What is 3/8 plus 7/9?
3/8 plus 7/9 equals 83/72 (or 1 11/72 as a mixed number) (or 1.152778 in decimal form). Learn the step-by-step solution to add 3/8 and 7/9 using Least Common Denominator and simplification.
Exact Answer
3/8 + 7/9 = 83/72
Simplified Fraction
83/72
Mixed Number
1 11/72
Decimal Value
1.152778
Percentage
115.2778%
Step-by-Step Solution: 3/8 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 8 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 9 = 72.
LCD(8, 9) = 72
Step 2
Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 3/8 by 9, and multiply the numerator and denominator of 7/9 by 8 so both fractions share the common base 72.
3 × 9/8 × 9 = 27/72 and 7 × 8/9 × 8 = 56/72
Step 3
Add the Numerators
Now add the numerators (27 + 56 = 83) and keep the common denominator 72 unchanged.
27 + 56/72 = 83/72
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 72 is 1, confirming that 83/72 cannot be reduced further—it is already in its simplest irreducible form.
83/72
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (83) is greater than the denominator (72), divide 83 by 72: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/72.
83/72 = 111/72
Step 6
Decimal & Percentage Representation
Dividing the numerator 83 by denominator 72 produces a repeating decimal (approximately 1.152778, or 115.2778%).
83 ÷ 72 = 1.152778 (115.2778%)
Visual Representation
The diagram below illustrates 3/8 plus 7/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 83/72 |
| Mixed Number Form | 1 11/72 |
| Decimal Form | 1.152778 |
| Percentage | 115.2778% |
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Frequently Asked Questions
What is 3/8 plus 7/9 as a fraction?
3/8 + 7/9 in simplest fraction form is 83/72 (or 1 11/72 as a mixed number).
What is 3/8 plus 7/9 as a decimal?
3/8 + 7/9 converted to a decimal is 1.152778.
What is 3/8 plus 7/9 as a percentage?
3/8 + 7/9 expressed as a percentage is 115.2778%.
How do you write 3/8 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 83/72 can be written as the mixed number 1 11/72.
Does 3/8 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.152778...) because the denominator contains prime factors other than 2 and 5.