What is 4/19 plus 7/9?
4/19 plus 7/9 equals 169/171 (or 0.988304 in decimal form). Learn the step-by-step solution to add 4/19 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/19 + 7/9 = 169/171
Simplified Fraction
169/171
Mixed Number
Proper (169/171)
Decimal Value
0.988304
Percentage
98.8304%
Step-by-Step Solution: 4/19 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 19 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 9 = 171.
LCD(19, 9) = 171
Step 2
Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 4/19 by 9, and multiply the numerator and denominator of 7/9 by 19 so both fractions share the common base 171.
4 × 9/19 × 9 = 36/171 and 7 × 19/9 × 19 = 133/171
Step 3
Add the Numerators
Now add the numerators (36 + 133 = 169) and keep the common denominator 171 unchanged.
36 + 133/171 = 169/171
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 169 and 171 is 1, confirming that 169/171 cannot be reduced further—it is already in its simplest irreducible form.
169/171
Step 5
Decimal & Percentage Representation
Dividing the numerator 169 by denominator 171 produces a repeating decimal (approximately 0.988304, or 98.8304%).
169 ÷ 171 = 0.988304 (98.8304%)
Visual Representation
The diagram below illustrates 4/19 plus 7/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 169/171 |
| Mixed Number Form | 169/171 |
| Decimal Form | 0.988304 |
| Percentage | 98.8304% |
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Frequently Asked Questions
What is 4/19 plus 7/9 as a fraction?
4/19 + 7/9 in simplest fraction form is 169/171.
What is 4/19 plus 7/9 as a decimal?
4/19 + 7/9 converted to a decimal is 0.988304.
What is 4/19 plus 7/9 as a percentage?
4/19 + 7/9 expressed as a percentage is 98.8304%.
Does 4/19 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.988304...) because the denominator contains prime factors other than 2 and 5.