What is 3/5 plus 7/9?
3/5 plus 7/9 equals 62/45 (or 1 17/45 as a mixed number) (or 1.377778 in decimal form). Learn the step-by-step solution to add 3/5 and 7/9 using Least Common Denominator and simplification.
Exact Answer
3/5 + 7/9 = 62/45
Simplified Fraction
62/45
Mixed Number
1 17/45
Decimal Value
1.377778
Percentage
137.7778%
Step-by-Step Solution: 3/5 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 9 = 45.
LCD(5, 9) = 45
Step 2
Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 3/5 by 9, and multiply the numerator and denominator of 7/9 by 5 so both fractions share the common base 45.
3 × 9/5 × 9 = 27/45 and 7 × 5/9 × 5 = 35/45
Step 3
Add the Numerators
Now add the numerators (27 + 35 = 62) and keep the common denominator 45 unchanged.
27 + 35/45 = 62/45
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 62 and 45 is 1, confirming that 62/45 cannot be reduced further—it is already in its simplest irreducible form.
62/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (62) is greater than the denominator (45), divide 62 by 45: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/45.
62/45 = 117/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 62 by denominator 45 produces a repeating decimal (approximately 1.377778, or 137.7778%).
62 ÷ 45 = 1.377778 (137.7778%)
Visual Representation
The diagram below illustrates 3/5 plus 7/9 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 62/45 |
| Mixed Number Form | 1 17/45 |
| Decimal Form | 1.377778 |
| Percentage | 137.7778% |
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Frequently Asked Questions
What is 3/5 plus 7/9 as a fraction?
3/5 + 7/9 in simplest fraction form is 62/45 (or 1 17/45 as a mixed number).
What is 3/5 plus 7/9 as a decimal?
3/5 + 7/9 converted to a decimal is 1.377778.
What is 3/5 plus 7/9 as a percentage?
3/5 + 7/9 expressed as a percentage is 137.7778%.
How do you write 3/5 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 62/45 can be written as the mixed number 1 17/45.
Does 3/5 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.377778...) because the denominator contains prime factors other than 2 and 5.