What is 4/7 plus 5/6? (Answer: 59/42)

Exact Answer

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Problem: What is 4/7 plus 5/6?
Formula / Expression: 4/7 + 5/6
Final Answer: 1 17/42 (59/42)
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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 4/7 by 6, and multiply the numerator and denominator of 5/6 by 7 so both fractions share the common base 42.
Working: 4 × 6/7 × 6 = 24/42 and 5 × 7/6 × 7 = 35/42

Step 3: Add the Numerators
Now add the numerators (24 + 35 = 59) and keep the common denominator 42 unchanged.
Working: 24 + 35/42 = 59/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 42 is 1, confirming that 59/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/42

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (42), divide 59 by 42: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/42.
Working: 59/42 = 1 17/42

Step 6: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 42 produces a repeating decimal (approximately 1.404762, or 140.4762%).
Working: 59 ÷ 42 = 1.404762 (140.4762%)

Key Values:
- Simplified Fraction: 59/42
- Mixed Number Form: 1 17/42
- Decimal Value: 1.404762
- Percentage: 140.4762%

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Solved with FractionsCalc:
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4/7 + 5/6 = 59/42

Simplified Fraction

59/42

Mixed Number

1 17/42

Decimal Value

1.404762

Percentage

140.4762%

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Step-by-Step Solution: 4/7 + 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 4/7 by 6, and multiply the numerator and denominator of 5/6 by 7 so both fractions share the common base 42.

4 × 6/7 × 6 = 24/42 and 5 × 7/6 × 7 = 35/42

Step 3

Add the Numerators

Now add the numerators (24 + 35 = 59) and keep the common denominator 42 unchanged.

24 + 35/42 = 59/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 42 is 1, confirming that 59/42 cannot be reduced further—it is already in its simplest irreducible form.

59/42

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (59) is greater than the denominator (42), divide 59 by 42: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/42.

59/42 = 117/42

Step 6

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 42 produces a repeating decimal (approximately 1.404762, or 140.4762%).

59 ÷ 42 = 1.404762 (140.4762%)

Visual Representation

The diagram below illustrates 4/7 plus 5/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/42`
Mixed Number Form	`1 17/42`
Decimal Form	`1.404762`
Percentage	`140.4762%`

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Frequently Asked Questions

What is 4/7 plus 5/6 as a fraction?

4/7 + 5/6 in simplest fraction form is 59/42 (or 1 17/42 as a mixed number).

What is 4/7 plus 5/6 as a decimal?

4/7 + 5/6 converted to a decimal is 1.404762.

What is 4/7 plus 5/6 as a percentage?

4/7 + 5/6 expressed as a percentage is 140.4762%.

How do you write 4/7 plus 5/6 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 59/42 can be written as the mixed number 1 17/42.

Does 4/7 plus 5/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.404762...) because the denominator contains prime factors other than 2 and 5.