What is 4/5 plus 5/6? (Answer: 49/30)

Exact Answer

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Problem: What is 4/5 plus 5/6?
Formula / Expression: 4/5 + 5/6
Final Answer: 1 19/30 (49/30)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 6 = 30.
Working: LCD(5, 6) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 4/5 by 6, and multiply the numerator and denominator of 5/6 by 5 so both fractions share the common base 30.
Working: 4 × 6/5 × 6 = 24/30 and 5 × 5/6 × 5 = 25/30

Step 3: Add the Numerators
Now add the numerators (24 + 25 = 49) and keep the common denominator 30 unchanged.
Working: 24 + 25/30 = 49/30

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 30 is 1, confirming that 49/30 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/30

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (49) is greater than the denominator (30), divide 49 by 30: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/30.
Working: 49/30 = 1 19/30

Step 6: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 30 produces a repeating decimal (approximately 1.633333, or 163.3333%).
Working: 49 ÷ 30 = 1.633333 (163.3333%)

Key Values:
- Simplified Fraction: 49/30
- Mixed Number Form: 1 19/30
- Decimal Value: 1.633333
- Percentage: 163.3333%

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Solved with FractionsCalc:
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4/5 + 5/6 = 49/30

Simplified Fraction

49/30

Mixed Number

1 19/30

Decimal Value

1.633333

Percentage

163.3333%

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Step-by-Step Solution: 4/5 + 5/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 6 = 30.

LCD(5, 6) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 4/5 by 6, and multiply the numerator and denominator of 5/6 by 5 so both fractions share the common base 30.

4 × 6/5 × 6 = 24/30 and 5 × 5/6 × 5 = 25/30

Step 3

Add the Numerators

Now add the numerators (24 + 25 = 49) and keep the common denominator 30 unchanged.

24 + 25/30 = 49/30

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 30 is 1, confirming that 49/30 cannot be reduced further—it is already in its simplest irreducible form.

49/30

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (49) is greater than the denominator (30), divide 49 by 30: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/30.

49/30 = 119/30

Step 6

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 30 produces a repeating decimal (approximately 1.633333, or 163.3333%).

49 ÷ 30 = 1.633333 (163.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/30`
Mixed Number Form	`1 19/30`
Decimal Form	`1.633333`
Percentage	`163.3333%`

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Frequently Asked Questions

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

4/5 + 5/6 in simplest fraction form is 49/30 (or 1 19/30 as a mixed number).

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

4/5 + 5/6 converted to a decimal is 1.633333.

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

4/5 + 5/6 expressed as a percentage is 163.3333%.

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

Because the numerator is greater than the denominator, the improper fraction 49/30 can be written as the mixed number 1 19/30.

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

It results in a repeating decimal (approximately 1.633333...) because the denominator contains prime factors other than 2 and 5.