What is 7/20 plus 4/9? (Answer: 143/180)

Exact Answer

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Problem: What is 7/20 plus 4/9?
Formula / Expression: 7/20 + 4/9
Final Answer: 143/180
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 9 = 180.
Working: LCD(20, 9) = 180

Step 2: Convert to Equivalent Fractions with Common Denominator 180
Multiply the numerator and denominator of 7/20 by 9, and multiply the numerator and denominator of 4/9 by 20 so both fractions share the common base 180.
Working: 7 × 9/20 × 9 = 63/180 and 4 × 20/9 × 20 = 80/180

Step 3: Add the Numerators
Now add the numerators (63 + 80 = 143) and keep the common denominator 180 unchanged.
Working: 63 + 80/180 = 143/180

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 180 is 1, confirming that 143/180 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/180

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 180 produces a repeating decimal (approximately 0.794444, or 79.4444%).
Working: 143 ÷ 180 = 0.794444 (79.4444%)

Key Values:
- Simplified Fraction: 143/180
- Mixed Number Form: 143/180
- Decimal Value: 0.794444
- Percentage: 79.4444%

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7/20 + 4/9 = 143/180

Simplified Fraction

143/180

Mixed Number

Proper (143/180)

Decimal Value

0.794444

Percentage

79.4444%

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Step-by-Step Solution: 7/20 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 9 = 180.

LCD(20, 9) = 180

Step 2

Convert to Equivalent Fractions with Common Denominator 180

Multiply the numerator and denominator of 7/20 by 9, and multiply the numerator and denominator of 4/9 by 20 so both fractions share the common base 180.

7 × 9/20 × 9 = 63/180 and 4 × 20/9 × 20 = 80/180

Step 3

Add the Numerators

Now add the numerators (63 + 80 = 143) and keep the common denominator 180 unchanged.

63 + 80/180 = 143/180

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 180 is 1, confirming that 143/180 cannot be reduced further—it is already in its simplest irreducible form.

143/180

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 180 produces a repeating decimal (approximately 0.794444, or 79.4444%).

143 ÷ 180 = 0.794444 (79.4444%)

Visual Representation

The diagram below illustrates 7/20 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/180`
Mixed Number Form	`143/180`
Decimal Form	`0.794444`
Percentage	`79.4444%`

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Frequently Asked Questions

What is 7/20 plus 4/9 as a fraction?

7/20 + 4/9 in simplest fraction form is 143/180.

What is 7/20 plus 4/9 as a decimal?

7/20 + 4/9 converted to a decimal is 0.794444.

What is 7/20 plus 4/9 as a percentage?

7/20 + 4/9 expressed as a percentage is 79.4444%.

Does 7/20 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.794444...) because the denominator contains prime factors other than 2 and 5.