What is 16/35 plus 11/21? (Answer: 103/105)

Exact Answer

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Problem: What is 16/35 plus 11/21?
Formula / Expression: 16/35 + 11/21
Final Answer: 103/105
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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 16/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 16 × 3/35 × 3 = 48/105 and 11 × 5/21 × 5 = 55/105

Step 3: Add the Numerators
Now add the numerators (48 + 55 = 103) and keep the common denominator 105 unchanged.
Working: 48 + 55/105 = 103/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 105 is 1, confirming that 103/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 105 produces a repeating decimal (approximately 0.980952, or 98.0952%).
Working: 103 ÷ 105 = 0.980952 (98.0952%)

Key Values:
- Simplified Fraction: 103/105
- Mixed Number Form: 103/105
- Decimal Value: 0.980952
- Percentage: 98.0952%

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Solved with FractionsCalc:
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16/35 + 11/21 = 103/105

Simplified Fraction

103/105

Mixed Number

Proper (103/105)

Decimal Value

0.980952

Percentage

98.0952%

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Step-by-Step Solution: 16/35 + 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 16/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

16 × 3/35 × 3 = 48/105 and 11 × 5/21 × 5 = 55/105

Step 3

Add the Numerators

Now add the numerators (48 + 55 = 103) and keep the common denominator 105 unchanged.

48 + 55/105 = 103/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 105 is 1, confirming that 103/105 cannot be reduced further—it is already in its simplest irreducible form.

103/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 105 produces a repeating decimal (approximately 0.980952, or 98.0952%).

103 ÷ 105 = 0.980952 (98.0952%)

Visual Representation

The diagram below illustrates 16/35 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/105`
Mixed Number Form	`103/105`
Decimal Form	`0.980952`
Percentage	`98.0952%`

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Frequently Asked Questions

What is 16/35 plus 11/21 as a fraction?

16/35 + 11/21 in simplest fraction form is 103/105.

What is 16/35 plus 11/21 as a decimal?

16/35 + 11/21 converted to a decimal is 0.980952.

What is 16/35 plus 11/21 as a percentage?

16/35 + 11/21 expressed as a percentage is 98.0952%.

Does 16/35 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.980952...) because the denominator contains prime factors other than 2 and 5.