What is 6/7 plus 8/9?
6/7 plus 8/9 equals 110/63 (or 1 47/63 as a mixed number) (or 1.746032 in decimal form). Learn the step-by-step solution to add 6/7 and 8/9 using Least Common Denominator and simplification.
Exact Answer
6/7 + 8/9 = 110/63
Simplified Fraction
110/63
Mixed Number
1 47/63
Decimal Value
1.746032
Percentage
174.6032%
Step-by-Step Solution: 6/7 + 8/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.
LCD(7, 9) = 63
Step 2
Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 6/7 by 9, and multiply the numerator and denominator of 8/9 by 7 so both fractions share the common base 63.
6 × 9/7 × 9 = 54/63 and 8 × 7/9 × 7 = 56/63
Step 3
Add the Numerators
Now add the numerators (54 + 56 = 110) and keep the common denominator 63 unchanged.
54 + 56/63 = 110/63
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 110 and 63 is 1, confirming that 110/63 cannot be reduced further—it is already in its simplest irreducible form.
110/63
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (110) is greater than the denominator (63), divide 110 by 63: it goes in 1 whole time(s) with a remainder of 47, giving the mixed number 1 47/63.
110/63 = 147/63
Step 6
Decimal & Percentage Representation
Dividing the numerator 110 by denominator 63 produces a repeating decimal (approximately 1.746032, or 174.6032%).
110 ÷ 63 = 1.746032 (174.6032%)
Visual Representation
The diagram below illustrates 6/7 plus 8/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 110/63 |
| Mixed Number Form | 1 47/63 |
| Decimal Form | 1.746032 |
| Percentage | 174.6032% |
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Frequently Asked Questions
What is 6/7 plus 8/9 as a fraction?
6/7 + 8/9 in simplest fraction form is 110/63 (or 1 47/63 as a mixed number).
What is 6/7 plus 8/9 as a decimal?
6/7 + 8/9 converted to a decimal is 1.746032.
What is 6/7 plus 8/9 as a percentage?
6/7 + 8/9 expressed as a percentage is 174.6032%.
How do you write 6/7 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 110/63 can be written as the mixed number 1 47/63.
Does 6/7 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.746032...) because the denominator contains prime factors other than 2 and 5.