What is 4/17 plus 3/7? (Answer: 79/119)

Exact Answer

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Problem: What is 4/17 plus 3/7?
Formula / Expression: 4/17 + 3/7
Final Answer: 79/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 7 = 119.
Working: LCD(17, 7) = 119

Step 2: Convert to Equivalent Fractions with Common Denominator 119
Multiply the numerator and denominator of 4/17 by 7, and multiply the numerator and denominator of 3/7 by 17 so both fractions share the common base 119.
Working: 4 × 7/17 × 7 = 28/119 and 3 × 17/7 × 17 = 51/119

Step 3: Add the Numerators
Now add the numerators (28 + 51 = 79) and keep the common denominator 119 unchanged.
Working: 28 + 51/119 = 79/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 119 is 1, confirming that 79/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 119 produces a repeating decimal (approximately 0.663866, or 66.3866%).
Working: 79 ÷ 119 = 0.663866 (66.3866%)

Key Values:
- Simplified Fraction: 79/119
- Mixed Number Form: 79/119
- Decimal Value: 0.663866
- Percentage: 66.3866%

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4/17 + 3/7 = 79/119

Simplified Fraction

79/119

Mixed Number

Proper (79/119)

Decimal Value

0.663866

Percentage

66.3866%

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Step-by-Step Solution: 4/17 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 7 = 119.

LCD(17, 7) = 119

Step 2

Convert to Equivalent Fractions with Common Denominator 119

Multiply the numerator and denominator of 4/17 by 7, and multiply the numerator and denominator of 3/7 by 17 so both fractions share the common base 119.

4 × 7/17 × 7 = 28/119 and 3 × 17/7 × 17 = 51/119

Step 3

Add the Numerators

Now add the numerators (28 + 51 = 79) and keep the common denominator 119 unchanged.

28 + 51/119 = 79/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 119 is 1, confirming that 79/119 cannot be reduced further—it is already in its simplest irreducible form.

79/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 119 produces a repeating decimal (approximately 0.663866, or 66.3866%).

79 ÷ 119 = 0.663866 (66.3866%)

Visual Representation

The diagram below illustrates 4/17 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/119`
Mixed Number Form	`79/119`
Decimal Form	`0.663866`
Percentage	`66.3866%`

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Frequently Asked Questions

What is 4/17 plus 3/7 as a fraction?

4/17 + 3/7 in simplest fraction form is 79/119.

What is 4/17 plus 3/7 as a decimal?

4/17 + 3/7 converted to a decimal is 0.663866.

What is 4/17 plus 3/7 as a percentage?

4/17 + 3/7 expressed as a percentage is 66.3866%.

Does 4/17 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.663866...) because the denominator contains prime factors other than 2 and 5.