What is 2/20 plus 3/8? (Answer: 19/40)

Exact Answer

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Problem: What is 2/20 plus 3/8?
Formula / Expression: 2/20 + 3/8
Final Answer: 19/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 8 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 20 × 8 = 160, keeping the calculation simpler).
Working: LCD(20, 8) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 2/20 by 2, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.
Working: 2 × 2/20 × 2 = 4/40 and 3 × 5/8 × 5 = 15/40

Step 3: Add the Numerators
Now add the numerators (4 + 15 = 19) and keep the common denominator 40 unchanged.
Working: 4 + 15/40 = 19/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 40 is 1, confirming that 19/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 40 yields an exact terminating decimal of 0.475 (or 47.5%).
Working: 19 ÷ 40 = 0.475 (47.5%)

Key Values:
- Simplified Fraction: 19/40
- Mixed Number Form: 19/40
- Decimal Value: 0.475
- Percentage: 47.5%

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2/20 + 3/8 = 19/40

Simplified Fraction

19/40

Mixed Number

Proper (19/40)

Decimal Value

0.475

Percentage

47.5%

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Step-by-Step Solution: 2/20 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 8 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 20 × 8 = 160, keeping the calculation simpler).

LCD(20, 8) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 2/20 by 2, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.

2 × 2/20 × 2 = 4/40 and 3 × 5/8 × 5 = 15/40

Step 3

Add the Numerators

Now add the numerators (4 + 15 = 19) and keep the common denominator 40 unchanged.

4 + 15/40 = 19/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 40 is 1, confirming that 19/40 cannot be reduced further—it is already in its simplest irreducible form.

19/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 40 yields an exact terminating decimal of 0.475 (or 47.5%).

19 ÷ 40 = 0.475 (47.5%)

Visual Representation

The diagram below illustrates 2/20 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/40`
Mixed Number Form	`19/40`
Decimal Form	`0.475`
Percentage	`47.5%`

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Frequently Asked Questions

What is 2/20 plus 3/8 as a fraction?

2/20 + 3/8 in simplest fraction form is 19/40.

What is 2/20 plus 3/8 as a decimal?

2/20 + 3/8 converted to a decimal is 0.475.

What is 2/20 plus 3/8 as a percentage?

2/20 + 3/8 expressed as a percentage is 47.5%.

Does 2/20 plus 3/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.475) because the denominator in simplest terms contains only prime factors 2 and/or 5.