What is 1/45 plus 3/21? (Answer: 52/315)

Exact Answer

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Problem: What is 1/45 plus 3/21?
Formula / Expression: 1/45 + 3/21
Final Answer: 52/315
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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 1/45 by 7, and multiply the numerator and denominator of 3/21 by 15 so both fractions share the common base 315.
Working: 1 × 7/45 × 7 = 7/315 and 3 × 15/21 × 15 = 45/315

Step 3: Add the Numerators
Now add the numerators (7 + 45 = 52) and keep the common denominator 315 unchanged.
Working: 7 + 45/315 = 52/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 52 and 315 is 1, confirming that 52/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 52/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 315 produces a repeating decimal (approximately 0.165079, or 16.5079%).
Working: 52 ÷ 315 = 0.165079 (16.5079%)

Key Values:
- Simplified Fraction: 52/315
- Mixed Number Form: 52/315
- Decimal Value: 0.165079
- Percentage: 16.5079%

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Solved with FractionsCalc:
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1/45 + 3/21 = 52/315

Simplified Fraction

52/315

Mixed Number

Proper (52/315)

Decimal Value

0.165079

Percentage

16.5079%

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Step-by-Step Solution: 1/45 + 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 1/45 by 7, and multiply the numerator and denominator of 3/21 by 15 so both fractions share the common base 315.

1 × 7/45 × 7 = 7/315 and 3 × 15/21 × 15 = 45/315

Step 3

Add the Numerators

Now add the numerators (7 + 45 = 52) and keep the common denominator 315 unchanged.

7 + 45/315 = 52/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 52 and 315 is 1, confirming that 52/315 cannot be reduced further—it is already in its simplest irreducible form.

52/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 315 produces a repeating decimal (approximately 0.165079, or 16.5079%).

52 ÷ 315 = 0.165079 (16.5079%)

Visual Representation

The diagram below illustrates 1/45 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/315`
Mixed Number Form	`52/315`
Decimal Form	`0.165079`
Percentage	`16.5079%`

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Frequently Asked Questions

What is 1/45 plus 3/21 as a fraction?

1/45 + 3/21 in simplest fraction form is 52/315.

What is 1/45 plus 3/21 as a decimal?

1/45 + 3/21 converted to a decimal is 0.165079.

What is 1/45 plus 3/21 as a percentage?

1/45 + 3/21 expressed as a percentage is 16.5079%.

Does 1/45 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.165079...) because the denominator contains prime factors other than 2 and 5.