What is 15/28 plus 12/21? (Answer: 31/28)

Exact Answer

==================================================
Problem: What is 15/28 plus 12/21?
Formula / Expression: 15/28 + 12/21
Final Answer: 1 3/28 (31/28)
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 15/28 by 3, and multiply the numerator and denominator of 12/21 by 4 so both fractions share the common base 84.
Working: 15 × 3/28 × 3 = 45/84 and 12 × 4/21 × 4 = 48/84

Step 3: Add the Numerators
Now add the numerators (45 + 48 = 93) and keep the common denominator 84 unchanged.
Working: 45 + 48/84 = 93/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 84, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/84 ÷ 3 = 31/28

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (28), divide 31 by 28: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/28.
Working: 31/28 = 1 3/28

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 28 produces a repeating decimal (approximately 1.107143, or 110.7143%).
Working: 31 ÷ 28 = 1.107143 (110.7143%)

Key Values:
- Simplified Fraction: 31/28
- Mixed Number Form: 1 3/28
- Decimal Value: 1.107143
- Percentage: 110.7143%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-28-plus-12-21/
==================================================

15/28 + 12/21 = 31/28

Simplified Fraction

31/28

Mixed Number

1 3/28

Decimal Value

1.107143

Percentage

110.7143%

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: 15/28 + 12/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(28, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 15/28 by 3, and multiply the numerator and denominator of 12/21 by 4 so both fractions share the common base 84.

15 × 3/28 × 3 = 45/84 and 12 × 4/21 × 4 = 48/84

Step 3

Add the Numerators

Now add the numerators (45 + 48 = 93) and keep the common denominator 84 unchanged.

45 + 48/84 = 93/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 84, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/84 ÷ 3 = 31/28

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (28), divide 31 by 28: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/28.

31/28 = 13/28

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 28 produces a repeating decimal (approximately 1.107143, or 110.7143%).

31 ÷ 28 = 1.107143 (110.7143%)

Visual Representation

The diagram below illustrates 15/28 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/28`
Mixed Number Form	`1 3/28`
Decimal Form	`1.107143`
Percentage	`110.7143%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 15/28 plus 12/21 as a fraction?

15/28 + 12/21 in simplest fraction form is 31/28 (or 1 3/28 as a mixed number).

What is 15/28 plus 12/21 as a decimal?

15/28 + 12/21 converted to a decimal is 1.107143.

What is 15/28 plus 12/21 as a percentage?

15/28 + 12/21 expressed as a percentage is 110.7143%.

How do you write 15/28 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/28 can be written as the mixed number 1 3/28.

Does 15/28 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.107143...) because the denominator contains prime factors other than 2 and 5.