What is 2/35 plus 3/8? (Answer: 121/280)

Exact Answer

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Problem: What is 2/35 plus 3/8?
Formula / Expression: 2/35 + 3/8
Final Answer: 121/280
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 8 = 280.
Working: LCD(35, 8) = 280

Step 2: Convert to Equivalent Fractions with Common Denominator 280
Multiply the numerator and denominator of 2/35 by 8, and multiply the numerator and denominator of 3/8 by 35 so both fractions share the common base 280.
Working: 2 × 8/35 × 8 = 16/280 and 3 × 35/8 × 35 = 105/280

Step 3: Add the Numerators
Now add the numerators (16 + 105 = 121) and keep the common denominator 280 unchanged.
Working: 16 + 105/280 = 121/280

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 121 and 280 is 1, confirming that 121/280 cannot be reduced further—it is already in its simplest irreducible form.
Working: 121/280

Step 5: Decimal & Percentage Representation
Dividing the numerator 121 by denominator 280 produces a repeating decimal (approximately 0.432143, or 43.2143%).
Working: 121 ÷ 280 = 0.432143 (43.2143%)

Key Values:
- Simplified Fraction: 121/280
- Mixed Number Form: 121/280
- Decimal Value: 0.432143
- Percentage: 43.2143%

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2/35 + 3/8 = 121/280

Simplified Fraction

121/280

Mixed Number

Proper (121/280)

Decimal Value

0.432143

Percentage

43.2143%

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Step-by-Step Solution: 2/35 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 8 = 280.

LCD(35, 8) = 280

Step 2

Convert to Equivalent Fractions with Common Denominator 280

Multiply the numerator and denominator of 2/35 by 8, and multiply the numerator and denominator of 3/8 by 35 so both fractions share the common base 280.

2 × 8/35 × 8 = 16/280 and 3 × 35/8 × 35 = 105/280

Step 3

Add the Numerators

Now add the numerators (16 + 105 = 121) and keep the common denominator 280 unchanged.

16 + 105/280 = 121/280

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 121 and 280 is 1, confirming that 121/280 cannot be reduced further—it is already in its simplest irreducible form.

121/280

Step 5

Decimal & Percentage Representation

Dividing the numerator 121 by denominator 280 produces a repeating decimal (approximately 0.432143, or 43.2143%).

121 ÷ 280 = 0.432143 (43.2143%)

Visual Representation

The diagram below illustrates 2/35 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`121/280`
Mixed Number Form	`121/280`
Decimal Form	`0.432143`
Percentage	`43.2143%`

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Frequently Asked Questions

What is 2/35 plus 3/8 as a fraction?

2/35 + 3/8 in simplest fraction form is 121/280.

What is 2/35 plus 3/8 as a decimal?

2/35 + 3/8 converted to a decimal is 0.432143.

What is 2/35 plus 3/8 as a percentage?

2/35 + 3/8 expressed as a percentage is 43.2143%.

Does 2/35 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.432143...) because the denominator contains prime factors other than 2 and 5.