What is 17/35 plus 11/21? (Answer: 106/105)

Exact Answer

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Problem: What is 17/35 plus 11/21?
Formula / Expression: 17/35 + 11/21
Final Answer: 1 1/105 (106/105)
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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 17/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 17 × 3/35 × 3 = 51/105 and 11 × 5/21 × 5 = 55/105

Step 3: Add the Numerators
Now add the numerators (51 + 55 = 106) and keep the common denominator 105 unchanged.
Working: 51 + 55/105 = 106/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 105 is 1, confirming that 106/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 106/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (106) is greater than the denominator (105), divide 106 by 105: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/105.
Working: 106/105 = 1 1/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 106 by denominator 105 produces a repeating decimal (approximately 1.009524, or 100.9524%).
Working: 106 ÷ 105 = 1.009524 (100.9524%)

Key Values:
- Simplified Fraction: 106/105
- Mixed Number Form: 1 1/105
- Decimal Value: 1.009524
- Percentage: 100.9524%

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Solved with FractionsCalc:
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17/35 + 11/21 = 106/105

Simplified Fraction

106/105

Mixed Number

1 1/105

Decimal Value

1.009524

Percentage

100.9524%

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Step-by-Step Solution: 17/35 + 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 17/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

17 × 3/35 × 3 = 51/105 and 11 × 5/21 × 5 = 55/105

Step 3

Add the Numerators

Now add the numerators (51 + 55 = 106) and keep the common denominator 105 unchanged.

51 + 55/105 = 106/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 106 and 105 is 1, confirming that 106/105 cannot be reduced further—it is already in its simplest irreducible form.

106/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (106) is greater than the denominator (105), divide 106 by 105: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/105.

106/105 = 11/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 106 by denominator 105 produces a repeating decimal (approximately 1.009524, or 100.9524%).

106 ÷ 105 = 1.009524 (100.9524%)

Visual Representation

The diagram below illustrates 17/35 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`106/105`
Mixed Number Form	`1 1/105`
Decimal Form	`1.009524`
Percentage	`100.9524%`

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Frequently Asked Questions

What is 17/35 plus 11/21 as a fraction?

17/35 + 11/21 in simplest fraction form is 106/105 (or 1 1/105 as a mixed number).

What is 17/35 plus 11/21 as a decimal?

17/35 + 11/21 converted to a decimal is 1.009524.

What is 17/35 plus 11/21 as a percentage?

17/35 + 11/21 expressed as a percentage is 100.9524%.

How do you write 17/35 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 106/105 can be written as the mixed number 1 1/105.

Does 17/35 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.009524...) because the denominator contains prime factors other than 2 and 5.