What is 2/5 plus 7/16?
2/5 plus 7/16 equals 67/80 (or 0.8375 in decimal form). Learn the step-by-step solution to add 2/5 and 7/16 using Least Common Denominator and simplification.
Exact Answer
2/5 + 7/16 = 67/80
Simplified Fraction
67/80
Mixed Number
Proper (67/80)
Decimal Value
0.8375
Percentage
83.75%
Step-by-Step Solution: 2/5 + 7/16
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 16 = 80.
LCD(5, 16) = 80
Step 2
Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/5 by 16, and multiply the numerator and denominator of 7/16 by 5 so both fractions share the common base 80.
2 × 16/5 × 16 = 32/80 and 7 × 5/16 × 5 = 35/80
Step 3
Add the Numerators
Now add the numerators (32 + 35 = 67) and keep the common denominator 80 unchanged.
32 + 35/80 = 67/80
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 80 is 1, confirming that 67/80 cannot be reduced further—it is already in its simplest irreducible form.
67/80
Step 5
Decimal & Percentage Representation
Dividing the numerator 67 by denominator 80 yields an exact terminating decimal of 0.8375 (or 83.75%).
67 ÷ 80 = 0.8375 (83.75%)
Visual Representation
The diagram below illustrates 2/5 plus 7/16 visually:
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=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 67/80 |
| Mixed Number Form | 67/80 |
| Decimal Form | 0.8375 |
| Percentage | 83.75% |
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Frequently Asked Questions
What is 2/5 plus 7/16 as a fraction?
2/5 + 7/16 in simplest fraction form is 67/80.
What is 2/5 plus 7/16 as a decimal?
2/5 + 7/16 converted to a decimal is 0.8375.
What is 2/5 plus 7/16 as a percentage?
2/5 + 7/16 expressed as a percentage is 83.75%.
Does 2/5 plus 7/16 result in a terminating or repeating decimal?
It results in an exact terminating decimal (0.8375) because the denominator in simplest terms contains only prime factors 2 and/or 5.