What is 4/5 plus 7/8? (Answer: 67/40)

Exact Answer

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Problem: What is 4/5 plus 7/8?
Formula / Expression: 4/5 + 7/8
Final Answer: 1 27/40 (67/40)
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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 4/5 by 8, and multiply the numerator and denominator of 7/8 by 5 so both fractions share the common base 40.
Working: 4 × 8/5 × 8 = 32/40 and 7 × 5/8 × 5 = 35/40

Step 3: Add the Numerators
Now add the numerators (32 + 35 = 67) and keep the common denominator 40 unchanged.
Working: 32 + 35/40 = 67/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 40 is 1, confirming that 67/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (67) is greater than the denominator (40), divide 67 by 40: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/40.
Working: 67/40 = 1 27/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 40 yields an exact terminating decimal of 1.675 (or 167.5%).
Working: 67 ÷ 40 = 1.675 (167.5%)

Key Values:
- Simplified Fraction: 67/40
- Mixed Number Form: 1 27/40
- Decimal Value: 1.675
- Percentage: 167.5%

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Solved with FractionsCalc:
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4/5 + 7/8 = 67/40

Simplified Fraction

67/40

Mixed Number

1 27/40

Decimal Value

1.675

Percentage

167.5%

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Step-by-Step Solution: 4/5 + 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 4/5 by 8, and multiply the numerator and denominator of 7/8 by 5 so both fractions share the common base 40.

4 × 8/5 × 8 = 32/40 and 7 × 5/8 × 5 = 35/40

Step 3

Add the Numerators

Now add the numerators (32 + 35 = 67) and keep the common denominator 40 unchanged.

32 + 35/40 = 67/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 40 is 1, confirming that 67/40 cannot be reduced further—it is already in its simplest irreducible form.

67/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (67) is greater than the denominator (40), divide 67 by 40: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/40.

67/40 = 127/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 40 yields an exact terminating decimal of 1.675 (or 167.5%).

67 ÷ 40 = 1.675 (167.5%)

Visual Representation

The diagram below illustrates 4/5 plus 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/40`
Mixed Number Form	`1 27/40`
Decimal Form	`1.675`
Percentage	`167.5%`

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Frequently Asked Questions

What is 4/5 plus 7/8 as a fraction?

4/5 + 7/8 in simplest fraction form is 67/40 (or 1 27/40 as a mixed number).

What is 4/5 plus 7/8 as a decimal?

4/5 + 7/8 converted to a decimal is 1.675.

What is 4/5 plus 7/8 as a percentage?

4/5 + 7/8 expressed as a percentage is 167.5%.

How do you write 4/5 plus 7/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 67/40 can be written as the mixed number 1 27/40.

Does 4/5 plus 7/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.675) because the denominator in simplest terms contains only prime factors 2 and/or 5.