What is 9/20 plus 3/4? (Answer: 6/5)

Exact Answer

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Problem: What is 9/20 plus 3/4?
Formula / Expression: 9/20 + 3/4
Final Answer: 1 1/5 (6/5)
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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 9/20 by 1, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.
Working: 9 × 1/20 × 1 = 9/20 and 3 × 5/4 × 5 = 15/20

Step 3: Add the Numerators
Now add the numerators (9 + 15 = 24) and keep the common denominator 20 unchanged.
Working: 9 + 15/20 = 24/20

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 20, which is 4. Divide both the numerator and denominator by 4.
Working: 24 ÷ 4/20 ÷ 4 = 6/5

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (6) is greater than the denominator (5), divide 6 by 5: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/5.
Working: 6/5 = 1 1/5

Step 6: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 5 yields an exact terminating decimal of 1.2 (or 120%).
Working: 6 ÷ 5 = 1.2 (120%)

Key Values:
- Simplified Fraction: 6/5
- Mixed Number Form: 1 1/5
- Decimal Value: 1.2
- Percentage: 120%

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9/20 + 3/4 = 6/5

Simplified Fraction

6/5

Mixed Number

1 1/5

Decimal Value

1.2

Percentage

120%

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Step-by-Step Solution: 9/20 + 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 9/20 by 1, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.

9 × 1/20 × 1 = 9/20 and 3 × 5/4 × 5 = 15/20

Step 3

Add the Numerators

Now add the numerators (9 + 15 = 24) and keep the common denominator 20 unchanged.

9 + 15/20 = 24/20

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 20, which is 4. Divide both the numerator and denominator by 4.

24 ÷ 4/20 ÷ 4 = 6/5

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (6) is greater than the denominator (5), divide 6 by 5: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/5.

6/5 = 11/5

Step 6

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 5 yields an exact terminating decimal of 1.2 (or 120%).

6 ÷ 5 = 1.2 (120%)

Visual Representation

The diagram below illustrates 9/20 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/5`
Mixed Number Form	`1 1/5`
Decimal Form	`1.2`
Percentage	`120%`

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Frequently Asked Questions

What is 9/20 plus 3/4 as a fraction?

9/20 + 3/4 in simplest fraction form is 6/5 (or 1 1/5 as a mixed number).

What is 9/20 plus 3/4 as a decimal?

9/20 + 3/4 converted to a decimal is 1.2.

What is 9/20 plus 3/4 as a percentage?

9/20 + 3/4 expressed as a percentage is 120%.

How do you write 9/20 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 6/5 can be written as the mixed number 1 1/5.

Does 9/20 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.2) because the denominator in simplest terms contains only prime factors 2 and/or 5.