What is 3/15 plus 8/21? (Answer: 61/105)

Exact Answer

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Problem: What is 3/15 plus 8/21?
Formula / Expression: 3/15 + 8/21
Final Answer: 61/105
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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 3/15 by 7, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.
Working: 3 × 7/15 × 7 = 21/105 and 8 × 5/21 × 5 = 40/105

Step 3: Add the Numerators
Now add the numerators (21 + 40 = 61) and keep the common denominator 105 unchanged.
Working: 21 + 40/105 = 61/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 105 is 1, confirming that 61/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 105 produces a repeating decimal (approximately 0.580952, or 58.0952%).
Working: 61 ÷ 105 = 0.580952 (58.0952%)

Key Values:
- Simplified Fraction: 61/105
- Mixed Number Form: 61/105
- Decimal Value: 0.580952
- Percentage: 58.0952%

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Solved with FractionsCalc:
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3/15 + 8/21 = 61/105

Simplified Fraction

61/105

Mixed Number

Proper (61/105)

Decimal Value

0.580952

Percentage

58.0952%

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Step-by-Step Solution: 3/15 + 8/21

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 3/15 by 7, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.

3 × 7/15 × 7 = 21/105 and 8 × 5/21 × 5 = 40/105

Step 3

Add the Numerators

Now add the numerators (21 + 40 = 61) and keep the common denominator 105 unchanged.

21 + 40/105 = 61/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 105 is 1, confirming that 61/105 cannot be reduced further—it is already in its simplest irreducible form.

61/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 105 produces a repeating decimal (approximately 0.580952, or 58.0952%).

61 ÷ 105 = 0.580952 (58.0952%)

Visual Representation

The diagram below illustrates 3/15 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/105`
Mixed Number Form	`61/105`
Decimal Form	`0.580952`
Percentage	`58.0952%`

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Frequently Asked Questions

What is 3/15 plus 8/21 as a fraction?

3/15 + 8/21 in simplest fraction form is 61/105.

What is 3/15 plus 8/21 as a decimal?

3/15 + 8/21 converted to a decimal is 0.580952.

What is 3/15 plus 8/21 as a percentage?

3/15 + 8/21 expressed as a percentage is 58.0952%.

Does 3/15 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.580952...) because the denominator contains prime factors other than 2 and 5.