What is 7/9 plus 6/7?
7/9 plus 6/7 equals 103/63 (or 1 40/63 as a mixed number) (or 1.634921 in decimal form). Learn the step-by-step solution to add 7/9 and 6/7 using Least Common Denominator and simplification.
Exact Answer
7/9 + 6/7 = 103/63
Simplified Fraction
103/63
Mixed Number
1 40/63
Decimal Value
1.634921
Percentage
163.4921%
Step-by-Step Solution: 7/9 + 6/7
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 7 = 63.
LCD(9, 7) = 63
Step 2
Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 7/9 by 7, and multiply the numerator and denominator of 6/7 by 9 so both fractions share the common base 63.
7 × 7/9 × 7 = 49/63 and 6 × 9/7 × 9 = 54/63
Step 3
Add the Numerators
Now add the numerators (49 + 54 = 103) and keep the common denominator 63 unchanged.
49 + 54/63 = 103/63
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 63 is 1, confirming that 103/63 cannot be reduced further—it is already in its simplest irreducible form.
103/63
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (103) is greater than the denominator (63), divide 103 by 63: it goes in 1 whole time(s) with a remainder of 40, giving the mixed number 1 40/63.
103/63 = 140/63
Step 6
Decimal & Percentage Representation
Dividing the numerator 103 by denominator 63 produces a repeating decimal (approximately 1.634921, or 163.4921%).
103 ÷ 63 = 1.634921 (163.4921%)
Visual Representation
The diagram below illustrates 7/9 plus 6/7 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 103/63 |
| Mixed Number Form | 1 40/63 |
| Decimal Form | 1.634921 |
| Percentage | 163.4921% |
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Frequently Asked Questions
What is 7/9 plus 6/7 as a fraction?
7/9 + 6/7 in simplest fraction form is 103/63 (or 1 40/63 as a mixed number).
What is 7/9 plus 6/7 as a decimal?
7/9 + 6/7 converted to a decimal is 1.634921.
What is 7/9 plus 6/7 as a percentage?
7/9 + 6/7 expressed as a percentage is 163.4921%.
How do you write 7/9 plus 6/7 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 103/63 can be written as the mixed number 1 40/63.
Does 7/9 plus 6/7 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.634921...) because the denominator contains prime factors other than 2 and 5.