What is 11/21 plus 5/9? (Answer: 68/63)

Exact Answer

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Problem: What is 11/21 plus 5/9?
Formula / Expression: 11/21 + 5/9
Final Answer: 1 5/63 (68/63)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).
Working: LCD(21, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 11/21 by 3, and multiply the numerator and denominator of 5/9 by 7 so both fractions share the common base 63.
Working: 11 × 3/21 × 3 = 33/63 and 5 × 7/9 × 7 = 35/63

Step 3: Add the Numerators
Now add the numerators (33 + 35 = 68) and keep the common denominator 63 unchanged.
Working: 33 + 35/63 = 68/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 68 and 63 is 1, confirming that 68/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 68/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (68) is greater than the denominator (63), divide 68 by 63: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/63.
Working: 68/63 = 1 5/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 63 produces a repeating decimal (approximately 1.079365, or 107.9365%).
Working: 68 ÷ 63 = 1.079365 (107.9365%)

Key Values:
- Simplified Fraction: 68/63
- Mixed Number Form: 1 5/63
- Decimal Value: 1.079365
- Percentage: 107.9365%

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Solved with FractionsCalc:
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11/21 + 5/9 = 68/63

Simplified Fraction

68/63

Mixed Number

1 5/63

Decimal Value

1.079365

Percentage

107.9365%

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Step-by-Step Solution: 11/21 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).

LCD(21, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 11/21 by 3, and multiply the numerator and denominator of 5/9 by 7 so both fractions share the common base 63.

11 × 3/21 × 3 = 33/63 and 5 × 7/9 × 7 = 35/63

Step 3

Add the Numerators

Now add the numerators (33 + 35 = 68) and keep the common denominator 63 unchanged.

33 + 35/63 = 68/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 68 and 63 is 1, confirming that 68/63 cannot be reduced further—it is already in its simplest irreducible form.

68/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (68) is greater than the denominator (63), divide 68 by 63: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/63.

68/63 = 15/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 63 produces a repeating decimal (approximately 1.079365, or 107.9365%).

68 ÷ 63 = 1.079365 (107.9365%)

Visual Representation

The diagram below illustrates 11/21 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/63`
Mixed Number Form	`1 5/63`
Decimal Form	`1.079365`
Percentage	`107.9365%`

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Frequently Asked Questions

What is 11/21 plus 5/9 as a fraction?

11/21 + 5/9 in simplest fraction form is 68/63 (or 1 5/63 as a mixed number).

What is 11/21 plus 5/9 as a decimal?

11/21 + 5/9 converted to a decimal is 1.079365.

What is 11/21 plus 5/9 as a percentage?

11/21 + 5/9 expressed as a percentage is 107.9365%.

How do you write 11/21 plus 5/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 68/63 can be written as the mixed number 1 5/63.

Does 11/21 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.079365...) because the denominator contains prime factors other than 2 and 5.