What is 4/17 plus 7/9?
4/17 plus 7/9 equals 155/153 (or 1 2/153 as a mixed number) (or 1.013072 in decimal form). Learn the step-by-step solution to add 4/17 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/17 + 7/9 = 155/153
Simplified Fraction
155/153
Mixed Number
1 2/153
Decimal Value
1.013072
Percentage
101.3072%
Step-by-Step Solution: 4/17 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 17 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 9 = 153.
LCD(17, 9) = 153
Step 2
Convert to Equivalent Fractions with Common Denominator 153
Multiply the numerator and denominator of 4/17 by 9, and multiply the numerator and denominator of 7/9 by 17 so both fractions share the common base 153.
4 × 9/17 × 9 = 36/153 and 7 × 17/9 × 17 = 119/153
Step 3
Add the Numerators
Now add the numerators (36 + 119 = 155) and keep the common denominator 153 unchanged.
36 + 119/153 = 155/153
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 155 and 153 is 1, confirming that 155/153 cannot be reduced further—it is already in its simplest irreducible form.
155/153
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (155) is greater than the denominator (153), divide 155 by 153: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/153.
155/153 = 12/153
Step 6
Decimal & Percentage Representation
Dividing the numerator 155 by denominator 153 produces a repeating decimal (approximately 1.013072, or 101.3072%).
155 ÷ 153 = 1.013072 (101.3072%)
Visual Representation
The diagram below illustrates 4/17 plus 7/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 155/153 |
| Mixed Number Form | 1 2/153 |
| Decimal Form | 1.013072 |
| Percentage | 101.3072% |
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Frequently Asked Questions
What is 4/17 plus 7/9 as a fraction?
4/17 + 7/9 in simplest fraction form is 155/153 (or 1 2/153 as a mixed number).
What is 4/17 plus 7/9 as a decimal?
4/17 + 7/9 converted to a decimal is 1.013072.
What is 4/17 plus 7/9 as a percentage?
4/17 + 7/9 expressed as a percentage is 101.3072%.
How do you write 4/17 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 155/153 can be written as the mixed number 1 2/153.
Does 4/17 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.013072...) because the denominator contains prime factors other than 2 and 5.