What is 3/5 plus 5/8? (Answer: 49/40)

Exact Answer

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Problem: What is 3/5 plus 5/8?
Formula / Expression: 3/5 + 5/8
Final Answer: 1 9/40 (49/40)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 3/5 by 8, and multiply the numerator and denominator of 5/8 by 5 so both fractions share the common base 40.
Working: 3 × 8/5 × 8 = 24/40 and 5 × 5/8 × 5 = 25/40

Step 3: Add the Numerators
Now add the numerators (24 + 25 = 49) and keep the common denominator 40 unchanged.
Working: 24 + 25/40 = 49/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 40 is 1, confirming that 49/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (49) is greater than the denominator (40), divide 49 by 40: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/40.
Working: 49/40 = 1 9/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 40 yields an exact terminating decimal of 1.225 (or 122.5%).
Working: 49 ÷ 40 = 1.225 (122.5%)

Key Values:
- Simplified Fraction: 49/40
- Mixed Number Form: 1 9/40
- Decimal Value: 1.225
- Percentage: 122.5%

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3/5 + 5/8 = 49/40

Simplified Fraction

49/40

Mixed Number

1 9/40

Decimal Value

1.225

Percentage

122.5%

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Step-by-Step Solution: 3/5 + 5/8

Step 1

Find the Least Common Denominator (LCD)

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

LCD(5, 8) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 3/5 by 8, and multiply the numerator and denominator of 5/8 by 5 so both fractions share the common base 40.

3 × 8/5 × 8 = 24/40 and 5 × 5/8 × 5 = 25/40

Step 3

Add the Numerators

Now add the numerators (24 + 25 = 49) and keep the common denominator 40 unchanged.

24 + 25/40 = 49/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 40 is 1, confirming that 49/40 cannot be reduced further—it is already in its simplest irreducible form.

49/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (49) is greater than the denominator (40), divide 49 by 40: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/40.

49/40 = 19/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 40 yields an exact terminating decimal of 1.225 (or 122.5%).

49 ÷ 40 = 1.225 (122.5%)

Visual Representation

The diagram below illustrates 3/5 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/40`
Mixed Number Form	`1 9/40`
Decimal Form	`1.225`
Percentage	`122.5%`

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Frequently Asked Questions

What is 3/5 plus 5/8 as a fraction?

3/5 + 5/8 in simplest fraction form is 49/40 (or 1 9/40 as a mixed number).

What is 3/5 plus 5/8 as a decimal?

3/5 + 5/8 converted to a decimal is 1.225.

What is 3/5 plus 5/8 as a percentage?

3/5 + 5/8 expressed as a percentage is 122.5%.

How do you write 3/5 plus 5/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 49/40 can be written as the mixed number 1 9/40.

Does 3/5 plus 5/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.225) because the denominator in simplest terms contains only prime factors 2 and/or 5.