What is 7/18 plus 2/5? (Answer: 71/90)

Exact Answer

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Problem: What is 7/18 plus 2/5?
Formula / Expression: 7/18 + 2/5
Final Answer: 71/90
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 5 = 90.
Working: LCD(18, 5) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 7/18 by 5, and multiply the numerator and denominator of 2/5 by 18 so both fractions share the common base 90.
Working: 7 × 5/18 × 5 = 35/90 and 2 × 18/5 × 18 = 36/90

Step 3: Add the Numerators
Now add the numerators (35 + 36 = 71) and keep the common denominator 90 unchanged.
Working: 35 + 36/90 = 71/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 90 is 1, confirming that 71/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 90 produces a repeating decimal (approximately 0.788889, or 78.8889%).
Working: 71 ÷ 90 = 0.788889 (78.8889%)

Key Values:
- Simplified Fraction: 71/90
- Mixed Number Form: 71/90
- Decimal Value: 0.788889
- Percentage: 78.8889%

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Solved with FractionsCalc:
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7/18 + 2/5 = 71/90

Simplified Fraction

71/90

Mixed Number

Proper (71/90)

Decimal Value

0.788889

Percentage

78.8889%

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Step-by-Step Solution: 7/18 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 5 = 90.

LCD(18, 5) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 7/18 by 5, and multiply the numerator and denominator of 2/5 by 18 so both fractions share the common base 90.

7 × 5/18 × 5 = 35/90 and 2 × 18/5 × 18 = 36/90

Step 3

Add the Numerators

Now add the numerators (35 + 36 = 71) and keep the common denominator 90 unchanged.

35 + 36/90 = 71/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 90 is 1, confirming that 71/90 cannot be reduced further—it is already in its simplest irreducible form.

71/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 90 produces a repeating decimal (approximately 0.788889, or 78.8889%).

71 ÷ 90 = 0.788889 (78.8889%)

Visual Representation

The diagram below illustrates 7/18 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/90`
Mixed Number Form	`71/90`
Decimal Form	`0.788889`
Percentage	`78.8889%`

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Frequently Asked Questions

What is 7/18 plus 2/5 as a fraction?

7/18 + 2/5 in simplest fraction form is 71/90.

What is 7/18 plus 2/5 as a decimal?

7/18 + 2/5 converted to a decimal is 0.788889.

What is 7/18 plus 2/5 as a percentage?

7/18 + 2/5 expressed as a percentage is 78.8889%.

Does 7/18 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.788889...) because the denominator contains prime factors other than 2 and 5.