What is 11/28 plus 10/21? (Answer: 73/84)

Exact Answer

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Problem: What is 11/28 plus 10/21?
Formula / Expression: 11/28 + 10/21
Final Answer: 73/84
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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 11/28 by 3, and multiply the numerator and denominator of 10/21 by 4 so both fractions share the common base 84.
Working: 11 × 3/28 × 3 = 33/84 and 10 × 4/21 × 4 = 40/84

Step 3: Add the Numerators
Now add the numerators (33 + 40 = 73) and keep the common denominator 84 unchanged.
Working: 33 + 40/84 = 73/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 84 is 1, confirming that 73/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 84 produces a repeating decimal (approximately 0.869048, or 86.9048%).
Working: 73 ÷ 84 = 0.869048 (86.9048%)

Key Values:
- Simplified Fraction: 73/84
- Mixed Number Form: 73/84
- Decimal Value: 0.869048
- Percentage: 86.9048%

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Solved with FractionsCalc:
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11/28 + 10/21 = 73/84

Simplified Fraction

73/84

Mixed Number

Proper (73/84)

Decimal Value

0.869048

Percentage

86.9048%

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Step-by-Step Solution: 11/28 + 10/21

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 11/28 by 3, and multiply the numerator and denominator of 10/21 by 4 so both fractions share the common base 84.

11 × 3/28 × 3 = 33/84 and 10 × 4/21 × 4 = 40/84

Step 3

Add the Numerators

Now add the numerators (33 + 40 = 73) and keep the common denominator 84 unchanged.

33 + 40/84 = 73/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 84 is 1, confirming that 73/84 cannot be reduced further—it is already in its simplest irreducible form.

73/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 84 produces a repeating decimal (approximately 0.869048, or 86.9048%).

73 ÷ 84 = 0.869048 (86.9048%)

Visual Representation

The diagram below illustrates 11/28 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/84`
Mixed Number Form	`73/84`
Decimal Form	`0.869048`
Percentage	`86.9048%`

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Frequently Asked Questions

What is 11/28 plus 10/21 as a fraction?

11/28 + 10/21 in simplest fraction form is 73/84.

What is 11/28 plus 10/21 as a decimal?

11/28 + 10/21 converted to a decimal is 0.869048.

What is 11/28 plus 10/21 as a percentage?

11/28 + 10/21 expressed as a percentage is 86.9048%.

Does 11/28 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.869048...) because the denominator contains prime factors other than 2 and 5.