What is 2/9 plus 7/8?
2/9 plus 7/8 equals 79/72 (or 1 7/72 as a mixed number) (or 1.097222 in decimal form). Learn the step-by-step solution to add 2/9 and 7/8 using Least Common Denominator and simplification.
Exact Answer
2/9 + 7/8 = 79/72
Simplified Fraction
79/72
Mixed Number
1 7/72
Decimal Value
1.097222
Percentage
109.7222%
Step-by-Step Solution: 2/9 + 7/8
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 8 = 72.
LCD(9, 8) = 72
Step 2
Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 2/9 by 8, and multiply the numerator and denominator of 7/8 by 9 so both fractions share the common base 72.
2 × 8/9 × 8 = 16/72 and 7 × 9/8 × 9 = 63/72
Step 3
Add the Numerators
Now add the numerators (16 + 63 = 79) and keep the common denominator 72 unchanged.
16 + 63/72 = 79/72
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 72 is 1, confirming that 79/72 cannot be reduced further—it is already in its simplest irreducible form.
79/72
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (79) is greater than the denominator (72), divide 79 by 72: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/72.
79/72 = 17/72
Step 6
Decimal & Percentage Representation
Dividing the numerator 79 by denominator 72 produces a repeating decimal (approximately 1.097222, or 109.7222%).
79 ÷ 72 = 1.097222 (109.7222%)
Visual Representation
The diagram below illustrates 2/9 plus 7/8 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 79/72 |
| Mixed Number Form | 1 7/72 |
| Decimal Form | 1.097222 |
| Percentage | 109.7222% |
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Frequently Asked Questions
What is 2/9 plus 7/8 as a fraction?
2/9 + 7/8 in simplest fraction form is 79/72 (or 1 7/72 as a mixed number).
What is 2/9 plus 7/8 as a decimal?
2/9 + 7/8 converted to a decimal is 1.097222.
What is 2/9 plus 7/8 as a percentage?
2/9 + 7/8 expressed as a percentage is 109.7222%.
How do you write 2/9 plus 7/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 79/72 can be written as the mixed number 1 7/72.
Does 2/9 plus 7/8 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.097222...) because the denominator contains prime factors other than 2 and 5.