What is 6/18 plus 12/21? (Answer: 19/21)

Exact Answer

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Problem: What is 6/18 plus 12/21?
Formula / Expression: 6/18 + 12/21
Final Answer: 19/21
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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 6/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.
Working: 6 × 7/18 × 7 = 42/126 and 12 × 6/21 × 6 = 72/126

Step 3: Add the Numerators
Now add the numerators (42 + 72 = 114) and keep the common denominator 126 unchanged.
Working: 42 + 72/126 = 114/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 126, which is 6. Divide both the numerator and denominator by 6.
Working: 114 ÷ 6/126 ÷ 6 = 19/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 21 produces a repeating decimal (approximately 0.904762, or 90.4762%).
Working: 19 ÷ 21 = 0.904762 (90.4762%)

Key Values:
- Simplified Fraction: 19/21
- Mixed Number Form: 19/21
- Decimal Value: 0.904762
- Percentage: 90.4762%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-18-plus-12-21/
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6/18 + 12/21 = 19/21

Simplified Fraction

19/21

Mixed Number

Proper (19/21)

Decimal Value

0.904762

Percentage

90.4762%

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Step-by-Step Solution: 6/18 + 12/21

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 6/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.

6 × 7/18 × 7 = 42/126 and 12 × 6/21 × 6 = 72/126

Step 3

Add the Numerators

Now add the numerators (42 + 72 = 114) and keep the common denominator 126 unchanged.

42 + 72/126 = 114/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 126, which is 6. Divide both the numerator and denominator by 6.

114 ÷ 6/126 ÷ 6 = 19/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 21 produces a repeating decimal (approximately 0.904762, or 90.4762%).

19 ÷ 21 = 0.904762 (90.4762%)

Visual Representation

The diagram below illustrates 6/18 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/21`
Mixed Number Form	`19/21`
Decimal Form	`0.904762`
Percentage	`90.4762%`

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Frequently Asked Questions

What is 6/18 plus 12/21 as a fraction?

6/18 + 12/21 in simplest fraction form is 19/21.

What is 6/18 plus 12/21 as a decimal?

6/18 + 12/21 converted to a decimal is 0.904762.

What is 6/18 plus 12/21 as a percentage?

6/18 + 12/21 expressed as a percentage is 90.4762%.

Does 6/18 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.904762...) because the denominator contains prime factors other than 2 and 5.