What is 15/32 plus 7/13? (Answer: 419/416)

Exact Answer

==================================================
Problem: What is 15/32 plus 7/13?
Formula / Expression: 15/32 + 7/13
Final Answer: 1 3/416 (419/416)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.
Working: LCD(32, 13) = 416

Step 2: Convert to Equivalent Fractions with Common Denominator 416
Multiply the numerator and denominator of 15/32 by 13, and multiply the numerator and denominator of 7/13 by 32 so both fractions share the common base 416.
Working: 15 × 13/32 × 13 = 195/416 and 7 × 32/13 × 32 = 224/416

Step 3: Add the Numerators
Now add the numerators (195 + 224 = 419) and keep the common denominator 416 unchanged.
Working: 195 + 224/416 = 419/416

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 419 and 416 is 1, confirming that 419/416 cannot be reduced further—it is already in its simplest irreducible form.
Working: 419/416

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (419) is greater than the denominator (416), divide 419 by 416: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/416.
Working: 419/416 = 1 3/416

Step 6: Decimal & Percentage Representation
Dividing the numerator 419 by denominator 416 produces a repeating decimal (approximately 1.007212, or 100.7212%).
Working: 419 ÷ 416 = 1.007212 (100.7212%)

Key Values:
- Simplified Fraction: 419/416
- Mixed Number Form: 1 3/416
- Decimal Value: 1.007212
- Percentage: 100.7212%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-32-plus-7-13/
==================================================

15/32 + 7/13 = 419/416

Simplified Fraction

419/416

Mixed Number

1 3/416

Decimal Value

1.007212

Percentage

100.7212%

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: 15/32 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.

LCD(32, 13) = 416

Step 2

Convert to Equivalent Fractions with Common Denominator 416

Multiply the numerator and denominator of 15/32 by 13, and multiply the numerator and denominator of 7/13 by 32 so both fractions share the common base 416.

15 × 13/32 × 13 = 195/416 and 7 × 32/13 × 32 = 224/416

Step 3

Add the Numerators

Now add the numerators (195 + 224 = 419) and keep the common denominator 416 unchanged.

195 + 224/416 = 419/416

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 419 and 416 is 1, confirming that 419/416 cannot be reduced further—it is already in its simplest irreducible form.

419/416

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (419) is greater than the denominator (416), divide 419 by 416: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/416.

419/416 = 13/416

Step 6

Decimal & Percentage Representation

Dividing the numerator 419 by denominator 416 produces a repeating decimal (approximately 1.007212, or 100.7212%).

419 ÷ 416 = 1.007212 (100.7212%)

Visual Representation

The diagram below illustrates 15/32 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`419/416`
Mixed Number Form	`1 3/416`
Decimal Form	`1.007212`
Percentage	`100.7212%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 15/32 plus 7/13 as a fraction?

15/32 + 7/13 in simplest fraction form is 419/416 (or 1 3/416 as a mixed number).

What is 15/32 plus 7/13 as a decimal?

15/32 + 7/13 converted to a decimal is 1.007212.

What is 15/32 plus 7/13 as a percentage?

15/32 + 7/13 expressed as a percentage is 100.7212%.

How do you write 15/32 plus 7/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 419/416 can be written as the mixed number 1 3/416.

Does 15/32 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.007212...) because the denominator contains prime factors other than 2 and 5.