What is 2/20 plus 7/9? (Answer: 79/90)

Exact Answer

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Problem: What is 2/20 plus 7/9?
Formula / Expression: 2/20 + 7/9
Final Answer: 79/90
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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 2/20 by 9, and multiply the numerator and denominator of 7/9 by 20 so both fractions share the common base 180.
Working: 2 × 9/20 × 9 = 18/180 and 7 × 20/9 × 20 = 140/180

Step 3: Add the Numerators
Now add the numerators (18 + 140 = 158) and keep the common denominator 180 unchanged.
Working: 18 + 140/180 = 158/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 158 and 180, which is 2. Divide both the numerator and denominator by 2.
Working: 158 ÷ 2/180 ÷ 2 = 79/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 90 produces a repeating decimal (approximately 0.877778, or 87.7778%).
Working: 79 ÷ 90 = 0.877778 (87.7778%)

Key Values:
- Simplified Fraction: 79/90
- Mixed Number Form: 79/90
- Decimal Value: 0.877778
- Percentage: 87.7778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-20-plus-7-9/
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2/20 + 7/9 = 79/90

Simplified Fraction

79/90

Mixed Number

Proper (79/90)

Decimal Value

0.877778

Percentage

87.7778%

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Step-by-Step Solution: 2/20 + 7/9

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 2/20 by 9, and multiply the numerator and denominator of 7/9 by 20 so both fractions share the common base 180.

2 × 9/20 × 9 = 18/180 and 7 × 20/9 × 20 = 140/180

Step 3

Add the Numerators

Now add the numerators (18 + 140 = 158) and keep the common denominator 180 unchanged.

18 + 140/180 = 158/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 158 and 180, which is 2. Divide both the numerator and denominator by 2.

158 ÷ 2/180 ÷ 2 = 79/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 90 produces a repeating decimal (approximately 0.877778, or 87.7778%).

79 ÷ 90 = 0.877778 (87.7778%)

Visual Representation

The diagram below illustrates 2/20 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/90`
Mixed Number Form	`79/90`
Decimal Form	`0.877778`
Percentage	`87.7778%`

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Frequently Asked Questions

What is 2/20 plus 7/9 as a fraction?

2/20 + 7/9 in simplest fraction form is 79/90.

What is 2/20 plus 7/9 as a decimal?

2/20 + 7/9 converted to a decimal is 0.877778.

What is 2/20 plus 7/9 as a percentage?

2/20 + 7/9 expressed as a percentage is 87.7778%.

Does 2/20 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.877778...) because the denominator contains prime factors other than 2 and 5.