What is 1/28 plus 5/21? (Answer: 23/84)

Exact Answer

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Problem: What is 1/28 plus 5/21?
Formula / Expression: 1/28 + 5/21
Final Answer: 23/84
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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 1/28 by 3, and multiply the numerator and denominator of 5/21 by 4 so both fractions share the common base 84.
Working: 1 × 3/28 × 3 = 3/84 and 5 × 4/21 × 4 = 20/84

Step 3: Add the Numerators
Now add the numerators (3 + 20 = 23) and keep the common denominator 84 unchanged.
Working: 3 + 20/84 = 23/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 84 is 1, confirming that 23/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 84 produces a repeating decimal (approximately 0.27381, or 27.381%).
Working: 23 ÷ 84 = 0.27381 (27.381%)

Key Values:
- Simplified Fraction: 23/84
- Mixed Number Form: 23/84
- Decimal Value: 0.27381
- Percentage: 27.381%

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Solved with FractionsCalc:
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1/28 + 5/21 = 23/84

Simplified Fraction

23/84

Mixed Number

Proper (23/84)

Decimal Value

0.27381

Percentage

27.381%

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Step-by-Step Solution: 1/28 + 5/21

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 1/28 by 3, and multiply the numerator and denominator of 5/21 by 4 so both fractions share the common base 84.

1 × 3/28 × 3 = 3/84 and 5 × 4/21 × 4 = 20/84

Step 3

Add the Numerators

Now add the numerators (3 + 20 = 23) and keep the common denominator 84 unchanged.

3 + 20/84 = 23/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 84 is 1, confirming that 23/84 cannot be reduced further—it is already in its simplest irreducible form.

23/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 84 produces a repeating decimal (approximately 0.27381, or 27.381%).

23 ÷ 84 = 0.27381 (27.381%)

Visual Representation

The diagram below illustrates 1/28 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/84`
Mixed Number Form	`23/84`
Decimal Form	`0.27381`
Percentage	`27.381%`

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Frequently Asked Questions

What is 1/28 plus 5/21 as a fraction?

1/28 + 5/21 in simplest fraction form is 23/84.

What is 1/28 plus 5/21 as a decimal?

1/28 + 5/21 converted to a decimal is 0.27381.

What is 1/28 plus 5/21 as a percentage?

1/28 + 5/21 expressed as a percentage is 27.381%.

Does 1/28 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.27381...) because the denominator contains prime factors other than 2 and 5.