What is 3/4 plus 5/6?
3/4 plus 5/6 equals 19/12 (or 1 7/12 as a mixed number) (or 1.583333 in decimal form). Learn the step-by-step solution to add 3/4 and 5/6 using Least Common Denominator and simplification.
Exact Answer
3/4 + 5/6 = 19/12
Simplified Fraction
19/12
Mixed Number
1 7/12
Decimal Value
1.583333
Percentage
158.3333%
Step-by-Step Solution: 3/4 + 5/6
Step 1
Find the Least Common Denominator (LCD)
The denominators 4 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 12 (which is smaller than their product 4 × 6 = 24, keeping the calculation simpler).
LCD(4, 6) = 12
Step 2
Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 3/4 by 3, and multiply the numerator and denominator of 5/6 by 2 so both fractions share the common base 12.
3 × 3/4 × 3 = 9/12 and 5 × 2/6 × 2 = 10/12
Step 3
Add the Numerators
Now add the numerators (9 + 10 = 19) and keep the common denominator 12 unchanged.
9 + 10/12 = 19/12
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 12 is 1, confirming that 19/12 cannot be reduced further—it is already in its simplest irreducible form.
19/12
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (19) is greater than the denominator (12), divide 19 by 12: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/12.
19/12 = 17/12
Step 6
Decimal & Percentage Representation
Dividing the numerator 19 by denominator 12 produces a repeating decimal (approximately 1.583333, or 158.3333%).
19 ÷ 12 = 1.583333 (158.3333%)
Visual Representation
The diagram below illustrates 3/4 plus 5/6 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 19/12 |
| Mixed Number Form | 1 7/12 |
| Decimal Form | 1.583333 |
| Percentage | 158.3333% |
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Frequently Asked Questions
What is 3/4 plus 5/6 as a fraction?
3/4 + 5/6 in simplest fraction form is 19/12 (or 1 7/12 as a mixed number).
What is 3/4 plus 5/6 as a decimal?
3/4 + 5/6 converted to a decimal is 1.583333.
What is 3/4 plus 5/6 as a percentage?
3/4 + 5/6 expressed as a percentage is 158.3333%.
How do you write 3/4 plus 5/6 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 19/12 can be written as the mixed number 1 7/12.
Does 3/4 plus 5/6 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.583333...) because the denominator contains prime factors other than 2 and 5.