What is 2/20 plus 2/16? (Answer: 9/40)

Exact Answer

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Problem: What is 2/20 plus 2/16?
Formula / Expression: 2/20 + 2/16
Final Answer: 9/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 16 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 20 × 16 = 320, keeping the calculation simpler).
Working: LCD(20, 16) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/20 by 4, and multiply the numerator and denominator of 2/16 by 5 so both fractions share the common base 80.
Working: 2 × 4/20 × 4 = 8/80 and 2 × 5/16 × 5 = 10/80

Step 3: Add the Numerators
Now add the numerators (8 + 10 = 18) and keep the common denominator 80 unchanged.
Working: 8 + 10/80 = 18/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 80, which is 2. Divide both the numerator and denominator by 2.
Working: 18 ÷ 2/80 ÷ 2 = 9/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 40 yields an exact terminating decimal of 0.225 (or 22.5%).
Working: 9 ÷ 40 = 0.225 (22.5%)

Key Values:
- Simplified Fraction: 9/40
- Mixed Number Form: 9/40
- Decimal Value: 0.225
- Percentage: 22.5%

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Solved with FractionsCalc:
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2/20 + 2/16 = 9/40

Simplified Fraction

9/40

Mixed Number

Proper (9/40)

Decimal Value

0.225

Percentage

22.5%

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Step-by-Step Solution: 2/20 + 2/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 16 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 20 × 16 = 320, keeping the calculation simpler).

LCD(20, 16) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

Multiply the numerator and denominator of 2/20 by 4, and multiply the numerator and denominator of 2/16 by 5 so both fractions share the common base 80.

2 × 4/20 × 4 = 8/80 and 2 × 5/16 × 5 = 10/80

Step 3

Add the Numerators

Now add the numerators (8 + 10 = 18) and keep the common denominator 80 unchanged.

8 + 10/80 = 18/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 80, which is 2. Divide both the numerator and denominator by 2.

18 ÷ 2/80 ÷ 2 = 9/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 40 yields an exact terminating decimal of 0.225 (or 22.5%).

9 ÷ 40 = 0.225 (22.5%)

Visual Representation

The diagram below illustrates 2/20 plus 2/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/40`
Mixed Number Form	`9/40`
Decimal Form	`0.225`
Percentage	`22.5%`

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Frequently Asked Questions

What is 2/20 plus 2/16 as a fraction?

2/20 + 2/16 in simplest fraction form is 9/40.

What is 2/20 plus 2/16 as a decimal?

2/20 + 2/16 converted to a decimal is 0.225.

What is 2/20 plus 2/16 as a percentage?

2/20 + 2/16 expressed as a percentage is 22.5%.

Does 2/20 plus 2/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.225) because the denominator in simplest terms contains only prime factors 2 and/or 5.