What is 4/35 plus 2/8? (Answer: 51/140)

Exact Answer

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Problem: What is 4/35 plus 2/8?
Formula / Expression: 4/35 + 2/8
Final Answer: 51/140
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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 4/35 by 8, and multiply the numerator and denominator of 2/8 by 35 so both fractions share the common base 280.
Working: 4 × 8/35 × 8 = 32/280 and 2 × 35/8 × 35 = 70/280

Step 3: Add the Numerators
Now add the numerators (32 + 70 = 102) and keep the common denominator 280 unchanged.
Working: 32 + 70/280 = 102/280

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 280, which is 2. Divide both the numerator and denominator by 2.
Working: 102 ÷ 2/280 ÷ 2 = 51/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 140 produces a repeating decimal (approximately 0.364286, or 36.4286%).
Working: 51 ÷ 140 = 0.364286 (36.4286%)

Key Values:
- Simplified Fraction: 51/140
- Mixed Number Form: 51/140
- Decimal Value: 0.364286
- Percentage: 36.4286%

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4/35 + 2/8 = 51/140

Simplified Fraction

51/140

Mixed Number

Proper (51/140)

Decimal Value

0.364286

Percentage

36.4286%

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Step-by-Step Solution: 4/35 + 2/8

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 4/35 by 8, and multiply the numerator and denominator of 2/8 by 35 so both fractions share the common base 280.

4 × 8/35 × 8 = 32/280 and 2 × 35/8 × 35 = 70/280

Step 3

Add the Numerators

Now add the numerators (32 + 70 = 102) and keep the common denominator 280 unchanged.

32 + 70/280 = 102/280

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 280, which is 2. Divide both the numerator and denominator by 2.

102 ÷ 2/280 ÷ 2 = 51/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 140 produces a repeating decimal (approximately 0.364286, or 36.4286%).

51 ÷ 140 = 0.364286 (36.4286%)

Visual Representation

The diagram below illustrates 4/35 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/140`
Mixed Number Form	`51/140`
Decimal Form	`0.364286`
Percentage	`36.4286%`

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Frequently Asked Questions

What is 4/35 plus 2/8 as a fraction?

4/35 + 2/8 in simplest fraction form is 51/140.

What is 4/35 plus 2/8 as a decimal?

4/35 + 2/8 converted to a decimal is 0.364286.

What is 4/35 plus 2/8 as a percentage?

4/35 + 2/8 expressed as a percentage is 36.4286%.

Does 4/35 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.364286...) because the denominator contains prime factors other than 2 and 5.