What is 9/35 plus 11/21? (Answer: 82/105)

Exact Answer

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Problem: What is 9/35 plus 11/21?
Formula / Expression: 9/35 + 11/21
Final Answer: 82/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 9/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 9 × 3/35 × 3 = 27/105 and 11 × 5/21 × 5 = 55/105

Step 3: Add the Numerators
Now add the numerators (27 + 55 = 82) and keep the common denominator 105 unchanged.
Working: 27 + 55/105 = 82/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 82 and 105 is 1, confirming that 82/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 82/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).
Working: 82 ÷ 105 = 0.780952 (78.0952%)

Key Values:
- Simplified Fraction: 82/105
- Mixed Number Form: 82/105
- Decimal Value: 0.780952
- Percentage: 78.0952%

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Solved with FractionsCalc:
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9/35 + 11/21 = 82/105

Simplified Fraction

82/105

Mixed Number

Proper (82/105)

Decimal Value

0.780952

Percentage

78.0952%

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Step-by-Step Solution: 9/35 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 9/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

9 × 3/35 × 3 = 27/105 and 11 × 5/21 × 5 = 55/105

Step 3

Add the Numerators

Now add the numerators (27 + 55 = 82) and keep the common denominator 105 unchanged.

27 + 55/105 = 82/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 82 and 105 is 1, confirming that 82/105 cannot be reduced further—it is already in its simplest irreducible form.

82/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 105 produces a repeating decimal (approximately 0.780952, or 78.0952%).

82 ÷ 105 = 0.780952 (78.0952%)

Visual Representation

The diagram below illustrates 9/35 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/105`
Mixed Number Form	`82/105`
Decimal Form	`0.780952`
Percentage	`78.0952%`

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Frequently Asked Questions

What is 9/35 plus 11/21 as a fraction?

9/35 + 11/21 in simplest fraction form is 82/105.

What is 9/35 plus 11/21 as a decimal?

9/35 + 11/21 converted to a decimal is 0.780952.

What is 9/35 plus 11/21 as a percentage?

9/35 + 11/21 expressed as a percentage is 78.0952%.

Does 9/35 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.780952...) because the denominator contains prime factors other than 2 and 5.