What is 3/35 plus 2/4? (Answer: 41/70)

Exact Answer

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Problem: What is 3/35 plus 2/4?
Formula / Expression: 3/35 + 2/4
Final Answer: 41/70
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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 3/35 by 4, and multiply the numerator and denominator of 2/4 by 35 so both fractions share the common base 140.
Working: 3 × 4/35 × 4 = 12/140 and 2 × 35/4 × 35 = 70/140

Step 3: Add the Numerators
Now add the numerators (12 + 70 = 82) and keep the common denominator 140 unchanged.
Working: 12 + 70/140 = 82/140

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 140, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/140 ÷ 2 = 41/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 70 produces a repeating decimal (approximately 0.585714, or 58.5714%).
Working: 41 ÷ 70 = 0.585714 (58.5714%)

Key Values:
- Simplified Fraction: 41/70
- Mixed Number Form: 41/70
- Decimal Value: 0.585714
- Percentage: 58.5714%

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Solved with FractionsCalc:
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3/35 + 2/4 = 41/70

Simplified Fraction

41/70

Mixed Number

Proper (41/70)

Decimal Value

0.585714

Percentage

58.5714%

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

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

3 × 4/35 × 4 = 12/140 and 2 × 35/4 × 35 = 70/140

Step 3

Add the Numerators

Now add the numerators (12 + 70 = 82) and keep the common denominator 140 unchanged.

12 + 70/140 = 82/140

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 140, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/140 ÷ 2 = 41/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 70 produces a repeating decimal (approximately 0.585714, or 58.5714%).

41 ÷ 70 = 0.585714 (58.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/70`
Mixed Number Form	`41/70`
Decimal Form	`0.585714`
Percentage	`58.5714%`

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Frequently Asked Questions

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

3/35 + 2/4 in simplest fraction form is 41/70.

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

3/35 + 2/4 converted to a decimal is 0.585714.

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

3/35 + 2/4 expressed as a percentage is 58.5714%.

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

It results in a repeating decimal (approximately 0.585714...) because the denominator contains prime factors other than 2 and 5.