What is 4/8 plus 7/9?
4/8 plus 7/9 equals 23/18 (or 1 5/18 as a mixed number) (or 1.277778 in decimal form). Learn the step-by-step solution to add 4/8 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/8 + 7/9 = 23/18
Simplified Fraction
23/18
Mixed Number
1 5/18
Decimal Value
1.277778
Percentage
127.7778%
Step-by-Step Solution: 4/8 + 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 4/8 by 9, and multiply the numerator and denominator of 7/9 by 8 so both fractions share the common base 72.
4 × 9/8 × 9 = 36/72 and 7 × 8/9 × 8 = 56/72
Step 3
Add the Numerators
Now add the numerators (36 + 56 = 92) and keep the common denominator 72 unchanged.
36 + 56/72 = 92/72
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 92 and 72, which is 4. Divide both the numerator and denominator by 4.
92 ÷ 4/72 ÷ 4 = 23/18
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (23) is greater than the denominator (18), divide 23 by 18: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/18.
23/18 = 15/18
Step 6
Decimal & Percentage Representation
Dividing the numerator 23 by denominator 18 produces a repeating decimal (approximately 1.277778, or 127.7778%).
23 ÷ 18 = 1.277778 (127.7778%)
Visual Representation
The diagram below illustrates 4/8 plus 7/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 23/18 |
| Mixed Number Form | 1 5/18 |
| Decimal Form | 1.277778 |
| Percentage | 127.7778% |
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Frequently Asked Questions
What is 4/8 plus 7/9 as a fraction?
4/8 + 7/9 in simplest fraction form is 23/18 (or 1 5/18 as a mixed number).
What is 4/8 plus 7/9 as a decimal?
4/8 + 7/9 converted to a decimal is 1.277778.
What is 4/8 plus 7/9 as a percentage?
4/8 + 7/9 expressed as a percentage is 127.7778%.
How do you write 4/8 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 23/18 can be written as the mixed number 1 5/18.
Does 4/8 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.277778...) because the denominator contains prime factors other than 2 and 5.