What is 3/35 plus 2/8? (Answer: 47/140)

Exact Answer

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Problem: What is 3/35 plus 2/8?
Formula / Expression: 3/35 + 2/8
Final Answer: 47/140
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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 3/35 by 8, and multiply the numerator and denominator of 2/8 by 35 so both fractions share the common base 280.
Working: 3 × 8/35 × 8 = 24/280 and 2 × 35/8 × 35 = 70/280

Step 3: Add the Numerators
Now add the numerators (24 + 70 = 94) and keep the common denominator 280 unchanged.
Working: 24 + 70/280 = 94/280

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 280, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/280 ÷ 2 = 47/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 140 produces a repeating decimal (approximately 0.335714, or 33.5714%).
Working: 47 ÷ 140 = 0.335714 (33.5714%)

Key Values:
- Simplified Fraction: 47/140
- Mixed Number Form: 47/140
- Decimal Value: 0.335714
- Percentage: 33.5714%

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3/35 + 2/8 = 47/140

Simplified Fraction

47/140

Mixed Number

Proper (47/140)

Decimal Value

0.335714

Percentage

33.5714%

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Step-by-Step Solution: 3/35 + 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 3/35 by 8, and multiply the numerator and denominator of 2/8 by 35 so both fractions share the common base 280.

3 × 8/35 × 8 = 24/280 and 2 × 35/8 × 35 = 70/280

Step 3

Add the Numerators

Now add the numerators (24 + 70 = 94) and keep the common denominator 280 unchanged.

24 + 70/280 = 94/280

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 280, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/280 ÷ 2 = 47/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 140 produces a repeating decimal (approximately 0.335714, or 33.5714%).

47 ÷ 140 = 0.335714 (33.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/140`
Mixed Number Form	`47/140`
Decimal Form	`0.335714`
Percentage	`33.5714%`

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Frequently Asked Questions

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

3/35 + 2/8 in simplest fraction form is 47/140.

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

3/35 + 2/8 converted to a decimal is 0.335714.

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

3/35 + 2/8 expressed as a percentage is 33.5714%.

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

It results in a repeating decimal (approximately 0.335714...) because the denominator contains prime factors other than 2 and 5.