What is 21/35 plus 9/13? (Answer: 84/65)

Exact Answer

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Problem: What is 21/35 plus 9/13?
Formula / Expression: 21/35 + 9/13
Final Answer: 1 19/65 (84/65)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 13 = 455.
Working: LCD(35, 13) = 455

Step 2: Convert to Equivalent Fractions with Common Denominator 455
Multiply the numerator and denominator of 21/35 by 13, and multiply the numerator and denominator of 9/13 by 35 so both fractions share the common base 455.
Working: 21 × 13/35 × 13 = 273/455 and 9 × 35/13 × 35 = 315/455

Step 3: Add the Numerators
Now add the numerators (273 + 315 = 588) and keep the common denominator 455 unchanged.
Working: 273 + 315/455 = 588/455

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 588 and 455, which is 7. Divide both the numerator and denominator by 7.
Working: 588 ÷ 7/455 ÷ 7 = 84/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (84) is greater than the denominator (65), divide 84 by 65: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/65.
Working: 84/65 = 1 19/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 84 by denominator 65 produces a repeating decimal (approximately 1.292308, or 129.2308%).
Working: 84 ÷ 65 = 1.292308 (129.2308%)

Key Values:
- Simplified Fraction: 84/65
- Mixed Number Form: 1 19/65
- Decimal Value: 1.292308
- Percentage: 129.2308%

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Solved with FractionsCalc:
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21/35 + 9/13 = 84/65

Simplified Fraction

84/65

Mixed Number

1 19/65

Decimal Value

1.292308

Percentage

129.2308%

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Step-by-Step Solution: 21/35 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 13 = 455.

LCD(35, 13) = 455

Step 2

Convert to Equivalent Fractions with Common Denominator 455

Multiply the numerator and denominator of 21/35 by 13, and multiply the numerator and denominator of 9/13 by 35 so both fractions share the common base 455.

21 × 13/35 × 13 = 273/455 and 9 × 35/13 × 35 = 315/455

Step 3

Add the Numerators

Now add the numerators (273 + 315 = 588) and keep the common denominator 455 unchanged.

273 + 315/455 = 588/455

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 588 and 455, which is 7. Divide both the numerator and denominator by 7.

588 ÷ 7/455 ÷ 7 = 84/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (84) is greater than the denominator (65), divide 84 by 65: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/65.

84/65 = 119/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 84 by denominator 65 produces a repeating decimal (approximately 1.292308, or 129.2308%).

84 ÷ 65 = 1.292308 (129.2308%)

Visual Representation

The diagram below illustrates 21/35 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`84/65`
Mixed Number Form	`1 19/65`
Decimal Form	`1.292308`
Percentage	`129.2308%`

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Frequently Asked Questions

What is 21/35 plus 9/13 as a fraction?

21/35 + 9/13 in simplest fraction form is 84/65 (or 1 19/65 as a mixed number).

What is 21/35 plus 9/13 as a decimal?

21/35 + 9/13 converted to a decimal is 1.292308.

What is 21/35 plus 9/13 as a percentage?

21/35 + 9/13 expressed as a percentage is 129.2308%.

How do you write 21/35 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 84/65 can be written as the mixed number 1 19/65.

Does 21/35 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.292308...) because the denominator contains prime factors other than 2 and 5.