What is 2/5 plus 7/8? (Answer: 51/40)

Exact Answer

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Problem: What is 2/5 plus 7/8?
Formula / Expression: 2/5 + 7/8
Final Answer: 1 11/40 (51/40)
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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 2/5 by 8, and multiply the numerator and denominator of 7/8 by 5 so both fractions share the common base 40.
Working: 2 × 8/5 × 8 = 16/40 and 7 × 5/8 × 5 = 35/40

Step 3: Add the Numerators
Now add the numerators (16 + 35 = 51) and keep the common denominator 40 unchanged.
Working: 16 + 35/40 = 51/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 51 and 40 is 1, confirming that 51/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 51/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (51) is greater than the denominator (40), divide 51 by 40: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/40.
Working: 51/40 = 1 11/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 40 yields an exact terminating decimal of 1.275 (or 127.5%).
Working: 51 ÷ 40 = 1.275 (127.5%)

Key Values:
- Simplified Fraction: 51/40
- Mixed Number Form: 1 11/40
- Decimal Value: 1.275
- Percentage: 127.5%

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Solved with FractionsCalc:
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2/5 + 7/8 = 51/40

Simplified Fraction

51/40

Mixed Number

1 11/40

Decimal Value

1.275

Percentage

127.5%

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Step-by-Step Solution: 2/5 + 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 2/5 by 8, and multiply the numerator and denominator of 7/8 by 5 so both fractions share the common base 40.

2 × 8/5 × 8 = 16/40 and 7 × 5/8 × 5 = 35/40

Step 3

Add the Numerators

Now add the numerators (16 + 35 = 51) and keep the common denominator 40 unchanged.

16 + 35/40 = 51/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 51 and 40 is 1, confirming that 51/40 cannot be reduced further—it is already in its simplest irreducible form.

51/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (51) is greater than the denominator (40), divide 51 by 40: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/40.

51/40 = 111/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 40 yields an exact terminating decimal of 1.275 (or 127.5%).

51 ÷ 40 = 1.275 (127.5%)

Visual Representation

The diagram below illustrates 2/5 plus 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/40`
Mixed Number Form	`1 11/40`
Decimal Form	`1.275`
Percentage	`127.5%`

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Frequently Asked Questions

What is 2/5 plus 7/8 as a fraction?

2/5 + 7/8 in simplest fraction form is 51/40 (or 1 11/40 as a mixed number).

What is 2/5 plus 7/8 as a decimal?

2/5 + 7/8 converted to a decimal is 1.275.

What is 2/5 plus 7/8 as a percentage?

2/5 + 7/8 expressed as a percentage is 127.5%.

How do you write 2/5 plus 7/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 51/40 can be written as the mixed number 1 11/40.

Does 2/5 plus 7/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.275) because the denominator in simplest terms contains only prime factors 2 and/or 5.