What is 2/8 plus 9/20? (Answer: 7/10)

Exact Answer

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Problem: What is 2/8 plus 9/20?
Formula / Expression: 2/8 + 9/20
Final Answer: 7/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 20 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 8 × 20 = 160, keeping the calculation simpler).
Working: LCD(8, 20) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 2/8 by 5, and multiply the numerator and denominator of 9/20 by 2 so both fractions share the common base 40.
Working: 2 × 5/8 × 5 = 10/40 and 9 × 2/20 × 2 = 18/40

Step 3: Add the Numerators
Now add the numerators (10 + 18 = 28) and keep the common denominator 40 unchanged.
Working: 10 + 18/40 = 28/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 40, which is 4. Divide both the numerator and denominator by 4.
Working: 28 ÷ 4/40 ÷ 4 = 7/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).
Working: 7 ÷ 10 = 0.7 (70%)

Key Values:
- Simplified Fraction: 7/10
- Mixed Number Form: 7/10
- Decimal Value: 0.7
- Percentage: 70%

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Solved with FractionsCalc:
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2/8 + 9/20 = 7/10

Simplified Fraction

7/10

Mixed Number

Proper (7/10)

Decimal Value

0.7

Percentage

70%

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Step-by-Step Solution: 2/8 + 9/20

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 20 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 8 × 20 = 160, keeping the calculation simpler).

LCD(8, 20) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 2/8 by 5, and multiply the numerator and denominator of 9/20 by 2 so both fractions share the common base 40.

2 × 5/8 × 5 = 10/40 and 9 × 2/20 × 2 = 18/40

Step 3

Add the Numerators

Now add the numerators (10 + 18 = 28) and keep the common denominator 40 unchanged.

10 + 18/40 = 28/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 40, which is 4. Divide both the numerator and denominator by 4.

28 ÷ 4/40 ÷ 4 = 7/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).

7 ÷ 10 = 0.7 (70%)

Visual Representation

The diagram below illustrates 2/8 plus 9/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/10`
Mixed Number Form	`7/10`
Decimal Form	`0.7`
Percentage	`70%`

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Frequently Asked Questions

What is 2/8 plus 9/20 as a fraction?

2/8 + 9/20 in simplest fraction form is 7/10.

What is 2/8 plus 9/20 as a decimal?

2/8 + 9/20 converted to a decimal is 0.7.

What is 2/8 plus 9/20 as a percentage?

2/8 + 9/20 expressed as a percentage is 70%.

Does 2/8 plus 9/20 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.7) because the denominator in simplest terms contains only prime factors 2 and/or 5.