What is 4/34 plus 2/3? (Answer: 40/51)

Exact Answer

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Problem: What is 4/34 plus 2/3?
Formula / Expression: 4/34 + 2/3
Final Answer: 40/51
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 3 = 102.
Working: LCD(34, 3) = 102

Step 2: Convert to Equivalent Fractions with Common Denominator 102
Multiply the numerator and denominator of 4/34 by 3, and multiply the numerator and denominator of 2/3 by 34 so both fractions share the common base 102.
Working: 4 × 3/34 × 3 = 12/102 and 2 × 34/3 × 34 = 68/102

Step 3: Add the Numerators
Now add the numerators (12 + 68 = 80) and keep the common denominator 102 unchanged.
Working: 12 + 68/102 = 80/102

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 80 and 102, which is 2. Divide both the numerator and denominator by 2.
Working: 80 ÷ 2/102 ÷ 2 = 40/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 51 produces a repeating decimal (approximately 0.784314, or 78.4314%).
Working: 40 ÷ 51 = 0.784314 (78.4314%)

Key Values:
- Simplified Fraction: 40/51
- Mixed Number Form: 40/51
- Decimal Value: 0.784314
- Percentage: 78.4314%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-34-plus-2-3/
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4/34 + 2/3 = 40/51

Simplified Fraction

40/51

Mixed Number

Proper (40/51)

Decimal Value

0.784314

Percentage

78.4314%

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Step-by-Step Solution: 4/34 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 3 = 102.

LCD(34, 3) = 102

Step 2

Convert to Equivalent Fractions with Common Denominator 102

Multiply the numerator and denominator of 4/34 by 3, and multiply the numerator and denominator of 2/3 by 34 so both fractions share the common base 102.

4 × 3/34 × 3 = 12/102 and 2 × 34/3 × 34 = 68/102

Step 3

Add the Numerators

Now add the numerators (12 + 68 = 80) and keep the common denominator 102 unchanged.

12 + 68/102 = 80/102

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 80 and 102, which is 2. Divide both the numerator and denominator by 2.

80 ÷ 2/102 ÷ 2 = 40/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 51 produces a repeating decimal (approximately 0.784314, or 78.4314%).

40 ÷ 51 = 0.784314 (78.4314%)

Visual Representation

The diagram below illustrates 4/34 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/51`
Mixed Number Form	`40/51`
Decimal Form	`0.784314`
Percentage	`78.4314%`

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Frequently Asked Questions

What is 4/34 plus 2/3 as a fraction?

4/34 + 2/3 in simplest fraction form is 40/51.

What is 4/34 plus 2/3 as a decimal?

4/34 + 2/3 converted to a decimal is 0.784314.

What is 4/34 plus 2/3 as a percentage?

4/34 + 2/3 expressed as a percentage is 78.4314%.

Does 4/34 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.784314...) because the denominator contains prime factors other than 2 and 5.