What is 4/15 plus 7/9?
4/15 plus 7/9 equals 47/45 (or 1 2/45 as a mixed number) (or 1.044444 in decimal form). Learn the step-by-step solution to add 4/15 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/15 + 7/9 = 47/45
Simplified Fraction
47/45
Mixed Number
1 2/45
Decimal Value
1.044444
Percentage
104.4444%
Step-by-Step Solution: 4/15 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 15 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 15 × 9 = 135, keeping the calculation simpler).
LCD(15, 9) = 45
Step 2
Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 4/15 by 3, and multiply the numerator and denominator of 7/9 by 5 so both fractions share the common base 45.
4 × 3/15 × 3 = 12/45 and 7 × 5/9 × 5 = 35/45
Step 3
Add the Numerators
Now add the numerators (12 + 35 = 47) and keep the common denominator 45 unchanged.
12 + 35/45 = 47/45
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 45 is 1, confirming that 47/45 cannot be reduced further—it is already in its simplest irreducible form.
47/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (47) is greater than the denominator (45), divide 47 by 45: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/45.
47/45 = 12/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 47 by denominator 45 produces a repeating decimal (approximately 1.044444, or 104.4444%).
47 ÷ 45 = 1.044444 (104.4444%)
Visual Representation
The diagram below illustrates 4/15 plus 7/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 47/45 |
| Mixed Number Form | 1 2/45 |
| Decimal Form | 1.044444 |
| Percentage | 104.4444% |
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Frequently Asked Questions
What is 4/15 plus 7/9 as a fraction?
4/15 + 7/9 in simplest fraction form is 47/45 (or 1 2/45 as a mixed number).
What is 4/15 plus 7/9 as a decimal?
4/15 + 7/9 converted to a decimal is 1.044444.
What is 4/15 plus 7/9 as a percentage?
4/15 + 7/9 expressed as a percentage is 104.4444%.
How do you write 4/15 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 47/45 can be written as the mixed number 1 2/45.
Does 4/15 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.044444...) because the denominator contains prime factors other than 2 and 5.