What is 4/35 plus 2/4? (Answer: 43/70)

Exact Answer

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Problem: What is 4/35 plus 2/4?
Formula / Expression: 4/35 + 2/4
Final Answer: 43/70
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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 4/35 by 4, and multiply the numerator and denominator of 2/4 by 35 so both fractions share the common base 140.
Working: 4 × 4/35 × 4 = 16/140 and 2 × 35/4 × 35 = 70/140

Step 3: Add the Numerators
Now add the numerators (16 + 70 = 86) and keep the common denominator 140 unchanged.
Working: 16 + 70/140 = 86/140

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 140, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/140 ÷ 2 = 43/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 70 produces a repeating decimal (approximately 0.614286, or 61.4286%).
Working: 43 ÷ 70 = 0.614286 (61.4286%)

Key Values:
- Simplified Fraction: 43/70
- Mixed Number Form: 43/70
- Decimal Value: 0.614286
- Percentage: 61.4286%

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Solved with FractionsCalc:
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4/35 + 2/4 = 43/70

Simplified Fraction

43/70

Mixed Number

Proper (43/70)

Decimal Value

0.614286

Percentage

61.4286%

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Step-by-Step Solution: 4/35 + 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 4/35 by 4, and multiply the numerator and denominator of 2/4 by 35 so both fractions share the common base 140.

4 × 4/35 × 4 = 16/140 and 2 × 35/4 × 35 = 70/140

Step 3

Add the Numerators

Now add the numerators (16 + 70 = 86) and keep the common denominator 140 unchanged.

16 + 70/140 = 86/140

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 140, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/140 ÷ 2 = 43/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 70 produces a repeating decimal (approximately 0.614286, or 61.4286%).

43 ÷ 70 = 0.614286 (61.4286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/70`
Mixed Number Form	`43/70`
Decimal Form	`0.614286`
Percentage	`61.4286%`

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Frequently Asked Questions

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

4/35 + 2/4 in simplest fraction form is 43/70.

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

4/35 + 2/4 converted to a decimal is 0.614286.

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

4/35 + 2/4 expressed as a percentage is 61.4286%.

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

It results in a repeating decimal (approximately 0.614286...) because the denominator contains prime factors other than 2 and 5.