What is 7/15 plus 11/21? (Answer: 104/105)

Exact Answer

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Problem: What is 7/15 plus 11/21?
Formula / Expression: 7/15 + 11/21
Final Answer: 104/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).
Working: LCD(15, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 7/15 by 7, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 7 × 7/15 × 7 = 49/105 and 11 × 5/21 × 5 = 55/105

Step 3: Add the Numerators
Now add the numerators (49 + 55 = 104) and keep the common denominator 105 unchanged.
Working: 49 + 55/105 = 104/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 104 and 105 is 1, confirming that 104/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 104/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 104 by denominator 105 produces a repeating decimal (approximately 0.990476, or 99.0476%).
Working: 104 ÷ 105 = 0.990476 (99.0476%)

Key Values:
- Simplified Fraction: 104/105
- Mixed Number Form: 104/105
- Decimal Value: 0.990476
- Percentage: 99.0476%

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Solved with FractionsCalc:
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7/15 + 11/21 = 104/105

Simplified Fraction

104/105

Mixed Number

Proper (104/105)

Decimal Value

0.990476

Percentage

99.0476%

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Step-by-Step Solution: 7/15 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).

LCD(15, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 7/15 by 7, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

7 × 7/15 × 7 = 49/105 and 11 × 5/21 × 5 = 55/105

Step 3

Add the Numerators

Now add the numerators (49 + 55 = 104) and keep the common denominator 105 unchanged.

49 + 55/105 = 104/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 104 and 105 is 1, confirming that 104/105 cannot be reduced further—it is already in its simplest irreducible form.

104/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 104 by denominator 105 produces a repeating decimal (approximately 0.990476, or 99.0476%).

104 ÷ 105 = 0.990476 (99.0476%)

Visual Representation

The diagram below illustrates 7/15 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`104/105`
Mixed Number Form	`104/105`
Decimal Form	`0.990476`
Percentage	`99.0476%`

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Frequently Asked Questions

What is 7/15 plus 11/21 as a fraction?

7/15 + 11/21 in simplest fraction form is 104/105.

What is 7/15 plus 11/21 as a decimal?

7/15 + 11/21 converted to a decimal is 0.990476.

What is 7/15 plus 11/21 as a percentage?

7/15 + 11/21 expressed as a percentage is 99.0476%.

Does 7/15 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.990476...) because the denominator contains prime factors other than 2 and 5.