What is 3/34 plus 2/4? (Answer: 10/17)

Exact Answer

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Problem: What is 3/34 plus 2/4?
Formula / Expression: 3/34 + 2/4
Final Answer: 10/17
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 68 (which is smaller than their product 34 × 4 = 136, keeping the calculation simpler).
Working: LCD(34, 4) = 68

Step 2: Convert to Equivalent Fractions with Common Denominator 68
Multiply the numerator and denominator of 3/34 by 2, and multiply the numerator and denominator of 2/4 by 17 so both fractions share the common base 68.
Working: 3 × 2/34 × 2 = 6/68 and 2 × 17/4 × 17 = 34/68

Step 3: Add the Numerators
Now add the numerators (6 + 34 = 40) and keep the common denominator 68 unchanged.
Working: 6 + 34/68 = 40/68

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 40 and 68, which is 4. Divide both the numerator and denominator by 4.
Working: 40 ÷ 4/68 ÷ 4 = 10/17

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 17 produces a repeating decimal (approximately 0.588235, or 58.8235%).
Working: 10 ÷ 17 = 0.588235 (58.8235%)

Key Values:
- Simplified Fraction: 10/17
- Mixed Number Form: 10/17
- Decimal Value: 0.588235
- Percentage: 58.8235%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-34-plus-2-4/
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3/34 + 2/4 = 10/17

Simplified Fraction

10/17

Mixed Number

Proper (10/17)

Decimal Value

0.588235

Percentage

58.8235%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 68 (which is smaller than their product 34 × 4 = 136, keeping the calculation simpler).

LCD(34, 4) = 68

Step 2

Convert to Equivalent Fractions with Common Denominator 68

Multiply the numerator and denominator of 3/34 by 2, and multiply the numerator and denominator of 2/4 by 17 so both fractions share the common base 68.

3 × 2/34 × 2 = 6/68 and 2 × 17/4 × 17 = 34/68

Step 3

Add the Numerators

Now add the numerators (6 + 34 = 40) and keep the common denominator 68 unchanged.

6 + 34/68 = 40/68

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 40 and 68, which is 4. Divide both the numerator and denominator by 4.

40 ÷ 4/68 ÷ 4 = 10/17

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 17 produces a repeating decimal (approximately 0.588235, or 58.8235%).

10 ÷ 17 = 0.588235 (58.8235%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/17`
Mixed Number Form	`10/17`
Decimal Form	`0.588235`
Percentage	`58.8235%`

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Frequently Asked Questions

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

3/34 + 2/4 in simplest fraction form is 10/17.

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

3/34 + 2/4 converted to a decimal is 0.588235.

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

3/34 + 2/4 expressed as a percentage is 58.8235%.

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

It results in a repeating decimal (approximately 0.588235...) because the denominator contains prime factors other than 2 and 5.