What is 4/7 plus 5/8? (Answer: 67/56)

Exact Answer

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Problem: What is 4/7 plus 5/8?
Formula / Expression: 4/7 + 5/8
Final Answer: 1 11/56 (67/56)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 8 = 56.
Working: LCD(7, 8) = 56

Step 2: Convert to Equivalent Fractions with Common Denominator 56
Multiply the numerator and denominator of 4/7 by 8, and multiply the numerator and denominator of 5/8 by 7 so both fractions share the common base 56.
Working: 4 × 8/7 × 8 = 32/56 and 5 × 7/8 × 7 = 35/56

Step 3: Add the Numerators
Now add the numerators (32 + 35 = 67) and keep the common denominator 56 unchanged.
Working: 32 + 35/56 = 67/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 56 is 1, confirming that 67/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (67) is greater than the denominator (56), divide 67 by 56: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/56.
Working: 67/56 = 1 11/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 56 produces a repeating decimal (approximately 1.196429, or 119.6429%).
Working: 67 ÷ 56 = 1.196429 (119.6429%)

Key Values:
- Simplified Fraction: 67/56
- Mixed Number Form: 1 11/56
- Decimal Value: 1.196429
- Percentage: 119.6429%

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Solved with FractionsCalc:
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4/7 + 5/8 = 67/56

Simplified Fraction

67/56

Mixed Number

1 11/56

Decimal Value

1.196429

Percentage

119.6429%

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Step-by-Step Solution: 4/7 + 5/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 8 = 56.

LCD(7, 8) = 56

Step 2

Convert to Equivalent Fractions with Common Denominator 56

Multiply the numerator and denominator of 4/7 by 8, and multiply the numerator and denominator of 5/8 by 7 so both fractions share the common base 56.

4 × 8/7 × 8 = 32/56 and 5 × 7/8 × 7 = 35/56

Step 3

Add the Numerators

Now add the numerators (32 + 35 = 67) and keep the common denominator 56 unchanged.

32 + 35/56 = 67/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 56 is 1, confirming that 67/56 cannot be reduced further—it is already in its simplest irreducible form.

67/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (67) is greater than the denominator (56), divide 67 by 56: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/56.

67/56 = 111/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 56 produces a repeating decimal (approximately 1.196429, or 119.6429%).

67 ÷ 56 = 1.196429 (119.6429%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/56`
Mixed Number Form	`1 11/56`
Decimal Form	`1.196429`
Percentage	`119.6429%`

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Frequently Asked Questions

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

4/7 + 5/8 in simplest fraction form is 67/56 (or 1 11/56 as a mixed number).

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

4/7 + 5/8 converted to a decimal is 1.196429.

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

4/7 + 5/8 expressed as a percentage is 119.6429%.

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

Because the numerator is greater than the denominator, the improper fraction 67/56 can be written as the mixed number 1 11/56.

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

It results in a repeating decimal (approximately 1.196429...) because the denominator contains prime factors other than 2 and 5.