What is 3/6 plus 5/7? (Answer: 17/14)

Exact Answer

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Problem: What is 3/6 plus 5/7?
Formula / Expression: 3/6 + 5/7
Final Answer: 1 3/14 (17/14)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 7 = 42.
Working: LCD(6, 7) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 5/7 by 6 so both fractions share the common base 42.
Working: 3 × 7/6 × 7 = 21/42 and 5 × 6/7 × 6 = 30/42

Step 3: Add the Numerators
Now add the numerators (21 + 30 = 51) and keep the common denominator 42 unchanged.
Working: 21 + 30/42 = 51/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 51 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 51 ÷ 3/42 ÷ 3 = 17/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (14), divide 17 by 14: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/14.
Working: 17/14 = 1 3/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 14 produces a repeating decimal (approximately 1.214286, or 121.4286%).
Working: 17 ÷ 14 = 1.214286 (121.4286%)

Key Values:
- Simplified Fraction: 17/14
- Mixed Number Form: 1 3/14
- Decimal Value: 1.214286
- Percentage: 121.4286%

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3/6 + 5/7 = 17/14

Simplified Fraction

17/14

Mixed Number

1 3/14

Decimal Value

1.214286

Percentage

121.4286%

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Step-by-Step Solution: 3/6 + 5/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 7 = 42.

LCD(6, 7) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 5/7 by 6 so both fractions share the common base 42.

3 × 7/6 × 7 = 21/42 and 5 × 6/7 × 6 = 30/42

Step 3

Add the Numerators

Now add the numerators (21 + 30 = 51) and keep the common denominator 42 unchanged.

21 + 30/42 = 51/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 51 and 42, which is 3. Divide both the numerator and denominator by 3.

51 ÷ 3/42 ÷ 3 = 17/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (14), divide 17 by 14: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/14.

17/14 = 13/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 14 produces a repeating decimal (approximately 1.214286, or 121.4286%).

17 ÷ 14 = 1.214286 (121.4286%)

Visual Representation

The diagram below illustrates 3/6 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/14`
Mixed Number Form	`1 3/14`
Decimal Form	`1.214286`
Percentage	`121.4286%`

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Frequently Asked Questions

What is 3/6 plus 5/7 as a fraction?

3/6 + 5/7 in simplest fraction form is 17/14 (or 1 3/14 as a mixed number).

What is 3/6 plus 5/7 as a decimal?

3/6 + 5/7 converted to a decimal is 1.214286.

What is 3/6 plus 5/7 as a percentage?

3/6 + 5/7 expressed as a percentage is 121.4286%.

How do you write 3/6 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/14 can be written as the mixed number 1 3/14.

Does 3/6 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.214286...) because the denominator contains prime factors other than 2 and 5.