What is 2/8 plus 4/5? (Answer: 21/20)

Exact Answer

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Problem: What is 2/8 plus 4/5?
Formula / Expression: 2/8 + 4/5
Final Answer: 1 1/20 (21/20)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.
Working: LCD(8, 5) = 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 4/5 by 8 so both fractions share the common base 40.
Working: 2 × 5/8 × 5 = 10/40 and 4 × 8/5 × 8 = 32/40

Step 3: Add the Numerators
Now add the numerators (10 + 32 = 42) and keep the common denominator 40 unchanged.
Working: 10 + 32/40 = 42/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 40, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/40 ÷ 2 = 21/20

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (21) is greater than the denominator (20), divide 21 by 20: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/20.
Working: 21/20 = 1 1/20

Step 6: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 20 yields an exact terminating decimal of 1.05 (or 105%).
Working: 21 ÷ 20 = 1.05 (105%)

Key Values:
- Simplified Fraction: 21/20
- Mixed Number Form: 1 1/20
- Decimal Value: 1.05
- Percentage: 105%

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Solved with FractionsCalc:
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2/8 + 4/5 = 21/20

Simplified Fraction

21/20

Mixed Number

1 1/20

Decimal Value

1.05

Percentage

105%

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Step-by-Step Solution: 2/8 + 4/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.

LCD(8, 5) = 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 4/5 by 8 so both fractions share the common base 40.

2 × 5/8 × 5 = 10/40 and 4 × 8/5 × 8 = 32/40

Step 3

Add the Numerators

Now add the numerators (10 + 32 = 42) and keep the common denominator 40 unchanged.

10 + 32/40 = 42/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 40, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/40 ÷ 2 = 21/20

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (21) is greater than the denominator (20), divide 21 by 20: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/20.

21/20 = 11/20

Step 6

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 20 yields an exact terminating decimal of 1.05 (or 105%).

21 ÷ 20 = 1.05 (105%)

Visual Representation

The diagram below illustrates 2/8 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/20`
Mixed Number Form	`1 1/20`
Decimal Form	`1.05`
Percentage	`105%`

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Frequently Asked Questions

What is 2/8 plus 4/5 as a fraction?

2/8 + 4/5 in simplest fraction form is 21/20 (or 1 1/20 as a mixed number).

What is 2/8 plus 4/5 as a decimal?

2/8 + 4/5 converted to a decimal is 1.05.

What is 2/8 plus 4/5 as a percentage?

2/8 + 4/5 expressed as a percentage is 105%.

How do you write 2/8 plus 4/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 21/20 can be written as the mixed number 1 1/20.

Does 2/8 plus 4/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.05) because the denominator in simplest terms contains only prime factors 2 and/or 5.