What is 5/18 plus 15/21? (Answer: 125/126)

Exact Answer

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Problem: What is 5/18 plus 15/21?
Formula / Expression: 5/18 + 15/21
Final Answer: 125/126
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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 15/21 by 6 so both fractions share the common base 126.
Working: 5 × 7/18 × 7 = 35/126 and 15 × 6/21 × 6 = 90/126

Step 3: Add the Numerators
Now add the numerators (35 + 90 = 125) and keep the common denominator 126 unchanged.
Working: 35 + 90/126 = 125/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 125 and 126 is 1, confirming that 125/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 125/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 125 by denominator 126 produces a repeating decimal (approximately 0.992063, or 99.2063%).
Working: 125 ÷ 126 = 0.992063 (99.2063%)

Key Values:
- Simplified Fraction: 125/126
- Mixed Number Form: 125/126
- Decimal Value: 0.992063
- Percentage: 99.2063%

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Solved with FractionsCalc:
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5/18 + 15/21 = 125/126

Simplified Fraction

125/126

Mixed Number

Proper (125/126)

Decimal Value

0.992063

Percentage

99.2063%

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Step-by-Step Solution: 5/18 + 15/21

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 15/21 by 6 so both fractions share the common base 126.

5 × 7/18 × 7 = 35/126 and 15 × 6/21 × 6 = 90/126

Step 3

Add the Numerators

Now add the numerators (35 + 90 = 125) and keep the common denominator 126 unchanged.

35 + 90/126 = 125/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 125 and 126 is 1, confirming that 125/126 cannot be reduced further—it is already in its simplest irreducible form.

125/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 125 by denominator 126 produces a repeating decimal (approximately 0.992063, or 99.2063%).

125 ÷ 126 = 0.992063 (99.2063%)

Visual Representation

The diagram below illustrates 5/18 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`125/126`
Mixed Number Form	`125/126`
Decimal Form	`0.992063`
Percentage	`99.2063%`

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Frequently Asked Questions

What is 5/18 plus 15/21 as a fraction?

5/18 + 15/21 in simplest fraction form is 125/126.

What is 5/18 plus 15/21 as a decimal?

5/18 + 15/21 converted to a decimal is 0.992063.

What is 5/18 plus 15/21 as a percentage?

5/18 + 15/21 expressed as a percentage is 99.2063%.

Does 5/18 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.992063...) because the denominator contains prime factors other than 2 and 5.