What is 9/39 plus 12/21? (Answer: 73/91)

Exact Answer

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Problem: What is 9/39 plus 12/21?
Formula / Expression: 9/39 + 12/21
Final Answer: 73/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 9/39 by 7, and multiply the numerator and denominator of 12/21 by 13 so both fractions share the common base 273.
Working: 9 × 7/39 × 7 = 63/273 and 12 × 13/21 × 13 = 156/273

Step 3: Add the Numerators
Now add the numerators (63 + 156 = 219) and keep the common denominator 273 unchanged.
Working: 63 + 156/273 = 219/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 219 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 219 ÷ 3/273 ÷ 3 = 73/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 91 produces a repeating decimal (approximately 0.802198, or 80.2198%).
Working: 73 ÷ 91 = 0.802198 (80.2198%)

Key Values:
- Simplified Fraction: 73/91
- Mixed Number Form: 73/91
- Decimal Value: 0.802198
- Percentage: 80.2198%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-39-plus-12-21/
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9/39 + 12/21 = 73/91

Simplified Fraction

73/91

Mixed Number

Proper (73/91)

Decimal Value

0.802198

Percentage

80.2198%

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Step-by-Step Solution: 9/39 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 9/39 by 7, and multiply the numerator and denominator of 12/21 by 13 so both fractions share the common base 273.

9 × 7/39 × 7 = 63/273 and 12 × 13/21 × 13 = 156/273

Step 3

Add the Numerators

Now add the numerators (63 + 156 = 219) and keep the common denominator 273 unchanged.

63 + 156/273 = 219/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 219 and 273, which is 3. Divide both the numerator and denominator by 3.

219 ÷ 3/273 ÷ 3 = 73/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 91 produces a repeating decimal (approximately 0.802198, or 80.2198%).

73 ÷ 91 = 0.802198 (80.2198%)

Visual Representation

The diagram below illustrates 9/39 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/91`
Mixed Number Form	`73/91`
Decimal Form	`0.802198`
Percentage	`80.2198%`

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Frequently Asked Questions

What is 9/39 plus 12/21 as a fraction?

9/39 + 12/21 in simplest fraction form is 73/91.

What is 9/39 plus 12/21 as a decimal?

9/39 + 12/21 converted to a decimal is 0.802198.

What is 9/39 plus 12/21 as a percentage?

9/39 + 12/21 expressed as a percentage is 80.2198%.

Does 9/39 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.802198...) because the denominator contains prime factors other than 2 and 5.