What is 11/45 plus 8/21? (Answer: 197/315)

Exact Answer

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Problem: What is 11/45 plus 8/21?
Formula / Expression: 11/45 + 8/21
Final Answer: 197/315
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 11/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.
Working: 11 × 7/45 × 7 = 77/315 and 8 × 15/21 × 15 = 120/315

Step 3: Add the Numerators
Now add the numerators (77 + 120 = 197) and keep the common denominator 315 unchanged.
Working: 77 + 120/315 = 197/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 197 and 315 is 1, confirming that 197/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 197/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 197 by denominator 315 produces a repeating decimal (approximately 0.625397, or 62.5397%).
Working: 197 ÷ 315 = 0.625397 (62.5397%)

Key Values:
- Simplified Fraction: 197/315
- Mixed Number Form: 197/315
- Decimal Value: 0.625397
- Percentage: 62.5397%

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Solved with FractionsCalc:
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11/45 + 8/21 = 197/315

Simplified Fraction

197/315

Mixed Number

Proper (197/315)

Decimal Value

0.625397

Percentage

62.5397%

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Step-by-Step Solution: 11/45 + 8/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 11/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.

11 × 7/45 × 7 = 77/315 and 8 × 15/21 × 15 = 120/315

Step 3

Add the Numerators

Now add the numerators (77 + 120 = 197) and keep the common denominator 315 unchanged.

77 + 120/315 = 197/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 197 and 315 is 1, confirming that 197/315 cannot be reduced further—it is already in its simplest irreducible form.

197/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 197 by denominator 315 produces a repeating decimal (approximately 0.625397, or 62.5397%).

197 ÷ 315 = 0.625397 (62.5397%)

Visual Representation

The diagram below illustrates 11/45 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`197/315`
Mixed Number Form	`197/315`
Decimal Form	`0.625397`
Percentage	`62.5397%`

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Frequently Asked Questions

What is 11/45 plus 8/21 as a fraction?

11/45 + 8/21 in simplest fraction form is 197/315.

What is 11/45 plus 8/21 as a decimal?

11/45 + 8/21 converted to a decimal is 0.625397.

What is 11/45 plus 8/21 as a percentage?

11/45 + 8/21 expressed as a percentage is 62.5397%.

Does 11/45 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.625397...) because the denominator contains prime factors other than 2 and 5.