What is 3/8 plus 9/20? (Answer: 33/40)

Exact Answer

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Problem: What is 3/8 plus 9/20?
Formula / Expression: 3/8 + 9/20
Final Answer: 33/40
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 3/8 by 5, and multiply the numerator and denominator of 9/20 by 2 so both fractions share the common base 40.
Working: 3 × 5/8 × 5 = 15/40 and 9 × 2/20 × 2 = 18/40

Step 3: Add the Numerators
Now add the numerators (15 + 18 = 33) and keep the common denominator 40 unchanged.
Working: 15 + 18/40 = 33/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 33 and 40 is 1, confirming that 33/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 33/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 40 yields an exact terminating decimal of 0.825 (or 82.5%).
Working: 33 ÷ 40 = 0.825 (82.5%)

Key Values:
- Simplified Fraction: 33/40
- Mixed Number Form: 33/40
- Decimal Value: 0.825
- Percentage: 82.5%

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Solved with FractionsCalc:
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3/8 + 9/20 = 33/40

Simplified Fraction

33/40

Mixed Number

Proper (33/40)

Decimal Value

0.825

Percentage

82.5%

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Step-by-Step Solution: 3/8 + 9/20

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 20) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 3/8 by 5, and multiply the numerator and denominator of 9/20 by 2 so both fractions share the common base 40.

3 × 5/8 × 5 = 15/40 and 9 × 2/20 × 2 = 18/40

Step 3

Add the Numerators

Now add the numerators (15 + 18 = 33) and keep the common denominator 40 unchanged.

15 + 18/40 = 33/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 33 and 40 is 1, confirming that 33/40 cannot be reduced further—it is already in its simplest irreducible form.

33/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 40 yields an exact terminating decimal of 0.825 (or 82.5%).

33 ÷ 40 = 0.825 (82.5%)

Visual Representation

The diagram below illustrates 3/8 plus 9/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/40`
Mixed Number Form	`33/40`
Decimal Form	`0.825`
Percentage	`82.5%`

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Frequently Asked Questions

What is 3/8 plus 9/20 as a fraction?

3/8 + 9/20 in simplest fraction form is 33/40.

What is 3/8 plus 9/20 as a decimal?

3/8 + 9/20 converted to a decimal is 0.825.

What is 3/8 plus 9/20 as a percentage?

3/8 + 9/20 expressed as a percentage is 82.5%.

Does 3/8 plus 9/20 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.825) because the denominator in simplest terms contains only prime factors 2 and/or 5.