: 53.9683%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-18-plus-9-21/
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2/18 + 9/21 = 34/63

Simplified Fraction

34/63

Mixed Number

Proper (34/63)

Decimal Value

0.539683

Percentage

53.9683%

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Step-by-Step Solution: 2/18 + 9/21

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 9/21 by 6 so both fractions share the common base 126.

2 × 7/18 × 7 = 14/126 and 9 × 6/21 × 6 = 54/126

Step 3

Add the Numerators

Now add the numerators (14 + 54 = 68) and keep the common denominator 126 unchanged.

14 + 54/126 = 68/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 126, which is 2. Divide both the numerator and denominator by 2.

68 ÷ 2/126 ÷ 2 = 34/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 63 produces a repeating decimal (approximately 0.539683, or 53.9683%).

34 ÷ 63 = 0.539683 (53.9683%)

Visual Representation

The diagram below illustrates 2/18 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/63`
Mixed Number Form	`34/63`
Decimal Form	`0.539683`
Percentage	`53.9683%`

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Frequently Asked Questions

What is 2/18 plus 9/21 as a fraction?

2/18 + 9/21 in simplest fraction form is 34/63.

What is 2/18 plus 9/21 as a decimal?

2/18 + 9/21 converted to a decimal is 0.539683.

What is 2/18 plus 9/21 as a percentage?

2/18 + 9/21 expressed as a percentage is 53.9683%.

Does 2/18 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.539683...) because the denominator contains prime factors other than 2 and 5.