What is 5/8 plus 4/5? (Answer: 57/40)

Exact Answer

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Problem: What is 5/8 plus 4/5?
Formula / Expression: 5/8 + 4/5
Final Answer: 1 17/40 (57/40)
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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 5/8 by 5, and multiply the numerator and denominator of 4/5 by 8 so both fractions share the common base 40.
Working: 5 × 5/8 × 5 = 25/40 and 4 × 8/5 × 8 = 32/40

Step 3: Add the Numerators
Now add the numerators (25 + 32 = 57) and keep the common denominator 40 unchanged.
Working: 25 + 32/40 = 57/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 57 and 40 is 1, confirming that 57/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 57/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (57) is greater than the denominator (40), divide 57 by 40: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/40.
Working: 57/40 = 1 17/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 57 by denominator 40 yields an exact terminating decimal of 1.425 (or 142.5%).
Working: 57 ÷ 40 = 1.425 (142.5%)

Key Values:
- Simplified Fraction: 57/40
- Mixed Number Form: 1 17/40
- Decimal Value: 1.425
- Percentage: 142.5%

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Solved with FractionsCalc:
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5/8 + 4/5 = 57/40

Simplified Fraction

57/40

Mixed Number

1 17/40

Decimal Value

1.425

Percentage

142.5%

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Step-by-Step Solution: 5/8 + 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 5/8 by 5, and multiply the numerator and denominator of 4/5 by 8 so both fractions share the common base 40.

5 × 5/8 × 5 = 25/40 and 4 × 8/5 × 8 = 32/40

Step 3

Add the Numerators

Now add the numerators (25 + 32 = 57) and keep the common denominator 40 unchanged.

25 + 32/40 = 57/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 57 and 40 is 1, confirming that 57/40 cannot be reduced further—it is already in its simplest irreducible form.

57/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (57) is greater than the denominator (40), divide 57 by 40: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/40.

57/40 = 117/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 57 by denominator 40 yields an exact terminating decimal of 1.425 (or 142.5%).

57 ÷ 40 = 1.425 (142.5%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`57/40`
Mixed Number Form	`1 17/40`
Decimal Form	`1.425`
Percentage	`142.5%`

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Frequently Asked Questions

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

5/8 + 4/5 in simplest fraction form is 57/40 (or 1 17/40 as a mixed number).

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

5/8 + 4/5 converted to a decimal is 1.425.

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

5/8 + 4/5 expressed as a percentage is 142.5%.

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

Because the numerator is greater than the denominator, the improper fraction 57/40 can be written as the mixed number 1 17/40.

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

It results in an exact terminating decimal (1.425) because the denominator in simplest terms contains only prime factors 2 and/or 5.