What is 7/20 plus 3/4? (Answer: 11/10)

Exact Answer

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Problem: What is 7/20 plus 3/4?
Formula / Expression: 7/20 + 3/4
Final Answer: 1 1/10 (11/10)
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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 7/20 by 1, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.
Working: 7 × 1/20 × 1 = 7/20 and 3 × 5/4 × 5 = 15/20

Step 3: Add the Numerators
Now add the numerators (7 + 15 = 22) and keep the common denominator 20 unchanged.
Working: 7 + 15/20 = 22/20

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 20, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/20 ÷ 2 = 11/10

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (11) is greater than the denominator (10), divide 11 by 10: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/10.
Working: 11/10 = 1 1/10

Step 6: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 10 yields an exact terminating decimal of 1.1 (or 110%).
Working: 11 ÷ 10 = 1.1 (110%)

Key Values:
- Simplified Fraction: 11/10
- Mixed Number Form: 1 1/10
- Decimal Value: 1.1
- Percentage: 110%

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7/20 + 3/4 = 11/10

Simplified Fraction

11/10

Mixed Number

1 1/10

Decimal Value

1.1

Percentage

110%

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Step-by-Step Solution: 7/20 + 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 7/20 by 1, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.

7 × 1/20 × 1 = 7/20 and 3 × 5/4 × 5 = 15/20

Step 3

Add the Numerators

Now add the numerators (7 + 15 = 22) and keep the common denominator 20 unchanged.

7 + 15/20 = 22/20

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 20, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/20 ÷ 2 = 11/10

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (11) is greater than the denominator (10), divide 11 by 10: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/10.

11/10 = 11/10

Step 6

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 10 yields an exact terminating decimal of 1.1 (or 110%).

11 ÷ 10 = 1.1 (110%)

Visual Representation

The diagram below illustrates 7/20 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/10`
Mixed Number Form	`1 1/10`
Decimal Form	`1.1`
Percentage	`110%`

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Frequently Asked Questions

What is 7/20 plus 3/4 as a fraction?

7/20 + 3/4 in simplest fraction form is 11/10 (or 1 1/10 as a mixed number).

What is 7/20 plus 3/4 as a decimal?

7/20 + 3/4 converted to a decimal is 1.1.

What is 7/20 plus 3/4 as a percentage?

7/20 + 3/4 expressed as a percentage is 110%.

How do you write 7/20 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 11/10 can be written as the mixed number 1 1/10.

Does 7/20 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.1) because the denominator in simplest terms contains only prime factors 2 and/or 5.