What is 5/21 plus 5/18? (Answer: 65/126)

Exact Answer

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Problem: What is 5/21 plus 5/18?
Formula / Expression: 5/21 + 5/18
Final Answer: 65/126
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 18 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 21 × 18 = 378, keeping the calculation simpler).
Working: LCD(21, 18) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 5/21 by 6, and multiply the numerator and denominator of 5/18 by 7 so both fractions share the common base 126.
Working: 5 × 6/21 × 6 = 30/126 and 5 × 7/18 × 7 = 35/126

Step 3: Add the Numerators
Now add the numerators (30 + 35 = 65) and keep the common denominator 126 unchanged.
Working: 30 + 35/126 = 65/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 126 is 1, confirming that 65/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 126 produces a repeating decimal (approximately 0.515873, or 51.5873%).
Working: 65 ÷ 126 = 0.515873 (51.5873%)

Key Values:
- Simplified Fraction: 65/126
- Mixed Number Form: 65/126
- Decimal Value: 0.515873
- Percentage: 51.5873%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-21-plus-5-18/
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5/21 + 5/18 = 65/126

Simplified Fraction

65/126

Mixed Number

Proper (65/126)

Decimal Value

0.515873

Percentage

51.5873%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 18 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 21 × 18 = 378, keeping the calculation simpler).

LCD(21, 18) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

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

5 × 6/21 × 6 = 30/126 and 5 × 7/18 × 7 = 35/126

Step 3

Add the Numerators

Now add the numerators (30 + 35 = 65) and keep the common denominator 126 unchanged.

30 + 35/126 = 65/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 126 is 1, confirming that 65/126 cannot be reduced further—it is already in its simplest irreducible form.

65/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 126 produces a repeating decimal (approximately 0.515873, or 51.5873%).

65 ÷ 126 = 0.515873 (51.5873%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/126`
Mixed Number Form	`65/126`
Decimal Form	`0.515873`
Percentage	`51.5873%`

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Frequently Asked Questions

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

5/21 + 5/18 in simplest fraction form is 65/126.

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

5/21 + 5/18 converted to a decimal is 0.515873.

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

5/21 + 5/18 expressed as a percentage is 51.5873%.

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

It results in a repeating decimal (approximately 0.515873...) because the denominator contains prime factors other than 2 and 5.