What is 3/20 plus 3/4? (Answer: 9/10)

Exact Answer

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Problem: What is 3/20 plus 3/4?
Formula / Expression: 3/20 + 3/4
Final Answer: 9/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 20 is an exact multiple of 4 (4 × 5 = 20). The Least Common Denominator (LCD) is simply 20, meaning we only need to scale one fraction.
Working: LCD(20, 4) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 3/20 by 1, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.
Working: 3 × 1/20 × 1 = 3/20 and 3 × 5/4 × 5 = 15/20

Step 3: Add the Numerators
Now add the numerators (3 + 15 = 18) and keep the common denominator 20 unchanged.
Working: 3 + 15/20 = 18/20

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 20, which is 2. Divide both the numerator and denominator by 2.
Working: 18 ÷ 2/20 ÷ 2 = 9/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 10 yields an exact terminating decimal of 0.9 (or 90%).
Working: 9 ÷ 10 = 0.9 (90%)

Key Values:
- Simplified Fraction: 9/10
- Mixed Number Form: 9/10
- Decimal Value: 0.9
- Percentage: 90%

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Solved with FractionsCalc:
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3/20 + 3/4 = 9/10

Simplified Fraction

9/10

Mixed Number

Proper (9/10)

Decimal Value

0.9

Percentage

90%

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Step-by-Step Solution: 3/20 + 3/4

Step 1

Find the Least Common Denominator (LCD)

Notice that 20 is an exact multiple of 4 (4 × 5 = 20). The Least Common Denominator (LCD) is simply 20, meaning we only need to scale one fraction.

LCD(20, 4) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 3/20 by 1, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.

3 × 1/20 × 1 = 3/20 and 3 × 5/4 × 5 = 15/20

Step 3

Add the Numerators

Now add the numerators (3 + 15 = 18) and keep the common denominator 20 unchanged.

3 + 15/20 = 18/20

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 20, which is 2. Divide both the numerator and denominator by 2.

18 ÷ 2/20 ÷ 2 = 9/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 10 yields an exact terminating decimal of 0.9 (or 90%).

9 ÷ 10 = 0.9 (90%)

Visual Representation

The diagram below illustrates 3/20 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/10`
Mixed Number Form	`9/10`
Decimal Form	`0.9`
Percentage	`90%`

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Frequently Asked Questions

What is 3/20 plus 3/4 as a fraction?

3/20 + 3/4 in simplest fraction form is 9/10.

What is 3/20 plus 3/4 as a decimal?

3/20 + 3/4 converted to a decimal is 0.9.

What is 3/20 plus 3/4 as a percentage?

3/20 + 3/4 expressed as a percentage is 90%.

Does 3/20 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.9) because the denominator in simplest terms contains only prime factors 2 and/or 5.