What is 4/9 plus 6/7?
4/9 plus 6/7 equals 82/63 (or 1 19/63 as a mixed number) (or 1.301587 in decimal form). Learn the step-by-step solution to add 4/9 and 6/7 using Least Common Denominator and simplification.
Exact Answer
4/9 + 6/7 = 82/63
Simplified Fraction
82/63
Mixed Number
1 19/63
Decimal Value
1.301587
Percentage
130.1587%
Step-by-Step Solution: 4/9 + 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 4/9 by 7, and multiply the numerator and denominator of 6/7 by 9 so both fractions share the common base 63.
4 × 7/9 × 7 = 28/63 and 6 × 9/7 × 9 = 54/63
Step 3
Add the Numerators
Now add the numerators (28 + 54 = 82) and keep the common denominator 63 unchanged.
28 + 54/63 = 82/63
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 82 and 63 is 1, confirming that 82/63 cannot be reduced further—it is already in its simplest irreducible form.
82/63
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (82) is greater than the denominator (63), divide 82 by 63: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/63.
82/63 = 119/63
Step 6
Decimal & Percentage Representation
Dividing the numerator 82 by denominator 63 produces a repeating decimal (approximately 1.301587, or 130.1587%).
82 ÷ 63 = 1.301587 (130.1587%)
Visual Representation
The diagram below illustrates 4/9 plus 6/7 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 82/63 |
| Mixed Number Form | 1 19/63 |
| Decimal Form | 1.301587 |
| Percentage | 130.1587% |
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Frequently Asked Questions
What is 4/9 plus 6/7 as a fraction?
4/9 + 6/7 in simplest fraction form is 82/63 (or 1 19/63 as a mixed number).
What is 4/9 plus 6/7 as a decimal?
4/9 + 6/7 converted to a decimal is 1.301587.
What is 4/9 plus 6/7 as a percentage?
4/9 + 6/7 expressed as a percentage is 130.1587%.
How do you write 4/9 plus 6/7 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 82/63 can be written as the mixed number 1 19/63.
Does 4/9 plus 6/7 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.301587...) because the denominator contains prime factors other than 2 and 5.