What is 5/18 plus 8/21? (Answer: 83/126)

Exact Answer

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Problem: What is 5/18 plus 8/21?
Formula / Expression: 5/18 + 8/21
Final Answer: 83/126
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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 8/21 by 6 so both fractions share the common base 126.
Working: 5 × 7/18 × 7 = 35/126 and 8 × 6/21 × 6 = 48/126

Step 3: Add the Numerators
Now add the numerators (35 + 48 = 83) and keep the common denominator 126 unchanged.
Working: 35 + 48/126 = 83/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 126 is 1, confirming that 83/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 126 produces a repeating decimal (approximately 0.65873, or 65.873%).
Working: 83 ÷ 126 = 0.65873 (65.873%)

Key Values:
- Simplified Fraction: 83/126
- Mixed Number Form: 83/126
- Decimal Value: 0.65873
- Percentage: 65.873%

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Solved with FractionsCalc:
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5/18 + 8/21 = 83/126

Simplified Fraction

83/126

Mixed Number

Proper (83/126)

Decimal Value

0.65873

Percentage

65.873%

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Step-by-Step Solution: 5/18 + 8/21

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 8/21 by 6 so both fractions share the common base 126.

5 × 7/18 × 7 = 35/126 and 8 × 6/21 × 6 = 48/126

Step 3

Add the Numerators

Now add the numerators (35 + 48 = 83) and keep the common denominator 126 unchanged.

35 + 48/126 = 83/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 126 is 1, confirming that 83/126 cannot be reduced further—it is already in its simplest irreducible form.

83/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 126 produces a repeating decimal (approximately 0.65873, or 65.873%).

83 ÷ 126 = 0.65873 (65.873%)

Visual Representation

The diagram below illustrates 5/18 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/126`
Mixed Number Form	`83/126`
Decimal Form	`0.65873`
Percentage	`65.873%`

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Frequently Asked Questions

What is 5/18 plus 8/21 as a fraction?

5/18 + 8/21 in simplest fraction form is 83/126.

What is 5/18 plus 8/21 as a decimal?

5/18 + 8/21 converted to a decimal is 0.65873.

What is 5/18 plus 8/21 as a percentage?

5/18 + 8/21 expressed as a percentage is 65.873%.

Does 5/18 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.65873...) because the denominator contains prime factors other than 2 and 5.