What is 3/40 plus 4/9?
3/40 plus 4/9 equals 187/360 (or 0.519444 in decimal form). Learn the step-by-step solution to add 3/40 and 4/9 using Least Common Denominator and simplification.
Exact Answer
3/40 + 4/9 = 187/360
Simplified Fraction
187/360
Mixed Number
Proper (187/360)
Decimal Value
0.519444
Percentage
51.9444%
Step-by-Step Solution: 3/40 + 4/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 40 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 9 = 360.
LCD(40, 9) = 360
Step 2
Convert to Equivalent Fractions with Common Denominator 360
Multiply the numerator and denominator of 3/40 by 9, and multiply the numerator and denominator of 4/9 by 40 so both fractions share the common base 360.
3 × 9/40 × 9 = 27/360 and 4 × 40/9 × 40 = 160/360
Step 3
Add the Numerators
Now add the numerators (27 + 160 = 187) and keep the common denominator 360 unchanged.
27 + 160/360 = 187/360
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 187 and 360 is 1, confirming that 187/360 cannot be reduced further—it is already in its simplest irreducible form.
187/360
Step 5
Decimal & Percentage Representation
Dividing the numerator 187 by denominator 360 produces a repeating decimal (approximately 0.519444, or 51.9444%).
187 ÷ 360 = 0.519444 (51.9444%)
Visual Representation
The diagram below illustrates 3/40 plus 4/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 187/360 |
| Mixed Number Form | 187/360 |
| Decimal Form | 0.519444 |
| Percentage | 51.9444% |
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Frequently Asked Questions
What is 3/40 plus 4/9 as a fraction?
3/40 + 4/9 in simplest fraction form is 187/360.
What is 3/40 plus 4/9 as a decimal?
3/40 + 4/9 converted to a decimal is 0.519444.
What is 3/40 plus 4/9 as a percentage?
3/40 + 4/9 expressed as a percentage is 51.9444%.
Does 3/40 plus 4/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.519444...) because the denominator contains prime factors other than 2 and 5.