What is 7/13 plus 4/7? (Answer: 101/91)

Exact Answer

==================================================
Problem: What is 7/13 plus 4/7?
Formula / Expression: 7/13 + 4/7
Final Answer: 1 10/91 (101/91)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.
Working: LCD(13, 7) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 7/13 by 7, and multiply the numerator and denominator of 4/7 by 13 so both fractions share the common base 91.
Working: 7 × 7/13 × 7 = 49/91 and 4 × 13/7 × 13 = 52/91

Step 3: Add the Numerators
Now add the numerators (49 + 52 = 101) and keep the common denominator 91 unchanged.
Working: 49 + 52/91 = 101/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 91 is 1, confirming that 101/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (101) is greater than the denominator (91), divide 101 by 91: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/91.
Working: 101/91 = 1 10/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 91 produces a repeating decimal (approximately 1.10989, or 110.989%).
Working: 101 ÷ 91 = 1.10989 (110.989%)

Key Values:
- Simplified Fraction: 101/91
- Mixed Number Form: 1 10/91
- Decimal Value: 1.10989
- Percentage: 110.989%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-13-plus-4-7/
==================================================

7/13 + 4/7 = 101/91

Simplified Fraction

101/91

Mixed Number

1 10/91

Decimal Value

1.10989

Percentage

110.989%

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: 7/13 + 4/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.

LCD(13, 7) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 7/13 by 7, and multiply the numerator and denominator of 4/7 by 13 so both fractions share the common base 91.

7 × 7/13 × 7 = 49/91 and 4 × 13/7 × 13 = 52/91

Step 3

Add the Numerators

Now add the numerators (49 + 52 = 101) and keep the common denominator 91 unchanged.

49 + 52/91 = 101/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 91 is 1, confirming that 101/91 cannot be reduced further—it is already in its simplest irreducible form.

101/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (101) is greater than the denominator (91), divide 101 by 91: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/91.

101/91 = 110/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 91 produces a repeating decimal (approximately 1.10989, or 110.989%).

101 ÷ 91 = 1.10989 (110.989%)

Visual Representation

The diagram below illustrates 7/13 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/91`
Mixed Number Form	`1 10/91`
Decimal Form	`1.10989`
Percentage	`110.989%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/13 plus 4/7 as a fraction?

7/13 + 4/7 in simplest fraction form is 101/91 (or 1 10/91 as a mixed number).

What is 7/13 plus 4/7 as a decimal?

7/13 + 4/7 converted to a decimal is 1.10989.

What is 7/13 plus 4/7 as a percentage?

7/13 + 4/7 expressed as a percentage is 110.989%.

How do you write 7/13 plus 4/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 101/91 can be written as the mixed number 1 10/91.

Does 7/13 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.10989...) because the denominator contains prime factors other than 2 and 5.