What is 5/35 plus 2/9? (Answer: 23/63)

Exact Answer

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Problem: What is 5/35 plus 2/9?
Formula / Expression: 5/35 + 2/9
Final Answer: 23/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 9 = 315.
Working: LCD(35, 9) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 5/35 by 9, and multiply the numerator and denominator of 2/9 by 35 so both fractions share the common base 315.
Working: 5 × 9/35 × 9 = 45/315 and 2 × 35/9 × 35 = 70/315

Step 3: Add the Numerators
Now add the numerators (45 + 70 = 115) and keep the common denominator 315 unchanged.
Working: 45 + 70/315 = 115/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 115 and 315, which is 5. Divide both the numerator and denominator by 5.
Working: 115 ÷ 5/315 ÷ 5 = 23/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 63 produces a repeating decimal (approximately 0.365079, or 36.5079%).
Working: 23 ÷ 63 = 0.365079 (36.5079%)

Key Values:
- Simplified Fraction: 23/63
- Mixed Number Form: 23/63
- Decimal Value: 0.365079
- Percentage: 36.5079%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-35-plus-2-9/
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5/35 + 2/9 = 23/63

Simplified Fraction

23/63

Mixed Number

Proper (23/63)

Decimal Value

0.365079

Percentage

36.5079%

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Step-by-Step Solution: 5/35 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 9 = 315.

LCD(35, 9) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 5/35 by 9, and multiply the numerator and denominator of 2/9 by 35 so both fractions share the common base 315.

5 × 9/35 × 9 = 45/315 and 2 × 35/9 × 35 = 70/315

Step 3

Add the Numerators

Now add the numerators (45 + 70 = 115) and keep the common denominator 315 unchanged.

45 + 70/315 = 115/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 115 and 315, which is 5. Divide both the numerator and denominator by 5.

115 ÷ 5/315 ÷ 5 = 23/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 63 produces a repeating decimal (approximately 0.365079, or 36.5079%).

23 ÷ 63 = 0.365079 (36.5079%)

Visual Representation

The diagram below illustrates 5/35 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/63`
Mixed Number Form	`23/63`
Decimal Form	`0.365079`
Percentage	`36.5079%`

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Frequently Asked Questions

What is 5/35 plus 2/9 as a fraction?

5/35 + 2/9 in simplest fraction form is 23/63.

What is 5/35 plus 2/9 as a decimal?

5/35 + 2/9 converted to a decimal is 0.365079.

What is 5/35 plus 2/9 as a percentage?

5/35 + 2/9 expressed as a percentage is 36.5079%.

Does 5/35 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.365079...) because the denominator contains prime factors other than 2 and 5.