What is 2/45 plus 3/21? (Answer: 59/315)

Exact Answer

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Problem: What is 2/45 plus 3/21?
Formula / Expression: 2/45 + 3/21
Final Answer: 59/315
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 2/45 by 7, and multiply the numerator and denominator of 3/21 by 15 so both fractions share the common base 315.
Working: 2 × 7/45 × 7 = 14/315 and 3 × 15/21 × 15 = 45/315

Step 3: Add the Numerators
Now add the numerators (14 + 45 = 59) and keep the common denominator 315 unchanged.
Working: 14 + 45/315 = 59/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 315 is 1, confirming that 59/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 315 produces a repeating decimal (approximately 0.187302, or 18.7302%).
Working: 59 ÷ 315 = 0.187302 (18.7302%)

Key Values:
- Simplified Fraction: 59/315
- Mixed Number Form: 59/315
- Decimal Value: 0.187302
- Percentage: 18.7302%

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Solved with FractionsCalc:
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2/45 + 3/21 = 59/315

Simplified Fraction

59/315

Mixed Number

Proper (59/315)

Decimal Value

0.187302

Percentage

18.7302%

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Step-by-Step Solution: 2/45 + 3/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 2/45 by 7, and multiply the numerator and denominator of 3/21 by 15 so both fractions share the common base 315.

2 × 7/45 × 7 = 14/315 and 3 × 15/21 × 15 = 45/315

Step 3

Add the Numerators

Now add the numerators (14 + 45 = 59) and keep the common denominator 315 unchanged.

14 + 45/315 = 59/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 315 is 1, confirming that 59/315 cannot be reduced further—it is already in its simplest irreducible form.

59/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 315 produces a repeating decimal (approximately 0.187302, or 18.7302%).

59 ÷ 315 = 0.187302 (18.7302%)

Visual Representation

The diagram below illustrates 2/45 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/315`
Mixed Number Form	`59/315`
Decimal Form	`0.187302`
Percentage	`18.7302%`

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Frequently Asked Questions

What is 2/45 plus 3/21 as a fraction?

2/45 + 3/21 in simplest fraction form is 59/315.

What is 2/45 plus 3/21 as a decimal?

2/45 + 3/21 converted to a decimal is 0.187302.

What is 2/45 plus 3/21 as a percentage?

2/45 + 3/21 expressed as a percentage is 18.7302%.

Does 2/45 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.187302...) because the denominator contains prime factors other than 2 and 5.