What is 7/17 plus 3/4? (Answer: 79/68)

Exact Answer

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Problem: What is 7/17 plus 3/4?
Formula / Expression: 7/17 + 3/4
Final Answer: 1 11/68 (79/68)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 4 = 68.
Working: LCD(17, 4) = 68

Step 2: Convert to Equivalent Fractions with Common Denominator 68
Multiply the numerator and denominator of 7/17 by 4, and multiply the numerator and denominator of 3/4 by 17 so both fractions share the common base 68.
Working: 7 × 4/17 × 4 = 28/68 and 3 × 17/4 × 17 = 51/68

Step 3: Add the Numerators
Now add the numerators (28 + 51 = 79) and keep the common denominator 68 unchanged.
Working: 28 + 51/68 = 79/68

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 68 is 1, confirming that 79/68 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/68

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (79) is greater than the denominator (68), divide 79 by 68: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/68.
Working: 79/68 = 1 11/68

Step 6: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 68 produces a repeating decimal (approximately 1.161765, or 116.1765%).
Working: 79 ÷ 68 = 1.161765 (116.1765%)

Key Values:
- Simplified Fraction: 79/68
- Mixed Number Form: 1 11/68
- Decimal Value: 1.161765
- Percentage: 116.1765%

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Solved with FractionsCalc:
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7/17 + 3/4 = 79/68

Simplified Fraction

79/68

Mixed Number

1 11/68

Decimal Value

1.161765

Percentage

116.1765%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 4 = 68.

LCD(17, 4) = 68

Step 2

Convert to Equivalent Fractions with Common Denominator 68

Multiply the numerator and denominator of 7/17 by 4, and multiply the numerator and denominator of 3/4 by 17 so both fractions share the common base 68.

7 × 4/17 × 4 = 28/68 and 3 × 17/4 × 17 = 51/68

Step 3

Add the Numerators

Now add the numerators (28 + 51 = 79) and keep the common denominator 68 unchanged.

28 + 51/68 = 79/68

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 68 is 1, confirming that 79/68 cannot be reduced further—it is already in its simplest irreducible form.

79/68

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (79) is greater than the denominator (68), divide 79 by 68: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/68.

79/68 = 111/68

Step 6

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 68 produces a repeating decimal (approximately 1.161765, or 116.1765%).

79 ÷ 68 = 1.161765 (116.1765%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/68`
Mixed Number Form	`1 11/68`
Decimal Form	`1.161765`
Percentage	`116.1765%`

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Frequently Asked Questions

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

7/17 + 3/4 in simplest fraction form is 79/68 (or 1 11/68 as a mixed number).

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

7/17 + 3/4 converted to a decimal is 1.161765.

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

7/17 + 3/4 expressed as a percentage is 116.1765%.

How do you write 7/17 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 79/68 can be written as the mixed number 1 11/68.

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

It results in a repeating decimal (approximately 1.161765...) because the denominator contains prime factors other than 2 and 5.