What is 13/45 plus 8/21? (Answer: 211/315)

Exact Answer

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Problem: What is 13/45 plus 8/21?
Formula / Expression: 13/45 + 8/21
Final Answer: 211/315
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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 13/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.
Working: 13 × 7/45 × 7 = 91/315 and 8 × 15/21 × 15 = 120/315

Step 3: Add the Numerators
Now add the numerators (91 + 120 = 211) and keep the common denominator 315 unchanged.
Working: 91 + 120/315 = 211/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 211 and 315 is 1, confirming that 211/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 211/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 211 by denominator 315 produces a repeating decimal (approximately 0.669841, or 66.9841%).
Working: 211 ÷ 315 = 0.669841 (66.9841%)

Key Values:
- Simplified Fraction: 211/315
- Mixed Number Form: 211/315
- Decimal Value: 0.669841
- Percentage: 66.9841%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-45-plus-8-21/
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13/45 + 8/21 = 211/315

Simplified Fraction

211/315

Mixed Number

Proper (211/315)

Decimal Value

0.669841

Percentage

66.9841%

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Step-by-Step Solution: 13/45 + 8/21

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 13/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.

13 × 7/45 × 7 = 91/315 and 8 × 15/21 × 15 = 120/315

Step 3

Add the Numerators

Now add the numerators (91 + 120 = 211) and keep the common denominator 315 unchanged.

91 + 120/315 = 211/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 211 and 315 is 1, confirming that 211/315 cannot be reduced further—it is already in its simplest irreducible form.

211/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 211 by denominator 315 produces a repeating decimal (approximately 0.669841, or 66.9841%).

211 ÷ 315 = 0.669841 (66.9841%)

Visual Representation

The diagram below illustrates 13/45 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`211/315`
Mixed Number Form	`211/315`
Decimal Form	`0.669841`
Percentage	`66.9841%`

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Frequently Asked Questions

What is 13/45 plus 8/21 as a fraction?

13/45 + 8/21 in simplest fraction form is 211/315.

What is 13/45 plus 8/21 as a decimal?

13/45 + 8/21 converted to a decimal is 0.669841.

What is 13/45 plus 8/21 as a percentage?

13/45 + 8/21 expressed as a percentage is 66.9841%.

Does 13/45 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.669841...) because the denominator contains prime factors other than 2 and 5.