What is 11/21 plus 15/28? (Answer: 89/84)

Exact Answer

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Problem: What is 11/21 plus 15/28?
Formula / Expression: 11/21 + 15/28
Final Answer: 1 5/84 (89/84)
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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 11/21 by 4, and multiply the numerator and denominator of 15/28 by 3 so both fractions share the common base 84.
Working: 11 × 4/21 × 4 = 44/84 and 15 × 3/28 × 3 = 45/84

Step 3: Add the Numerators
Now add the numerators (44 + 45 = 89) and keep the common denominator 84 unchanged.
Working: 44 + 45/84 = 89/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 84 is 1, confirming that 89/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/84

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (89) is greater than the denominator (84), divide 89 by 84: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/84.
Working: 89/84 = 1 5/84

Step 6: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 84 produces a repeating decimal (approximately 1.059524, or 105.9524%).
Working: 89 ÷ 84 = 1.059524 (105.9524%)

Key Values:
- Simplified Fraction: 89/84
- Mixed Number Form: 1 5/84
- Decimal Value: 1.059524
- Percentage: 105.9524%

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Solved with FractionsCalc:
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11/21 + 15/28 = 89/84

Simplified Fraction

89/84

Mixed Number

1 5/84

Decimal Value

1.059524

Percentage

105.9524%

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Step-by-Step Solution: 11/21 + 15/28

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 11/21 by 4, and multiply the numerator and denominator of 15/28 by 3 so both fractions share the common base 84.

11 × 4/21 × 4 = 44/84 and 15 × 3/28 × 3 = 45/84

Step 3

Add the Numerators

Now add the numerators (44 + 45 = 89) and keep the common denominator 84 unchanged.

44 + 45/84 = 89/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 84 is 1, confirming that 89/84 cannot be reduced further—it is already in its simplest irreducible form.

89/84

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (89) is greater than the denominator (84), divide 89 by 84: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/84.

89/84 = 15/84

Step 6

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 84 produces a repeating decimal (approximately 1.059524, or 105.9524%).

89 ÷ 84 = 1.059524 (105.9524%)

Visual Representation

The diagram below illustrates 11/21 plus 15/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/84`
Mixed Number Form	`1 5/84`
Decimal Form	`1.059524`
Percentage	`105.9524%`

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Frequently Asked Questions

What is 11/21 plus 15/28 as a fraction?

11/21 + 15/28 in simplest fraction form is 89/84 (or 1 5/84 as a mixed number).

What is 11/21 plus 15/28 as a decimal?

11/21 + 15/28 converted to a decimal is 1.059524.

What is 11/21 plus 15/28 as a percentage?

11/21 + 15/28 expressed as a percentage is 105.9524%.

How do you write 11/21 plus 15/28 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 89/84 can be written as the mixed number 1 5/84.

Does 11/21 plus 15/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.059524...) because the denominator contains prime factors other than 2 and 5.