What is 7/23 plus 4/9?
7/23 plus 4/9 equals 155/207 (or 0.748792 in decimal form). Learn the step-by-step solution to add 7/23 and 4/9 using Least Common Denominator and simplification.
Exact Answer
7/23 + 4/9 = 155/207
Simplified Fraction
155/207
Mixed Number
Proper (155/207)
Decimal Value
0.748792
Percentage
74.8792%
Step-by-Step Solution: 7/23 + 4/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.
LCD(23, 9) = 207
Step 2
Convert to Equivalent Fractions with Common Denominator 207
Multiply the numerator and denominator of 7/23 by 9, and multiply the numerator and denominator of 4/9 by 23 so both fractions share the common base 207.
7 × 9/23 × 9 = 63/207 and 4 × 23/9 × 23 = 92/207
Step 3
Add the Numerators
Now add the numerators (63 + 92 = 155) and keep the common denominator 207 unchanged.
63 + 92/207 = 155/207
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 155 and 207 is 1, confirming that 155/207 cannot be reduced further—it is already in its simplest irreducible form.
155/207
Step 5
Decimal & Percentage Representation
Dividing the numerator 155 by denominator 207 produces a repeating decimal (approximately 0.748792, or 74.8792%).
155 ÷ 207 = 0.748792 (74.8792%)
Visual Representation
The diagram below illustrates 7/23 plus 4/9 visually:
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=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 155/207 |
| Mixed Number Form | 155/207 |
| Decimal Form | 0.748792 |
| Percentage | 74.8792% |
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Frequently Asked Questions
What is 7/23 plus 4/9 as a fraction?
7/23 + 4/9 in simplest fraction form is 155/207.
What is 7/23 plus 4/9 as a decimal?
7/23 + 4/9 converted to a decimal is 0.748792.
What is 7/23 plus 4/9 as a percentage?
7/23 + 4/9 expressed as a percentage is 74.8792%.
Does 7/23 plus 4/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.748792...) because the denominator contains prime factors other than 2 and 5.