What is 12/21 plus 16/28? (Answer: 8/7)

Exact Answer

==================================================
Problem: What is 12/21 plus 16/28?
Formula / Expression: 12/21 + 16/28
Final Answer: 1 1/7 (8/7)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 28 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 28 = 588, keeping the calculation simpler).
Working: LCD(21, 28) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 12/21 by 4, and multiply the numerator and denominator of 16/28 by 3 so both fractions share the common base 84.
Working: 12 × 4/21 × 4 = 48/84 and 16 × 3/28 × 3 = 48/84

Step 3: Add the Numerators
Now add the numerators (48 + 48 = 96) and keep the common denominator 84 unchanged.
Working: 48 + 48/84 = 96/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 96 and 84, which is 12. Divide both the numerator and denominator by 12.
Working: 96 ÷ 12/84 ÷ 12 = 8/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.
Working: 8/7 = 1 1/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).
Working: 8 ÷ 7 = 1.142857 (114.2857%)

Key Values:
- Simplified Fraction: 8/7
- Mixed Number Form: 1 1/7
- Decimal Value: 1.142857
- Percentage: 114.2857%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-21-plus-16-28/
==================================================

12/21 + 16/28 = 8/7

Simplified Fraction

8/7

Mixed Number

1 1/7

Decimal Value

1.142857

Percentage

114.2857%

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: 12/21 + 16/28

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 28 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 28 = 588, keeping the calculation simpler).

LCD(21, 28) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 12/21 by 4, and multiply the numerator and denominator of 16/28 by 3 so both fractions share the common base 84.

12 × 4/21 × 4 = 48/84 and 16 × 3/28 × 3 = 48/84

Step 3

Add the Numerators

Now add the numerators (48 + 48 = 96) and keep the common denominator 84 unchanged.

48 + 48/84 = 96/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 96 and 84, which is 12. Divide both the numerator and denominator by 12.

96 ÷ 12/84 ÷ 12 = 8/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.

8/7 = 11/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).

8 ÷ 7 = 1.142857 (114.2857%)

Visual Representation

The diagram below illustrates 12/21 plus 16/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/7`
Mixed Number Form	`1 1/7`
Decimal Form	`1.142857`
Percentage	`114.2857%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 12/21 plus 16/28 as a fraction?

12/21 + 16/28 in simplest fraction form is 8/7 (or 1 1/7 as a mixed number).

What is 12/21 plus 16/28 as a decimal?

12/21 + 16/28 converted to a decimal is 1.142857.

What is 12/21 plus 16/28 as a percentage?

12/21 + 16/28 expressed as a percentage is 114.2857%.

How do you write 12/21 plus 16/28 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 8/7 can be written as the mixed number 1 1/7.

Does 12/21 plus 16/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.142857...) because the denominator contains prime factors other than 2 and 5.