What is 3/7 plus 7/8? (Answer: 73/56)

Exact Answer

==================================================
Problem: What is 3/7 plus 7/8?
Formula / Expression: 3/7 + 7/8
Final Answer: 1 17/56 (73/56)
==================================================

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 3/7 by 8, and multiply the numerator and denominator of 7/8 by 7 so both fractions share the common base 56.
Working: 3 × 8/7 × 8 = 24/56 and 7 × 7/8 × 7 = 49/56

Step 3: Add the Numerators
Now add the numerators (24 + 49 = 73) and keep the common denominator 56 unchanged.
Working: 24 + 49/56 = 73/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 56 is 1, confirming that 73/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (73) is greater than the denominator (56), divide 73 by 56: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/56.
Working: 73/56 = 1 17/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 56 produces a repeating decimal (approximately 1.303571, or 130.3571%).
Working: 73 ÷ 56 = 1.303571 (130.3571%)

Key Values:
- Simplified Fraction: 73/56
- Mixed Number Form: 1 17/56
- Decimal Value: 1.303571
- Percentage: 130.3571%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-7-8/
==================================================

3/7 + 7/8 = 73/56

Simplified Fraction

73/56

Mixed Number

1 17/56

Decimal Value

1.303571

Percentage

130.3571%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

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

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

3 × 8/7 × 8 = 24/56 and 7 × 7/8 × 7 = 49/56

Step 3

Add the Numerators

Now add the numerators (24 + 49 = 73) and keep the common denominator 56 unchanged.

24 + 49/56 = 73/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 56 is 1, confirming that 73/56 cannot be reduced further—it is already in its simplest irreducible form.

73/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (73) is greater than the denominator (56), divide 73 by 56: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/56.

73/56 = 117/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 56 produces a repeating decimal (approximately 1.303571, or 130.3571%).

73 ÷ 56 = 1.303571 (130.3571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/56`
Mixed Number Form	`1 17/56`
Decimal Form	`1.303571`
Percentage	`130.3571%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

3/7 + 7/8 in simplest fraction form is 73/56 (or 1 17/56 as a mixed number).

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

3/7 + 7/8 converted to a decimal is 1.303571.

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

3/7 + 7/8 expressed as a percentage is 130.3571%.

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

Because the numerator is greater than the denominator, the improper fraction 73/56 can be written as the mixed number 1 17/56.

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

It results in a repeating decimal (approximately 1.303571...) because the denominator contains prime factors other than 2 and 5.