What is 2/35 plus 3/4? (Answer: 113/140)

Exact Answer

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Problem: What is 2/35 plus 3/4?
Formula / Expression: 2/35 + 3/4
Final Answer: 113/140
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 4 = 140.
Working: LCD(35, 4) = 140

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 2/35 by 4, and multiply the numerator and denominator of 3/4 by 35 so both fractions share the common base 140.
Working: 2 × 4/35 × 4 = 8/140 and 3 × 35/4 × 35 = 105/140

Step 3: Add the Numerators
Now add the numerators (8 + 105 = 113) and keep the common denominator 140 unchanged.
Working: 8 + 105/140 = 113/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 140 is 1, confirming that 113/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 140 produces a repeating decimal (approximately 0.807143, or 80.7143%).
Working: 113 ÷ 140 = 0.807143 (80.7143%)

Key Values:
- Simplified Fraction: 113/140
- Mixed Number Form: 113/140
- Decimal Value: 0.807143
- Percentage: 80.7143%

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2/35 + 3/4 = 113/140

Simplified Fraction

113/140

Mixed Number

Proper (113/140)

Decimal Value

0.807143

Percentage

80.7143%

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Step-by-Step Solution: 2/35 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 4 = 140.

LCD(35, 4) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

Multiply the numerator and denominator of 2/35 by 4, and multiply the numerator and denominator of 3/4 by 35 so both fractions share the common base 140.

2 × 4/35 × 4 = 8/140 and 3 × 35/4 × 35 = 105/140

Step 3

Add the Numerators

Now add the numerators (8 + 105 = 113) and keep the common denominator 140 unchanged.

8 + 105/140 = 113/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 140 is 1, confirming that 113/140 cannot be reduced further—it is already in its simplest irreducible form.

113/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 140 produces a repeating decimal (approximately 0.807143, or 80.7143%).

113 ÷ 140 = 0.807143 (80.7143%)

Visual Representation

The diagram below illustrates 2/35 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/140`
Mixed Number Form	`113/140`
Decimal Form	`0.807143`
Percentage	`80.7143%`

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Frequently Asked Questions

What is 2/35 plus 3/4 as a fraction?

2/35 + 3/4 in simplest fraction form is 113/140.

What is 2/35 plus 3/4 as a decimal?

2/35 + 3/4 converted to a decimal is 0.807143.

What is 2/35 plus 3/4 as a percentage?

2/35 + 3/4 expressed as a percentage is 80.7143%.

Does 2/35 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.807143...) because the denominator contains prime factors other than 2 and 5.