What is 2/9 plus 8/35? (Answer: 142/315)

Exact Answer

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Problem: What is 2/9 plus 8/35?
Formula / Expression: 2/9 + 8/35
Final Answer: 142/315
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 2/9 by 35, and multiply the numerator and denominator of 8/35 by 9 so both fractions share the common base 315.
Working: 2 × 35/9 × 35 = 70/315 and 8 × 9/35 × 9 = 72/315

Step 3: Add the Numerators
Now add the numerators (70 + 72 = 142) and keep the common denominator 315 unchanged.
Working: 70 + 72/315 = 142/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 142 and 315 is 1, confirming that 142/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 142/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 142 by denominator 315 produces a repeating decimal (approximately 0.450794, or 45.0794%).
Working: 142 ÷ 315 = 0.450794 (45.0794%)

Key Values:
- Simplified Fraction: 142/315
- Mixed Number Form: 142/315
- Decimal Value: 0.450794
- Percentage: 45.0794%

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Solved with FractionsCalc:
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2/9 + 8/35 = 142/315

Simplified Fraction

142/315

Mixed Number

Proper (142/315)

Decimal Value

0.450794

Percentage

45.0794%

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Step-by-Step Solution: 2/9 + 8/35

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 35) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 2/9 by 35, and multiply the numerator and denominator of 8/35 by 9 so both fractions share the common base 315.

2 × 35/9 × 35 = 70/315 and 8 × 9/35 × 9 = 72/315

Step 3

Add the Numerators

Now add the numerators (70 + 72 = 142) and keep the common denominator 315 unchanged.

70 + 72/315 = 142/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 142 and 315 is 1, confirming that 142/315 cannot be reduced further—it is already in its simplest irreducible form.

142/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 142 by denominator 315 produces a repeating decimal (approximately 0.450794, or 45.0794%).

142 ÷ 315 = 0.450794 (45.0794%)

Visual Representation

The diagram below illustrates 2/9 plus 8/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`142/315`
Mixed Number Form	`142/315`
Decimal Form	`0.450794`
Percentage	`45.0794%`

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Frequently Asked Questions

What is 2/9 plus 8/35 as a fraction?

2/9 + 8/35 in simplest fraction form is 142/315.

What is 2/9 plus 8/35 as a decimal?

2/9 + 8/35 converted to a decimal is 0.450794.

What is 2/9 plus 8/35 as a percentage?

2/9 + 8/35 expressed as a percentage is 45.0794%.

Does 2/9 plus 8/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.450794...) because the denominator contains prime factors other than 2 and 5.