What is 1/18 plus 5/21? (Answer: 37/126)

Exact Answer

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Problem: What is 1/18 plus 5/21?
Formula / Expression: 1/18 + 5/21
Final Answer: 37/126
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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 1/18 by 7, and multiply the numerator and denominator of 5/21 by 6 so both fractions share the common base 126.
Working: 1 × 7/18 × 7 = 7/126 and 5 × 6/21 × 6 = 30/126

Step 3: Add the Numerators
Now add the numerators (7 + 30 = 37) and keep the common denominator 126 unchanged.
Working: 7 + 30/126 = 37/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 126 is 1, confirming that 37/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 126 produces a repeating decimal (approximately 0.293651, or 29.3651%).
Working: 37 ÷ 126 = 0.293651 (29.3651%)

Key Values:
- Simplified Fraction: 37/126
- Mixed Number Form: 37/126
- Decimal Value: 0.293651
- Percentage: 29.3651%

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Solved with FractionsCalc:
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1/18 + 5/21 = 37/126

Simplified Fraction

37/126

Mixed Number

Proper (37/126)

Decimal Value

0.293651

Percentage

29.3651%

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Step-by-Step Solution: 1/18 + 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 1/18 by 7, and multiply the numerator and denominator of 5/21 by 6 so both fractions share the common base 126.

1 × 7/18 × 7 = 7/126 and 5 × 6/21 × 6 = 30/126

Step 3

Add the Numerators

Now add the numerators (7 + 30 = 37) and keep the common denominator 126 unchanged.

7 + 30/126 = 37/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 126 is 1, confirming that 37/126 cannot be reduced further—it is already in its simplest irreducible form.

37/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 126 produces a repeating decimal (approximately 0.293651, or 29.3651%).

37 ÷ 126 = 0.293651 (29.3651%)

Visual Representation

The diagram below illustrates 1/18 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/126`
Mixed Number Form	`37/126`
Decimal Form	`0.293651`
Percentage	`29.3651%`

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Frequently Asked Questions

What is 1/18 plus 5/21 as a fraction?

1/18 + 5/21 in simplest fraction form is 37/126.

What is 1/18 plus 5/21 as a decimal?

1/18 + 5/21 converted to a decimal is 0.293651.

What is 1/18 plus 5/21 as a percentage?

1/18 + 5/21 expressed as a percentage is 29.3651%.

Does 1/18 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.293651...) because the denominator contains prime factors other than 2 and 5.