What is 3/28 plus 4/21? (Answer: 25/84)

Exact Answer

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Problem: What is 3/28 plus 4/21?
Formula / Expression: 3/28 + 4/21
Final Answer: 25/84
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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 3/28 by 3, and multiply the numerator and denominator of 4/21 by 4 so both fractions share the common base 84.
Working: 3 × 3/28 × 3 = 9/84 and 4 × 4/21 × 4 = 16/84

Step 3: Add the Numerators
Now add the numerators (9 + 16 = 25) and keep the common denominator 84 unchanged.
Working: 9 + 16/84 = 25/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 84 is 1, confirming that 25/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 84 produces a repeating decimal (approximately 0.297619, or 29.7619%).
Working: 25 ÷ 84 = 0.297619 (29.7619%)

Key Values:
- Simplified Fraction: 25/84
- Mixed Number Form: 25/84
- Decimal Value: 0.297619
- Percentage: 29.7619%

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Solved with FractionsCalc:
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3/28 + 4/21 = 25/84

Simplified Fraction

25/84

Mixed Number

Proper (25/84)

Decimal Value

0.297619

Percentage

29.7619%

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Step-by-Step Solution: 3/28 + 4/21

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

3 × 3/28 × 3 = 9/84 and 4 × 4/21 × 4 = 16/84

Step 3

Add the Numerators

Now add the numerators (9 + 16 = 25) and keep the common denominator 84 unchanged.

9 + 16/84 = 25/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 84 is 1, confirming that 25/84 cannot be reduced further—it is already in its simplest irreducible form.

25/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 84 produces a repeating decimal (approximately 0.297619, or 29.7619%).

25 ÷ 84 = 0.297619 (29.7619%)

Visual Representation

The diagram below illustrates 3/28 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/84`
Mixed Number Form	`25/84`
Decimal Form	`0.297619`
Percentage	`29.7619%`

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Frequently Asked Questions

What is 3/28 plus 4/21 as a fraction?

3/28 + 4/21 in simplest fraction form is 25/84.

What is 3/28 plus 4/21 as a decimal?

3/28 + 4/21 converted to a decimal is 0.297619.

What is 3/28 plus 4/21 as a percentage?

3/28 + 4/21 expressed as a percentage is 29.7619%.

Does 3/28 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.297619...) because the denominator contains prime factors other than 2 and 5.