What is 4/7 plus 7/9?
4/7 plus 7/9 equals 85/63 (or 1 22/63 as a mixed number) (or 1.349206 in decimal form). Learn the step-by-step solution to add 4/7 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/7 + 7/9 = 85/63
Simplified Fraction
85/63
Mixed Number
1 22/63
Decimal Value
1.349206
Percentage
134.9206%
Step-by-Step Solution: 4/7 + 7/9
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 4/7 by 9, and multiply the numerator and denominator of 7/9 by 7 so both fractions share the common base 63.
4 × 9/7 × 9 = 36/63 and 7 × 7/9 × 7 = 49/63
Step 3
Add the Numerators
Now add the numerators (36 + 49 = 85) and keep the common denominator 63 unchanged.
36 + 49/63 = 85/63
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 63 is 1, confirming that 85/63 cannot be reduced further—it is already in its simplest irreducible form.
85/63
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (85) is greater than the denominator (63), divide 85 by 63: it goes in 1 whole time(s) with a remainder of 22, giving the mixed number 1 22/63.
85/63 = 122/63
Step 6
Decimal & Percentage Representation
Dividing the numerator 85 by denominator 63 produces a repeating decimal (approximately 1.349206, or 134.9206%).
85 ÷ 63 = 1.349206 (134.9206%)
Visual Representation
The diagram below illustrates 4/7 plus 7/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 85/63 |
| Mixed Number Form | 1 22/63 |
| Decimal Form | 1.349206 |
| Percentage | 134.9206% |
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Frequently Asked Questions
What is 4/7 plus 7/9 as a fraction?
4/7 + 7/9 in simplest fraction form is 85/63 (or 1 22/63 as a mixed number).
What is 4/7 plus 7/9 as a decimal?
4/7 + 7/9 converted to a decimal is 1.349206.
What is 4/7 plus 7/9 as a percentage?
4/7 + 7/9 expressed as a percentage is 134.9206%.
How do you write 4/7 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 85/63 can be written as the mixed number 1 22/63.
Does 4/7 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.349206...) because the denominator contains prime factors other than 2 and 5.