What is 3/10 plus 7/9?
3/10 plus 7/9 equals 97/90 (or 1 7/90 as a mixed number) (or 1.077778 in decimal form). Learn the step-by-step solution to add 3/10 and 7/9 using Least Common Denominator and simplification.
Exact Answer
3/10 + 7/9 = 97/90
Simplified Fraction
97/90
Mixed Number
1 7/90
Decimal Value
1.077778
Percentage
107.7778%
Step-by-Step Solution: 3/10 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.
LCD(10, 9) = 90
Step 2
Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 3/10 by 9, and multiply the numerator and denominator of 7/9 by 10 so both fractions share the common base 90.
3 × 9/10 × 9 = 27/90 and 7 × 10/9 × 10 = 70/90
Step 3
Add the Numerators
Now add the numerators (27 + 70 = 97) and keep the common denominator 90 unchanged.
27 + 70/90 = 97/90
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 90 is 1, confirming that 97/90 cannot be reduced further—it is already in its simplest irreducible form.
97/90
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (97) is greater than the denominator (90), divide 97 by 90: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/90.
97/90 = 17/90
Step 6
Decimal & Percentage Representation
Dividing the numerator 97 by denominator 90 produces a repeating decimal (approximately 1.077778, or 107.7778%).
97 ÷ 90 = 1.077778 (107.7778%)
Visual Representation
The diagram below illustrates 3/10 plus 7/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 97/90 |
| Mixed Number Form | 1 7/90 |
| Decimal Form | 1.077778 |
| Percentage | 107.7778% |
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Frequently Asked Questions
What is 3/10 plus 7/9 as a fraction?
3/10 + 7/9 in simplest fraction form is 97/90 (or 1 7/90 as a mixed number).
What is 3/10 plus 7/9 as a decimal?
3/10 + 7/9 converted to a decimal is 1.077778.
What is 3/10 plus 7/9 as a percentage?
3/10 + 7/9 expressed as a percentage is 107.7778%.
How do you write 3/10 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 97/90 can be written as the mixed number 1 7/90.
Does 3/10 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.077778...) because the denominator contains prime factors other than 2 and 5.