What is 3/28 plus 7/21? (Answer: 37/84)

Exact Answer

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Problem: What is 3/28 plus 7/21?
Formula / Expression: 3/28 + 7/21
Final Answer: 37/84
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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 7/21 by 4 so both fractions share the common base 84.
Working: 3 × 3/28 × 3 = 9/84 and 7 × 4/21 × 4 = 28/84

Step 3: Add the Numerators
Now add the numerators (9 + 28 = 37) and keep the common denominator 84 unchanged.
Working: 9 + 28/84 = 37/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 84 is 1, confirming that 37/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 84 produces a repeating decimal (approximately 0.440476, or 44.0476%).
Working: 37 ÷ 84 = 0.440476 (44.0476%)

Key Values:
- Simplified Fraction: 37/84
- Mixed Number Form: 37/84
- Decimal Value: 0.440476
- Percentage: 44.0476%

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Solved with FractionsCalc:
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3/28 + 7/21 = 37/84

Simplified Fraction

37/84

Mixed Number

Proper (37/84)

Decimal Value

0.440476

Percentage

44.0476%

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Step-by-Step Solution: 3/28 + 7/21

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 7/21 by 4 so both fractions share the common base 84.

3 × 3/28 × 3 = 9/84 and 7 × 4/21 × 4 = 28/84

Step 3

Add the Numerators

Now add the numerators (9 + 28 = 37) and keep the common denominator 84 unchanged.

9 + 28/84 = 37/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 84 is 1, confirming that 37/84 cannot be reduced further—it is already in its simplest irreducible form.

37/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 84 produces a repeating decimal (approximately 0.440476, or 44.0476%).

37 ÷ 84 = 0.440476 (44.0476%)

Visual Representation

The diagram below illustrates 3/28 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/84`
Mixed Number Form	`37/84`
Decimal Form	`0.440476`
Percentage	`44.0476%`

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Frequently Asked Questions

What is 3/28 plus 7/21 as a fraction?

3/28 + 7/21 in simplest fraction form is 37/84.

What is 3/28 plus 7/21 as a decimal?

3/28 + 7/21 converted to a decimal is 0.440476.

What is 3/28 plus 7/21 as a percentage?

3/28 + 7/21 expressed as a percentage is 44.0476%.

Does 3/28 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.440476...) because the denominator contains prime factors other than 2 and 5.