What is 18/35 plus 11/21? (Answer: 109/105)

Exact Answer

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Problem: What is 18/35 plus 11/21?
Formula / Expression: 18/35 + 11/21
Final Answer: 1 4/105 (109/105)
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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 18/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 18 × 3/35 × 3 = 54/105 and 11 × 5/21 × 5 = 55/105

Step 3: Add the Numerators
Now add the numerators (54 + 55 = 109) and keep the common denominator 105 unchanged.
Working: 54 + 55/105 = 109/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 105 is 1, confirming that 109/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (109) is greater than the denominator (105), divide 109 by 105: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/105.
Working: 109/105 = 1 4/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 105 produces a repeating decimal (approximately 1.038095, or 103.8095%).
Working: 109 ÷ 105 = 1.038095 (103.8095%)

Key Values:
- Simplified Fraction: 109/105
- Mixed Number Form: 1 4/105
- Decimal Value: 1.038095
- Percentage: 103.8095%

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Solved with FractionsCalc:
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18/35 + 11/21 = 109/105

Simplified Fraction

109/105

Mixed Number

1 4/105

Decimal Value

1.038095

Percentage

103.8095%

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Step-by-Step Solution: 18/35 + 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 18/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

18 × 3/35 × 3 = 54/105 and 11 × 5/21 × 5 = 55/105

Step 3

Add the Numerators

Now add the numerators (54 + 55 = 109) and keep the common denominator 105 unchanged.

54 + 55/105 = 109/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 105 is 1, confirming that 109/105 cannot be reduced further—it is already in its simplest irreducible form.

109/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (109) is greater than the denominator (105), divide 109 by 105: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/105.

109/105 = 14/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 105 produces a repeating decimal (approximately 1.038095, or 103.8095%).

109 ÷ 105 = 1.038095 (103.8095%)

Visual Representation

The diagram below illustrates 18/35 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/105`
Mixed Number Form	`1 4/105`
Decimal Form	`1.038095`
Percentage	`103.8095%`

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Frequently Asked Questions

What is 18/35 plus 11/21 as a fraction?

18/35 + 11/21 in simplest fraction form is 109/105 (or 1 4/105 as a mixed number).

What is 18/35 plus 11/21 as a decimal?

18/35 + 11/21 converted to a decimal is 1.038095.

What is 18/35 plus 11/21 as a percentage?

18/35 + 11/21 expressed as a percentage is 103.8095%.

How do you write 18/35 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 109/105 can be written as the mixed number 1 4/105.

Does 18/35 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.038095...) because the denominator contains prime factors other than 2 and 5.