What is 3/18 plus 12/21? (Answer: 31/42)

Exact Answer

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Problem: What is 3/18 plus 12/21?
Formula / Expression: 3/18 + 12/21
Final Answer: 31/42
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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 3/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.
Working: 3 × 7/18 × 7 = 21/126 and 12 × 6/21 × 6 = 72/126

Step 3: Add the Numerators
Now add the numerators (21 + 72 = 93) and keep the common denominator 126 unchanged.
Working: 21 + 72/126 = 93/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 126, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/126 ÷ 3 = 31/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).
Working: 31 ÷ 42 = 0.738095 (73.8095%)

Key Values:
- Simplified Fraction: 31/42
- Mixed Number Form: 31/42
- Decimal Value: 0.738095
- Percentage: 73.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-18-plus-12-21/
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3/18 + 12/21 = 31/42

Simplified Fraction

31/42

Mixed Number

Proper (31/42)

Decimal Value

0.738095

Percentage

73.8095%

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Step-by-Step Solution: 3/18 + 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 3/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.

3 × 7/18 × 7 = 21/126 and 12 × 6/21 × 6 = 72/126

Step 3

Add the Numerators

Now add the numerators (21 + 72 = 93) and keep the common denominator 126 unchanged.

21 + 72/126 = 93/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 126, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/126 ÷ 3 = 31/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).

31 ÷ 42 = 0.738095 (73.8095%)

Visual Representation

The diagram below illustrates 3/18 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/42`
Mixed Number Form	`31/42`
Decimal Form	`0.738095`
Percentage	`73.8095%`

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Frequently Asked Questions

What is 3/18 plus 12/21 as a fraction?

3/18 + 12/21 in simplest fraction form is 31/42.

What is 3/18 plus 12/21 as a decimal?

3/18 + 12/21 converted to a decimal is 0.738095.

What is 3/18 plus 12/21 as a percentage?

3/18 + 12/21 expressed as a percentage is 73.8095%.

Does 3/18 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.738095...) because the denominator contains prime factors other than 2 and 5.