What is 9/21 plus 8/13? (Answer: 95/91)

Exact Answer

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Problem: What is 9/21 plus 8/13?
Formula / Expression: 9/21 + 8/13
Final Answer: 1 4/91 (95/91)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 13 = 273.
Working: LCD(21, 13) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 9/21 by 13, and multiply the numerator and denominator of 8/13 by 21 so both fractions share the common base 273.
Working: 9 × 13/21 × 13 = 117/273 and 8 × 21/13 × 21 = 168/273

Step 3: Add the Numerators
Now add the numerators (117 + 168 = 285) and keep the common denominator 273 unchanged.
Working: 117 + 168/273 = 285/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 285 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 285 ÷ 3/273 ÷ 3 = 95/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (95) is greater than the denominator (91), divide 95 by 91: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/91.
Working: 95/91 = 1 4/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 95 by denominator 91 produces a repeating decimal (approximately 1.043956, or 104.3956%).
Working: 95 ÷ 91 = 1.043956 (104.3956%)

Key Values:
- Simplified Fraction: 95/91
- Mixed Number Form: 1 4/91
- Decimal Value: 1.043956
- Percentage: 104.3956%

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Solved with FractionsCalc:
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9/21 + 8/13 = 95/91

Simplified Fraction

95/91

Mixed Number

1 4/91

Decimal Value

1.043956

Percentage

104.3956%

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Step-by-Step Solution: 9/21 + 8/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 13 = 273.

LCD(21, 13) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 9/21 by 13, and multiply the numerator and denominator of 8/13 by 21 so both fractions share the common base 273.

9 × 13/21 × 13 = 117/273 and 8 × 21/13 × 21 = 168/273

Step 3

Add the Numerators

Now add the numerators (117 + 168 = 285) and keep the common denominator 273 unchanged.

117 + 168/273 = 285/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 285 and 273, which is 3. Divide both the numerator and denominator by 3.

285 ÷ 3/273 ÷ 3 = 95/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (95) is greater than the denominator (91), divide 95 by 91: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/91.

95/91 = 14/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 95 by denominator 91 produces a repeating decimal (approximately 1.043956, or 104.3956%).

95 ÷ 91 = 1.043956 (104.3956%)

Visual Representation

The diagram below illustrates 9/21 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`95/91`
Mixed Number Form	`1 4/91`
Decimal Form	`1.043956`
Percentage	`104.3956%`

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Frequently Asked Questions

What is 9/21 plus 8/13 as a fraction?

9/21 + 8/13 in simplest fraction form is 95/91 (or 1 4/91 as a mixed number).

What is 9/21 plus 8/13 as a decimal?

9/21 + 8/13 converted to a decimal is 1.043956.

What is 9/21 plus 8/13 as a percentage?

9/21 + 8/13 expressed as a percentage is 104.3956%.

How do you write 9/21 plus 8/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 95/91 can be written as the mixed number 1 4/91.

Does 9/21 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.043956...) because the denominator contains prime factors other than 2 and 5.