What is 9/39 plus 9/21? (Answer: 60/91)

Exact Answer

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Problem: What is 9/39 plus 9/21?
Formula / Expression: 9/39 + 9/21
Final Answer: 60/91
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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 9/21 by 13 so both fractions share the common base 273.
Working: 9 × 7/39 × 7 = 63/273 and 9 × 13/21 × 13 = 117/273

Step 3: Add the Numerators
Now add the numerators (63 + 117 = 180) and keep the common denominator 273 unchanged.
Working: 63 + 117/273 = 180/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 180 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 180 ÷ 3/273 ÷ 3 = 60/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 60 by denominator 91 produces a repeating decimal (approximately 0.659341, or 65.9341%).
Working: 60 ÷ 91 = 0.659341 (65.9341%)

Key Values:
- Simplified Fraction: 60/91
- Mixed Number Form: 60/91
- Decimal Value: 0.659341
- Percentage: 65.9341%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-39-plus-9-21/
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9/39 + 9/21 = 60/91

Simplified Fraction

60/91

Mixed Number

Proper (60/91)

Decimal Value

0.659341

Percentage

65.9341%

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

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 9/21 by 13 so both fractions share the common base 273.

9 × 7/39 × 7 = 63/273 and 9 × 13/21 × 13 = 117/273

Step 3

Add the Numerators

Now add the numerators (63 + 117 = 180) and keep the common denominator 273 unchanged.

63 + 117/273 = 180/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 180 and 273, which is 3. Divide both the numerator and denominator by 3.

180 ÷ 3/273 ÷ 3 = 60/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 60 by denominator 91 produces a repeating decimal (approximately 0.659341, or 65.9341%).

60 ÷ 91 = 0.659341 (65.9341%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`60/91`
Mixed Number Form	`60/91`
Decimal Form	`0.659341`
Percentage	`65.9341%`

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Frequently Asked Questions

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

9/39 + 9/21 in simplest fraction form is 60/91.

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

9/39 + 9/21 converted to a decimal is 0.659341.

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

9/39 + 9/21 expressed as a percentage is 65.9341%.

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

It results in a repeating decimal (approximately 0.659341...) because the denominator contains prime factors other than 2 and 5.