What is 2/21 plus 5/45? (Answer: 13/63)

Exact Answer

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Problem: What is 2/21 plus 5/45?
Formula / Expression: 2/21 + 5/45
Final Answer: 13/63
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 2/21 by 15, and multiply the numerator and denominator of 5/45 by 7 so both fractions share the common base 315.
Working: 2 × 15/21 × 15 = 30/315 and 5 × 7/45 × 7 = 35/315

Step 3: Add the Numerators
Now add the numerators (30 + 35 = 65) and keep the common denominator 315 unchanged.
Working: 30 + 35/315 = 65/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 65 and 315, which is 5. Divide both the numerator and denominator by 5.
Working: 65 ÷ 5/315 ÷ 5 = 13/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 63 produces a repeating decimal (approximately 0.206349, or 20.6349%).
Working: 13 ÷ 63 = 0.206349 (20.6349%)

Key Values:
- Simplified Fraction: 13/63
- Mixed Number Form: 13/63
- Decimal Value: 0.206349
- Percentage: 20.6349%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-5-45/
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2/21 + 5/45 = 13/63

Simplified Fraction

13/63

Mixed Number

Proper (13/63)

Decimal Value

0.206349

Percentage

20.6349%

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Step-by-Step Solution: 2/21 + 5/45

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 45) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 2/21 by 15, and multiply the numerator and denominator of 5/45 by 7 so both fractions share the common base 315.

2 × 15/21 × 15 = 30/315 and 5 × 7/45 × 7 = 35/315

Step 3

Add the Numerators

Now add the numerators (30 + 35 = 65) and keep the common denominator 315 unchanged.

30 + 35/315 = 65/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 65 and 315, which is 5. Divide both the numerator and denominator by 5.

65 ÷ 5/315 ÷ 5 = 13/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 63 produces a repeating decimal (approximately 0.206349, or 20.6349%).

13 ÷ 63 = 0.206349 (20.6349%)

Visual Representation

The diagram below illustrates 2/21 plus 5/45 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/63`
Mixed Number Form	`13/63`
Decimal Form	`0.206349`
Percentage	`20.6349%`

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Frequently Asked Questions

What is 2/21 plus 5/45 as a fraction?

2/21 + 5/45 in simplest fraction form is 13/63.

What is 2/21 plus 5/45 as a decimal?

2/21 + 5/45 converted to a decimal is 0.206349.

What is 2/21 plus 5/45 as a percentage?

2/21 + 5/45 expressed as a percentage is 20.6349%.

Does 2/21 plus 5/45 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.206349...) because the denominator contains prime factors other than 2 and 5.