What is 3/7 plus 5/6? (Answer: 53/42)

Exact Answer

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Problem: What is 3/7 plus 5/6?
Formula / Expression: 3/7 + 5/6
Final Answer: 1 11/42 (53/42)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/7 by 6, and multiply the numerator and denominator of 5/6 by 7 so both fractions share the common base 42.
Working: 3 × 6/7 × 6 = 18/42 and 5 × 7/6 × 7 = 35/42

Step 3: Add the Numerators
Now add the numerators (18 + 35 = 53) and keep the common denominator 42 unchanged.
Working: 18 + 35/42 = 53/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 42 is 1, confirming that 53/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/42

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (53) is greater than the denominator (42), divide 53 by 42: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/42.
Working: 53/42 = 1 11/42

Step 6: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 42 produces a repeating decimal (approximately 1.261905, or 126.1905%).
Working: 53 ÷ 42 = 1.261905 (126.1905%)

Key Values:
- Simplified Fraction: 53/42
- Mixed Number Form: 1 11/42
- Decimal Value: 1.261905
- Percentage: 126.1905%

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Solved with FractionsCalc:
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3/7 + 5/6 = 53/42

Simplified Fraction

53/42

Mixed Number

1 11/42

Decimal Value

1.261905

Percentage

126.1905%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 6) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

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

3 × 6/7 × 6 = 18/42 and 5 × 7/6 × 7 = 35/42

Step 3

Add the Numerators

Now add the numerators (18 + 35 = 53) and keep the common denominator 42 unchanged.

18 + 35/42 = 53/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 42 is 1, confirming that 53/42 cannot be reduced further—it is already in its simplest irreducible form.

53/42

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (53) is greater than the denominator (42), divide 53 by 42: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/42.

53/42 = 111/42

Step 6

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 42 produces a repeating decimal (approximately 1.261905, or 126.1905%).

53 ÷ 42 = 1.261905 (126.1905%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/42`
Mixed Number Form	`1 11/42`
Decimal Form	`1.261905`
Percentage	`126.1905%`

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Frequently Asked Questions

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

3/7 + 5/6 in simplest fraction form is 53/42 (or 1 11/42 as a mixed number).

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

3/7 + 5/6 converted to a decimal is 1.261905.

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

3/7 + 5/6 expressed as a percentage is 126.1905%.

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

Because the numerator is greater than the denominator, the improper fraction 53/42 can be written as the mixed number 1 11/42.

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

It results in a repeating decimal (approximately 1.261905...) because the denominator contains prime factors other than 2 and 5.