What is 1/5 plus 7/8? (Answer: 43/40)

Exact Answer

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Problem: What is 1/5 plus 7/8?
Formula / Expression: 1/5 + 7/8
Final Answer: 1 3/40 (43/40)
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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 1/5 by 8, and multiply the numerator and denominator of 7/8 by 5 so both fractions share the common base 40.
Working: 1 × 8/5 × 8 = 8/40 and 7 × 5/8 × 5 = 35/40

Step 3: Add the Numerators
Now add the numerators (8 + 35 = 43) and keep the common denominator 40 unchanged.
Working: 8 + 35/40 = 43/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 40 is 1, confirming that 43/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (40), divide 43 by 40: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/40.
Working: 43/40 = 1 3/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 40 yields an exact terminating decimal of 1.075 (or 107.5%).
Working: 43 ÷ 40 = 1.075 (107.5%)

Key Values:
- Simplified Fraction: 43/40
- Mixed Number Form: 1 3/40
- Decimal Value: 1.075
- Percentage: 107.5%

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Solved with FractionsCalc:
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1/5 + 7/8 = 43/40

Simplified Fraction

43/40

Mixed Number

1 3/40

Decimal Value

1.075

Percentage

107.5%

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Step-by-Step Solution: 1/5 + 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 1/5 by 8, and multiply the numerator and denominator of 7/8 by 5 so both fractions share the common base 40.

1 × 8/5 × 8 = 8/40 and 7 × 5/8 × 5 = 35/40

Step 3

Add the Numerators

Now add the numerators (8 + 35 = 43) and keep the common denominator 40 unchanged.

8 + 35/40 = 43/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 40 is 1, confirming that 43/40 cannot be reduced further—it is already in its simplest irreducible form.

43/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (43) is greater than the denominator (40), divide 43 by 40: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/40.

43/40 = 13/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 40 yields an exact terminating decimal of 1.075 (or 107.5%).

43 ÷ 40 = 1.075 (107.5%)

Visual Representation

The diagram below illustrates 1/5 plus 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/40`
Mixed Number Form	`1 3/40`
Decimal Form	`1.075`
Percentage	`107.5%`

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Frequently Asked Questions

What is 1/5 plus 7/8 as a fraction?

1/5 + 7/8 in simplest fraction form is 43/40 (or 1 3/40 as a mixed number).

What is 1/5 plus 7/8 as a decimal?

1/5 + 7/8 converted to a decimal is 1.075.

What is 1/5 plus 7/8 as a percentage?

1/5 + 7/8 expressed as a percentage is 107.5%.

How do you write 1/5 plus 7/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 43/40 can be written as the mixed number 1 3/40.

Does 1/5 plus 7/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.075) because the denominator in simplest terms contains only prime factors 2 and/or 5.