What is 5/45 plus 2/13? (Answer: 31/117)

Exact Answer

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Problem: What is 5/45 plus 2/13?
Formula / Expression: 5/45 + 2/13
Final Answer: 31/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.
Working: LCD(45, 13) = 585

Step 2: Convert to Equivalent Fractions with Common Denominator 585
Multiply the numerator and denominator of 5/45 by 13, and multiply the numerator and denominator of 2/13 by 45 so both fractions share the common base 585.
Working: 5 × 13/45 × 13 = 65/585 and 2 × 45/13 × 45 = 90/585

Step 3: Add the Numerators
Now add the numerators (65 + 90 = 155) and keep the common denominator 585 unchanged.
Working: 65 + 90/585 = 155/585

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 155 and 585, which is 5. Divide both the numerator and denominator by 5.
Working: 155 ÷ 5/585 ÷ 5 = 31/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 117 produces a repeating decimal (approximately 0.264957, or 26.4957%).
Working: 31 ÷ 117 = 0.264957 (26.4957%)

Key Values:
- Simplified Fraction: 31/117
- Mixed Number Form: 31/117
- Decimal Value: 0.264957
- Percentage: 26.4957%

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Solved with FractionsCalc:
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5/45 + 2/13 = 31/117

Simplified Fraction

31/117

Mixed Number

Proper (31/117)

Decimal Value

0.264957

Percentage

26.4957%

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Step-by-Step Solution: 5/45 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.

LCD(45, 13) = 585

Step 2

Convert to Equivalent Fractions with Common Denominator 585

Multiply the numerator and denominator of 5/45 by 13, and multiply the numerator and denominator of 2/13 by 45 so both fractions share the common base 585.

5 × 13/45 × 13 = 65/585 and 2 × 45/13 × 45 = 90/585

Step 3

Add the Numerators

Now add the numerators (65 + 90 = 155) and keep the common denominator 585 unchanged.

65 + 90/585 = 155/585

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 155 and 585, which is 5. Divide both the numerator and denominator by 5.

155 ÷ 5/585 ÷ 5 = 31/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 117 produces a repeating decimal (approximately 0.264957, or 26.4957%).

31 ÷ 117 = 0.264957 (26.4957%)

Visual Representation

The diagram below illustrates 5/45 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/117`
Mixed Number Form	`31/117`
Decimal Form	`0.264957`
Percentage	`26.4957%`

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Frequently Asked Questions

What is 5/45 plus 2/13 as a fraction?

5/45 + 2/13 in simplest fraction form is 31/117.

What is 5/45 plus 2/13 as a decimal?

5/45 + 2/13 converted to a decimal is 0.264957.

What is 5/45 plus 2/13 as a percentage?

5/45 + 2/13 expressed as a percentage is 26.4957%.

Does 5/45 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.264957...) because the denominator contains prime factors other than 2 and 5.