What is 1/45 plus 5/21? (Answer: 82/315)

Exact Answer

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Problem: What is 1/45 plus 5/21?
Formula / Expression: 1/45 + 5/21
Final Answer: 82/315
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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 5/21 by 15 so both fractions share the common base 315.
Working: 1 × 7/45 × 7 = 7/315 and 5 × 15/21 × 15 = 75/315

Step 3: Add the Numerators
Now add the numerators (7 + 75 = 82) and keep the common denominator 315 unchanged.
Working: 7 + 75/315 = 82/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 82 and 315 is 1, confirming that 82/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 82/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 315 produces a repeating decimal (approximately 0.260317, or 26.0317%).
Working: 82 ÷ 315 = 0.260317 (26.0317%)

Key Values:
- Simplified Fraction: 82/315
- Mixed Number Form: 82/315
- Decimal Value: 0.260317
- Percentage: 26.0317%

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Solved with FractionsCalc:
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1/45 + 5/21 = 82/315

Simplified Fraction

82/315

Mixed Number

Proper (82/315)

Decimal Value

0.260317

Percentage

26.0317%

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Step-by-Step Solution: 1/45 + 5/21

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 5/21 by 15 so both fractions share the common base 315.

1 × 7/45 × 7 = 7/315 and 5 × 15/21 × 15 = 75/315

Step 3

Add the Numerators

Now add the numerators (7 + 75 = 82) and keep the common denominator 315 unchanged.

7 + 75/315 = 82/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 82 and 315 is 1, confirming that 82/315 cannot be reduced further—it is already in its simplest irreducible form.

82/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 315 produces a repeating decimal (approximately 0.260317, or 26.0317%).

82 ÷ 315 = 0.260317 (26.0317%)

Visual Representation

The diagram below illustrates 1/45 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/315`
Mixed Number Form	`82/315`
Decimal Form	`0.260317`
Percentage	`26.0317%`

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Frequently Asked Questions

What is 1/45 plus 5/21 as a fraction?

1/45 + 5/21 in simplest fraction form is 82/315.

What is 1/45 plus 5/21 as a decimal?

1/45 + 5/21 converted to a decimal is 0.260317.

What is 1/45 plus 5/21 as a percentage?

1/45 + 5/21 expressed as a percentage is 26.0317%.

Does 1/45 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.260317...) because the denominator contains prime factors other than 2 and 5.