What is 3/5 plus 7/8? (Answer: 59/40)

Exact Answer

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Problem: What is 3/5 plus 7/8?
Formula / Expression: 3/5 + 7/8
Final Answer: 1 19/40 (59/40)
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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 7/8 by 5 so both fractions share the common base 40.
Working: 3 × 8/5 × 8 = 24/40 and 7 × 5/8 × 5 = 35/40

Step 3: Add the Numerators
Now add the numerators (24 + 35 = 59) and keep the common denominator 40 unchanged.
Working: 24 + 35/40 = 59/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 40 is 1, confirming that 59/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (40), divide 59 by 40: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/40.
Working: 59/40 = 1 19/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 40 yields an exact terminating decimal of 1.475 (or 147.5%).
Working: 59 ÷ 40 = 1.475 (147.5%)

Key Values:
- Simplified Fraction: 59/40
- Mixed Number Form: 1 19/40
- Decimal Value: 1.475
- Percentage: 147.5%

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3/5 + 7/8 = 59/40

Simplified Fraction

59/40

Mixed Number

1 19/40

Decimal Value

1.475

Percentage

147.5%

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Step-by-Step Solution: 3/5 + 7/8

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 7/8 by 5 so both fractions share the common base 40.

3 × 8/5 × 8 = 24/40 and 7 × 5/8 × 5 = 35/40

Step 3

Add the Numerators

Now add the numerators (24 + 35 = 59) and keep the common denominator 40 unchanged.

24 + 35/40 = 59/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 40 is 1, confirming that 59/40 cannot be reduced further—it is already in its simplest irreducible form.

59/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (59) is greater than the denominator (40), divide 59 by 40: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/40.

59/40 = 119/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 40 yields an exact terminating decimal of 1.475 (or 147.5%).

59 ÷ 40 = 1.475 (147.5%)

Visual Representation

The diagram below illustrates 3/5 plus 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/40`
Mixed Number Form	`1 19/40`
Decimal Form	`1.475`
Percentage	`147.5%`

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Frequently Asked Questions

What is 3/5 plus 7/8 as a fraction?

3/5 + 7/8 in simplest fraction form is 59/40 (or 1 19/40 as a mixed number).

What is 3/5 plus 7/8 as a decimal?

3/5 + 7/8 converted to a decimal is 1.475.

What is 3/5 plus 7/8 as a percentage?

3/5 + 7/8 expressed as a percentage is 147.5%.

How do you write 3/5 plus 7/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 59/40 can be written as the mixed number 1 19/40.

Does 3/5 plus 7/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.475) because the denominator in simplest terms contains only prime factors 2 and/or 5.