What is 6/21 plus 13/45? (Answer: 181/315)

Exact Answer

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Problem: What is 6/21 plus 13/45?
Formula / Expression: 6/21 + 13/45
Final Answer: 181/315
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 45 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 21 × 45 = 945, keeping the calculation simpler).
Working: LCD(21, 45) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 6/21 by 15, and multiply the numerator and denominator of 13/45 by 7 so both fractions share the common base 315.
Working: 6 × 15/21 × 15 = 90/315 and 13 × 7/45 × 7 = 91/315

Step 3: Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 315 unchanged.
Working: 90 + 91/315 = 181/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 315 is 1, confirming that 181/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 315 produces a repeating decimal (approximately 0.574603, or 57.4603%).
Working: 181 ÷ 315 = 0.574603 (57.4603%)

Key Values:
- Simplified Fraction: 181/315
- Mixed Number Form: 181/315
- Decimal Value: 0.574603
- Percentage: 57.4603%

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Solved with FractionsCalc:
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6/21 + 13/45 = 181/315

Simplified Fraction

181/315

Mixed Number

Proper (181/315)

Decimal Value

0.574603

Percentage

57.4603%

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Step-by-Step Solution: 6/21 + 13/45

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 45 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 21 × 45 = 945, keeping the calculation simpler).

LCD(21, 45) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 6/21 by 15, and multiply the numerator and denominator of 13/45 by 7 so both fractions share the common base 315.

6 × 15/21 × 15 = 90/315 and 13 × 7/45 × 7 = 91/315

Step 3

Add the Numerators

Now add the numerators (90 + 91 = 181) and keep the common denominator 315 unchanged.

90 + 91/315 = 181/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 315 is 1, confirming that 181/315 cannot be reduced further—it is already in its simplest irreducible form.

181/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 315 produces a repeating decimal (approximately 0.574603, or 57.4603%).

181 ÷ 315 = 0.574603 (57.4603%)

Visual Representation

The diagram below illustrates 6/21 plus 13/45 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/315`
Mixed Number Form	`181/315`
Decimal Form	`0.574603`
Percentage	`57.4603%`

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Frequently Asked Questions

What is 6/21 plus 13/45 as a fraction?

6/21 + 13/45 in simplest fraction form is 181/315.

What is 6/21 plus 13/45 as a decimal?

6/21 + 13/45 converted to a decimal is 0.574603.

What is 6/21 plus 13/45 as a percentage?

6/21 + 13/45 expressed as a percentage is 57.4603%.

Does 6/21 plus 13/45 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.574603...) because the denominator contains prime factors other than 2 and 5.