What is 10/45 plus 3/13? (Answer: 53/117)

Exact Answer

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Problem: What is 10/45 plus 3/13?
Formula / Expression: 10/45 + 3/13
Final Answer: 53/117
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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 10/45 by 13, and multiply the numerator and denominator of 3/13 by 45 so both fractions share the common base 585.
Working: 10 × 13/45 × 13 = 130/585 and 3 × 45/13 × 45 = 135/585

Step 3: Add the Numerators
Now add the numerators (130 + 135 = 265) and keep the common denominator 585 unchanged.
Working: 130 + 135/585 = 265/585

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 265 and 585, which is 5. Divide both the numerator and denominator by 5.
Working: 265 ÷ 5/585 ÷ 5 = 53/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).
Working: 53 ÷ 117 = 0.452991 (45.2991%)

Key Values:
- Simplified Fraction: 53/117
- Mixed Number Form: 53/117
- Decimal Value: 0.452991
- Percentage: 45.2991%

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Solved with FractionsCalc:
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10/45 + 3/13 = 53/117

Simplified Fraction

53/117

Mixed Number

Proper (53/117)

Decimal Value

0.452991

Percentage

45.2991%

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Step-by-Step Solution: 10/45 + 3/13

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 10/45 by 13, and multiply the numerator and denominator of 3/13 by 45 so both fractions share the common base 585.

10 × 13/45 × 13 = 130/585 and 3 × 45/13 × 45 = 135/585

Step 3

Add the Numerators

Now add the numerators (130 + 135 = 265) and keep the common denominator 585 unchanged.

130 + 135/585 = 265/585

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 265 and 585, which is 5. Divide both the numerator and denominator by 5.

265 ÷ 5/585 ÷ 5 = 53/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).

53 ÷ 117 = 0.452991 (45.2991%)

Visual Representation

The diagram below illustrates 10/45 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/117`
Mixed Number Form	`53/117`
Decimal Form	`0.452991`
Percentage	`45.2991%`

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Frequently Asked Questions

What is 10/45 plus 3/13 as a fraction?

10/45 + 3/13 in simplest fraction form is 53/117.

What is 10/45 plus 3/13 as a decimal?

10/45 + 3/13 converted to a decimal is 0.452991.

What is 10/45 plus 3/13 as a percentage?

10/45 + 3/13 expressed as a percentage is 45.2991%.

Does 10/45 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452991...) because the denominator contains prime factors other than 2 and 5.