What is 13/28 plus 12/21? (Answer: 29/28)

Exact Answer

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Problem: What is 13/28 plus 12/21?
Formula / Expression: 13/28 + 12/21
Final Answer: 1 1/28 (29/28)
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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 13/28 by 3, and multiply the numerator and denominator of 12/21 by 4 so both fractions share the common base 84.
Working: 13 × 3/28 × 3 = 39/84 and 12 × 4/21 × 4 = 48/84

Step 3: Add the Numerators
Now add the numerators (39 + 48 = 87) and keep the common denominator 84 unchanged.
Working: 39 + 48/84 = 87/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 87 and 84, which is 3. Divide both the numerator and denominator by 3.
Working: 87 ÷ 3/84 ÷ 3 = 29/28

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (29) is greater than the denominator (28), divide 29 by 28: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/28.
Working: 29/28 = 1 1/28

Step 6: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 28 produces a repeating decimal (approximately 1.035714, or 103.5714%).
Working: 29 ÷ 28 = 1.035714 (103.5714%)

Key Values:
- Simplified Fraction: 29/28
- Mixed Number Form: 1 1/28
- Decimal Value: 1.035714
- Percentage: 103.5714%

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Solved with FractionsCalc:
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13/28 + 12/21 = 29/28

Simplified Fraction

29/28

Mixed Number

1 1/28

Decimal Value

1.035714

Percentage

103.5714%

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Step-by-Step Solution: 13/28 + 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 13/28 by 3, and multiply the numerator and denominator of 12/21 by 4 so both fractions share the common base 84.

13 × 3/28 × 3 = 39/84 and 12 × 4/21 × 4 = 48/84

Step 3

Add the Numerators

Now add the numerators (39 + 48 = 87) and keep the common denominator 84 unchanged.

39 + 48/84 = 87/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 87 and 84, which is 3. Divide both the numerator and denominator by 3.

87 ÷ 3/84 ÷ 3 = 29/28

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (29) is greater than the denominator (28), divide 29 by 28: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/28.

29/28 = 11/28

Step 6

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 28 produces a repeating decimal (approximately 1.035714, or 103.5714%).

29 ÷ 28 = 1.035714 (103.5714%)

Visual Representation

The diagram below illustrates 13/28 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/28`
Mixed Number Form	`1 1/28`
Decimal Form	`1.035714`
Percentage	`103.5714%`

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Frequently Asked Questions

What is 13/28 plus 12/21 as a fraction?

13/28 + 12/21 in simplest fraction form is 29/28 (or 1 1/28 as a mixed number).

What is 13/28 plus 12/21 as a decimal?

13/28 + 12/21 converted to a decimal is 1.035714.

What is 13/28 plus 12/21 as a percentage?

13/28 + 12/21 expressed as a percentage is 103.5714%.

How do you write 13/28 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 29/28 can be written as the mixed number 1 1/28.

Does 13/28 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.035714...) because the denominator contains prime factors other than 2 and 5.