What is 4/9 plus 7/8?
4/9 plus 7/8 equals 95/72 (or 1 23/72 as a mixed number) (or 1.319444 in decimal form). Learn the step-by-step solution to add 4/9 and 7/8 using Least Common Denominator and simplification.
Exact Answer
4/9 + 7/8 = 95/72
Simplified Fraction
95/72
Mixed Number
1 23/72
Decimal Value
1.319444
Percentage
131.9444%
Step-by-Step Solution: 4/9 + 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 4/9 by 8, and multiply the numerator and denominator of 7/8 by 9 so both fractions share the common base 72.
4 × 8/9 × 8 = 32/72 and 7 × 9/8 × 9 = 63/72
Step 3
Add the Numerators
Now add the numerators (32 + 63 = 95) and keep the common denominator 72 unchanged.
32 + 63/72 = 95/72
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 95 and 72 is 1, confirming that 95/72 cannot be reduced further—it is already in its simplest irreducible form.
95/72
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (95) is greater than the denominator (72), divide 95 by 72: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/72.
95/72 = 123/72
Step 6
Decimal & Percentage Representation
Dividing the numerator 95 by denominator 72 produces a repeating decimal (approximately 1.319444, or 131.9444%).
95 ÷ 72 = 1.319444 (131.9444%)
Visual Representation
The diagram below illustrates 4/9 plus 7/8 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 95/72 |
| Mixed Number Form | 1 23/72 |
| Decimal Form | 1.319444 |
| Percentage | 131.9444% |
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Frequently Asked Questions
What is 4/9 plus 7/8 as a fraction?
4/9 + 7/8 in simplest fraction form is 95/72 (or 1 23/72 as a mixed number).
What is 4/9 plus 7/8 as a decimal?
4/9 + 7/8 converted to a decimal is 1.319444.
What is 4/9 plus 7/8 as a percentage?
4/9 + 7/8 expressed as a percentage is 131.9444%.
How do you write 4/9 plus 7/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 95/72 can be written as the mixed number 1 23/72.
Does 4/9 plus 7/8 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.319444...) because the denominator contains prime factors other than 2 and 5.