What is 5/18 plus 6/21? (Answer: 71/126)

Exact Answer

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Problem: What is 5/18 plus 6/21?
Formula / Expression: 5/18 + 6/21
Final Answer: 71/126
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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 5/18 by 7, and multiply the numerator and denominator of 6/21 by 6 so both fractions share the common base 126.
Working: 5 × 7/18 × 7 = 35/126 and 6 × 6/21 × 6 = 36/126

Step 3: Add the Numerators
Now add the numerators (35 + 36 = 71) and keep the common denominator 126 unchanged.
Working: 35 + 36/126 = 71/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 126 is 1, confirming that 71/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 126 produces a repeating decimal (approximately 0.563492, or 56.3492%).
Working: 71 ÷ 126 = 0.563492 (56.3492%)

Key Values:
- Simplified Fraction: 71/126
- Mixed Number Form: 71/126
- Decimal Value: 0.563492
- Percentage: 56.3492%

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Solved with FractionsCalc:
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5/18 + 6/21 = 71/126

Simplified Fraction

71/126

Mixed Number

Proper (71/126)

Decimal Value

0.563492

Percentage

56.3492%

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Step-by-Step Solution: 5/18 + 6/21

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 5/18 by 7, and multiply the numerator and denominator of 6/21 by 6 so both fractions share the common base 126.

5 × 7/18 × 7 = 35/126 and 6 × 6/21 × 6 = 36/126

Step 3

Add the Numerators

Now add the numerators (35 + 36 = 71) and keep the common denominator 126 unchanged.

35 + 36/126 = 71/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 126 is 1, confirming that 71/126 cannot be reduced further—it is already in its simplest irreducible form.

71/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 126 produces a repeating decimal (approximately 0.563492, or 56.3492%).

71 ÷ 126 = 0.563492 (56.3492%)

Visual Representation

The diagram below illustrates 5/18 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/126`
Mixed Number Form	`71/126`
Decimal Form	`0.563492`
Percentage	`56.3492%`

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Frequently Asked Questions

What is 5/18 plus 6/21 as a fraction?

5/18 + 6/21 in simplest fraction form is 71/126.

What is 5/18 plus 6/21 as a decimal?

5/18 + 6/21 converted to a decimal is 0.563492.

What is 5/18 plus 6/21 as a percentage?

5/18 + 6/21 expressed as a percentage is 56.3492%.

Does 5/18 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.563492...) because the denominator contains prime factors other than 2 and 5.