What is 3/8 plus 5/7? (Answer: 61/56)

Exact Answer

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Problem: What is 3/8 plus 5/7?
Formula / Expression: 3/8 + 5/7
Final Answer: 1 5/56 (61/56)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 56
Multiply the numerator and denominator of 3/8 by 7, and multiply the numerator and denominator of 5/7 by 8 so both fractions share the common base 56.
Working: 3 × 7/8 × 7 = 21/56 and 5 × 8/7 × 8 = 40/56

Step 3: Add the Numerators
Now add the numerators (21 + 40 = 61) and keep the common denominator 56 unchanged.
Working: 21 + 40/56 = 61/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 56 is 1, confirming that 61/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (61) is greater than the denominator (56), divide 61 by 56: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/56.
Working: 61/56 = 1 5/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 56 produces a repeating decimal (approximately 1.089286, or 108.9286%).
Working: 61 ÷ 56 = 1.089286 (108.9286%)

Key Values:
- Simplified Fraction: 61/56
- Mixed Number Form: 1 5/56
- Decimal Value: 1.089286
- Percentage: 108.9286%

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Solved with FractionsCalc:
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3/8 + 5/7 = 61/56

Simplified Fraction

61/56

Mixed Number

1 5/56

Decimal Value

1.089286

Percentage

108.9286%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 7) = 56

Step 2

Convert to Equivalent Fractions with Common Denominator 56

Multiply the numerator and denominator of 3/8 by 7, and multiply the numerator and denominator of 5/7 by 8 so both fractions share the common base 56.

3 × 7/8 × 7 = 21/56 and 5 × 8/7 × 8 = 40/56

Step 3

Add the Numerators

Now add the numerators (21 + 40 = 61) and keep the common denominator 56 unchanged.

21 + 40/56 = 61/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 56 is 1, confirming that 61/56 cannot be reduced further—it is already in its simplest irreducible form.

61/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (61) is greater than the denominator (56), divide 61 by 56: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/56.

61/56 = 15/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 56 produces a repeating decimal (approximately 1.089286, or 108.9286%).

61 ÷ 56 = 1.089286 (108.9286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/56`
Mixed Number Form	`1 5/56`
Decimal Form	`1.089286`
Percentage	`108.9286%`

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Frequently Asked Questions

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

3/8 + 5/7 in simplest fraction form is 61/56 (or 1 5/56 as a mixed number).

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

3/8 + 5/7 converted to a decimal is 1.089286.

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

3/8 + 5/7 expressed as a percentage is 108.9286%.

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

Because the numerator is greater than the denominator, the improper fraction 61/56 can be written as the mixed number 1 5/56.

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

It results in a repeating decimal (approximately 1.089286...) because the denominator contains prime factors other than 2 and 5.