What is 11/21 plus 17/32? (Answer: 709/672)

Exact Answer

==================================================
Problem: What is 11/21 plus 17/32?
Formula / Expression: 11/21 + 17/32
Final Answer: 1 37/672 (709/672)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 32 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 32 = 672.
Working: LCD(21, 32) = 672

Step 2: Convert to Equivalent Fractions with Common Denominator 672
Multiply the numerator and denominator of 11/21 by 32, and multiply the numerator and denominator of 17/32 by 21 so both fractions share the common base 672.
Working: 11 × 32/21 × 32 = 352/672 and 17 × 21/32 × 21 = 357/672

Step 3: Add the Numerators
Now add the numerators (352 + 357 = 709) and keep the common denominator 672 unchanged.
Working: 352 + 357/672 = 709/672

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 709 and 672 is 1, confirming that 709/672 cannot be reduced further—it is already in its simplest irreducible form.
Working: 709/672

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (709) is greater than the denominator (672), divide 709 by 672: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/672.
Working: 709/672 = 1 37/672

Step 6: Decimal & Percentage Representation
Dividing the numerator 709 by denominator 672 produces a repeating decimal (approximately 1.05506, or 105.506%).
Working: 709 ÷ 672 = 1.05506 (105.506%)

Key Values:
- Simplified Fraction: 709/672
- Mixed Number Form: 1 37/672
- Decimal Value: 1.05506
- Percentage: 105.506%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-21-plus-17-32/
==================================================

11/21 + 17/32 = 709/672

Simplified Fraction

709/672

Mixed Number

1 37/672

Decimal Value

1.05506

Percentage

105.506%

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: 11/21 + 17/32

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 32 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 32 = 672.

LCD(21, 32) = 672

Step 2

Convert to Equivalent Fractions with Common Denominator 672

Multiply the numerator and denominator of 11/21 by 32, and multiply the numerator and denominator of 17/32 by 21 so both fractions share the common base 672.

11 × 32/21 × 32 = 352/672 and 17 × 21/32 × 21 = 357/672

Step 3

Add the Numerators

Now add the numerators (352 + 357 = 709) and keep the common denominator 672 unchanged.

352 + 357/672 = 709/672

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 709 and 672 is 1, confirming that 709/672 cannot be reduced further—it is already in its simplest irreducible form.

709/672

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (709) is greater than the denominator (672), divide 709 by 672: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/672.

709/672 = 137/672

Step 6

Decimal & Percentage Representation

Dividing the numerator 709 by denominator 672 produces a repeating decimal (approximately 1.05506, or 105.506%).

709 ÷ 672 = 1.05506 (105.506%)

Visual Representation

The diagram below illustrates 11/21 plus 17/32 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`709/672`
Mixed Number Form	`1 37/672`
Decimal Form	`1.05506`
Percentage	`105.506%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 11/21 plus 17/32 as a fraction?

11/21 + 17/32 in simplest fraction form is 709/672 (or 1 37/672 as a mixed number).

What is 11/21 plus 17/32 as a decimal?

11/21 + 17/32 converted to a decimal is 1.05506.

What is 11/21 plus 17/32 as a percentage?

11/21 + 17/32 expressed as a percentage is 105.506%.

How do you write 11/21 plus 17/32 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 709/672 can be written as the mixed number 1 37/672.

Does 11/21 plus 17/32 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.05506...) because the denominator contains prime factors other than 2 and 5.