What is 4/18 plus 4/5? (Answer: 46/45)

Exact Answer

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Problem: What is 4/18 plus 4/5?
Formula / Expression: 4/18 + 4/5
Final Answer: 1 1/45 (46/45)
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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 4/18 by 5, and multiply the numerator and denominator of 4/5 by 18 so both fractions share the common base 90.
Working: 4 × 5/18 × 5 = 20/90 and 4 × 18/5 × 18 = 72/90

Step 3: Add the Numerators
Now add the numerators (20 + 72 = 92) and keep the common denominator 90 unchanged.
Working: 20 + 72/90 = 92/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 92 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 92 ÷ 2/90 ÷ 2 = 46/45

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (46) is greater than the denominator (45), divide 46 by 45: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/45.
Working: 46/45 = 1 1/45

Step 6: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 45 produces a repeating decimal (approximately 1.022222, or 102.2222%).
Working: 46 ÷ 45 = 1.022222 (102.2222%)

Key Values:
- Simplified Fraction: 46/45
- Mixed Number Form: 1 1/45
- Decimal Value: 1.022222
- Percentage: 102.2222%

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Solved with FractionsCalc:
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4/18 + 4/5 = 46/45

Simplified Fraction

46/45

Mixed Number

1 1/45

Decimal Value

1.022222

Percentage

102.2222%

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Step-by-Step Solution: 4/18 + 4/5

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 4/18 by 5, and multiply the numerator and denominator of 4/5 by 18 so both fractions share the common base 90.

4 × 5/18 × 5 = 20/90 and 4 × 18/5 × 18 = 72/90

Step 3

Add the Numerators

Now add the numerators (20 + 72 = 92) and keep the common denominator 90 unchanged.

20 + 72/90 = 92/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 92 and 90, which is 2. Divide both the numerator and denominator by 2.

92 ÷ 2/90 ÷ 2 = 46/45

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (46) is greater than the denominator (45), divide 46 by 45: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/45.

46/45 = 11/45

Step 6

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 45 produces a repeating decimal (approximately 1.022222, or 102.2222%).

46 ÷ 45 = 1.022222 (102.2222%)

Visual Representation

The diagram below illustrates 4/18 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/45`
Mixed Number Form	`1 1/45`
Decimal Form	`1.022222`
Percentage	`102.2222%`

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Frequently Asked Questions

What is 4/18 plus 4/5 as a fraction?

4/18 + 4/5 in simplest fraction form is 46/45 (or 1 1/45 as a mixed number).

What is 4/18 plus 4/5 as a decimal?

4/18 + 4/5 converted to a decimal is 1.022222.

What is 4/18 plus 4/5 as a percentage?

4/18 + 4/5 expressed as a percentage is 102.2222%.

How do you write 4/18 plus 4/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 46/45 can be written as the mixed number 1 1/45.

Does 4/18 plus 4/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.022222...) because the denominator contains prime factors other than 2 and 5.