What is 16/63 plus 9/21? (Answer: 43/63)

Exact Answer

==================================================
Problem: What is 16/63 plus 9/21?
Formula / Expression: 16/63 + 9/21
Final Answer: 43/63
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.
Working: LCD(63, 21) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 16/63 by 1, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.
Working: 16 × 1/63 × 1 = 16/63 and 9 × 3/21 × 3 = 27/63

Step 3: Add the Numerators
Now add the numerators (16 + 27 = 43) and keep the common denominator 63 unchanged.
Working: 16 + 27/63 = 43/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 63 is 1, confirming that 43/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 63 produces a repeating decimal (approximately 0.68254, or 68.254%).
Working: 43 ÷ 63 = 0.68254 (68.254%)

Key Values:
- Simplified Fraction: 43/63
- Mixed Number Form: 43/63
- Decimal Value: 0.68254
- Percentage: 68.254%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-63-plus-9-21/
==================================================

16/63 + 9/21 = 43/63

Simplified Fraction

43/63

Mixed Number

Proper (43/63)

Decimal Value

0.68254

Percentage

68.254%

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: 16/63 + 9/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.

LCD(63, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 16/63 by 1, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.

16 × 1/63 × 1 = 16/63 and 9 × 3/21 × 3 = 27/63

Step 3

Add the Numerators

Now add the numerators (16 + 27 = 43) and keep the common denominator 63 unchanged.

16 + 27/63 = 43/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 63 is 1, confirming that 43/63 cannot be reduced further—it is already in its simplest irreducible form.

43/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 63 produces a repeating decimal (approximately 0.68254, or 68.254%).

43 ÷ 63 = 0.68254 (68.254%)

Visual Representation

The diagram below illustrates 16/63 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/63`
Mixed Number Form	`43/63`
Decimal Form	`0.68254`
Percentage	`68.254%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 16/63 plus 9/21 as a fraction?

16/63 + 9/21 in simplest fraction form is 43/63.

What is 16/63 plus 9/21 as a decimal?

16/63 + 9/21 converted to a decimal is 0.68254.

What is 16/63 plus 9/21 as a percentage?

16/63 + 9/21 expressed as a percentage is 68.254%.

Does 16/63 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.68254...) because the denominator contains prime factors other than 2 and 5.