What is 1/5 plus 3/4? (Answer: 19/20)

Exact Answer

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Problem: What is 1/5 plus 3/4?
Formula / Expression: 1/5 + 3/4
Final Answer: 19/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 4 = 20.
Working: LCD(5, 4) = 20

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

Step 3: Add the Numerators
Now add the numerators (4 + 15 = 19) and keep the common denominator 20 unchanged.
Working: 4 + 15/20 = 19/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 20 is 1, confirming that 19/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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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1/5 + 3/4 = 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: 1/5 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 4 = 20.

LCD(5, 4) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

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

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

Step 3

Add the Numerators

Now add the numerators (4 + 15 = 19) and keep the common denominator 20 unchanged.

4 + 15/20 = 19/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 20 is 1, confirming that 19/20 cannot be reduced further—it is already in its simplest irreducible form.

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 1/5 plus 3/4 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 1/5 plus 3/4 as a fraction?

1/5 + 3/4 in simplest fraction form is 19/20.

What is 1/5 plus 3/4 as a decimal?

1/5 + 3/4 converted to a decimal is 0.95.

What is 1/5 plus 3/4 as a percentage?

1/5 + 3/4 expressed as a percentage is 95%.

Does 1/5 plus 3/4 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.