What is 11/45 plus 9/21? (Answer: 212/315)

Exact Answer

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Problem: What is 11/45 plus 9/21?
Formula / Expression: 11/45 + 9/21
Final Answer: 212/315
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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 9/21 by 15 so both fractions share the common base 315.
Working: 11 × 7/45 × 7 = 77/315 and 9 × 15/21 × 15 = 135/315

Step 3: Add the Numerators
Now add the numerators (77 + 135 = 212) and keep the common denominator 315 unchanged.
Working: 77 + 135/315 = 212/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 212 and 315 is 1, confirming that 212/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 212/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 212 by denominator 315 produces a repeating decimal (approximately 0.673016, or 67.3016%).
Working: 212 ÷ 315 = 0.673016 (67.3016%)

Key Values:
- Simplified Fraction: 212/315
- Mixed Number Form: 212/315
- Decimal Value: 0.673016
- Percentage: 67.3016%

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Solved with FractionsCalc:
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11/45 + 9/21 = 212/315

Simplified Fraction

212/315

Mixed Number

Proper (212/315)

Decimal Value

0.673016

Percentage

67.3016%

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Step-by-Step Solution: 11/45 + 9/21

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 9/21 by 15 so both fractions share the common base 315.

11 × 7/45 × 7 = 77/315 and 9 × 15/21 × 15 = 135/315

Step 3

Add the Numerators

Now add the numerators (77 + 135 = 212) and keep the common denominator 315 unchanged.

77 + 135/315 = 212/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 212 and 315 is 1, confirming that 212/315 cannot be reduced further—it is already in its simplest irreducible form.

212/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 212 by denominator 315 produces a repeating decimal (approximately 0.673016, or 67.3016%).

212 ÷ 315 = 0.673016 (67.3016%)

Visual Representation

The diagram below illustrates 11/45 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`212/315`
Mixed Number Form	`212/315`
Decimal Form	`0.673016`
Percentage	`67.3016%`

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Frequently Asked Questions

What is 11/45 plus 9/21 as a fraction?

11/45 + 9/21 in simplest fraction form is 212/315.

What is 11/45 plus 9/21 as a decimal?

11/45 + 9/21 converted to a decimal is 0.673016.

What is 11/45 plus 9/21 as a percentage?

11/45 + 9/21 expressed as a percentage is 67.3016%.

Does 11/45 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.673016...) because the denominator contains prime factors other than 2 and 5.