What is 7/20 plus 2/5? (Answer: 3/4)

Exact Answer

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Problem: What is 7/20 plus 2/5?
Formula / Expression: 7/20 + 2/5
Final Answer: 3/4
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 20 is an exact multiple of 5 (5 × 4 = 20). The Least Common Denominator (LCD) is simply 20, meaning we only need to scale one fraction.
Working: LCD(20, 5) = 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 2/5 by 4 so both fractions share the common base 20.
Working: 7 × 1/20 × 1 = 7/20 and 2 × 4/5 × 4 = 8/20

Step 3: Add the Numerators
Now add the numerators (7 + 8 = 15) and keep the common denominator 20 unchanged.
Working: 7 + 8/20 = 15/20

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 15 and 20, which is 5. Divide both the numerator and denominator by 5.
Working: 15 ÷ 5/20 ÷ 5 = 3/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).
Working: 3 ÷ 4 = 0.75 (75%)

Key Values:
- Simplified Fraction: 3/4
- Mixed Number Form: 3/4
- Decimal Value: 0.75
- Percentage: 75%

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Solved with FractionsCalc:
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7/20 + 2/5 = 3/4

Simplified Fraction

3/4

Mixed Number

Proper (3/4)

Decimal Value

0.75

Percentage

75%

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Step-by-Step Solution: 7/20 + 2/5

Step 1

Find the Least Common Denominator (LCD)

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

LCD(20, 5) = 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 2/5 by 4 so both fractions share the common base 20.

7 × 1/20 × 1 = 7/20 and 2 × 4/5 × 4 = 8/20

Step 3

Add the Numerators

Now add the numerators (7 + 8 = 15) and keep the common denominator 20 unchanged.

7 + 8/20 = 15/20

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 15 and 20, which is 5. Divide both the numerator and denominator by 5.

15 ÷ 5/20 ÷ 5 = 3/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).

3 ÷ 4 = 0.75 (75%)

Visual Representation

The diagram below illustrates 7/20 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/4`
Mixed Number Form	`3/4`
Decimal Form	`0.75`
Percentage	`75%`

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Frequently Asked Questions

What is 7/20 plus 2/5 as a fraction?

7/20 + 2/5 in simplest fraction form is 3/4.

What is 7/20 plus 2/5 as a decimal?

7/20 + 2/5 converted to a decimal is 0.75.

What is 7/20 plus 2/5 as a percentage?

7/20 + 2/5 expressed as a percentage is 75%.

Does 7/20 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.