What is 9/20 plus 4/8? (Answer: 19/20)

Exact Answer

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Problem: What is 9/20 plus 4/8?
Formula / Expression: 9/20 + 4/8
Final Answer: 19/20
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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 9/20 by 2, and multiply the numerator and denominator of 4/8 by 5 so both fractions share the common base 40.
Working: 9 × 2/20 × 2 = 18/40 and 4 × 5/8 × 5 = 20/40

Step 3: Add the Numerators
Now add the numerators (18 + 20 = 38) and keep the common denominator 40 unchanged.
Working: 18 + 20/40 = 38/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 40, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/40 ÷ 2 = 19/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 20 yields an exact terminating decimal of 0.95 (or 95%).
Working: 19 ÷ 20 = 0.95 (95%)

Key Values:
- Simplified Fraction: 19/20
- Mixed Number Form: 19/20
- Decimal Value: 0.95
- Percentage: 95%

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Solved with FractionsCalc:
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9/20 + 4/8 = 19/20

Simplified Fraction

19/20

Mixed Number

Proper (19/20)

Decimal Value

0.95

Percentage

95%

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Step-by-Step Solution: 9/20 + 4/8

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 9/20 by 2, and multiply the numerator and denominator of 4/8 by 5 so both fractions share the common base 40.

9 × 2/20 × 2 = 18/40 and 4 × 5/8 × 5 = 20/40

Step 3

Add the Numerators

Now add the numerators (18 + 20 = 38) and keep the common denominator 40 unchanged.

18 + 20/40 = 38/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 40, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/40 ÷ 2 = 19/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 20 yields an exact terminating decimal of 0.95 (or 95%).

19 ÷ 20 = 0.95 (95%)

Visual Representation

The diagram below illustrates 9/20 plus 4/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/20`
Mixed Number Form	`19/20`
Decimal Form	`0.95`
Percentage	`95%`

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Frequently Asked Questions

What is 9/20 plus 4/8 as a fraction?

9/20 + 4/8 in simplest fraction form is 19/20.

What is 9/20 plus 4/8 as a decimal?

9/20 + 4/8 converted to a decimal is 0.95.

What is 9/20 plus 4/8 as a percentage?

9/20 + 4/8 expressed as a percentage is 95%.

Does 9/20 plus 4/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.95) because the denominator in simplest terms contains only prime factors 2 and/or 5.