What is 3/56 plus 8/21? (Answer: 73/168)

Exact Answer

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Problem: What is 3/56 plus 8/21?
Formula / Expression: 3/56 + 8/21
Final Answer: 73/168
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 56 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 56 × 21 = 1176, keeping the calculation simpler).
Working: LCD(56, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 3/56 by 3, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.
Working: 3 × 3/56 × 3 = 9/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (9 + 64 = 73) and keep the common denominator 168 unchanged.
Working: 9 + 64/168 = 73/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 168 is 1, confirming that 73/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 168 produces a repeating decimal (approximately 0.434524, or 43.4524%).
Working: 73 ÷ 168 = 0.434524 (43.4524%)

Key Values:
- Simplified Fraction: 73/168
- Mixed Number Form: 73/168
- Decimal Value: 0.434524
- Percentage: 43.4524%

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Solved with FractionsCalc:
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3/56 + 8/21 = 73/168

Simplified Fraction

73/168

Mixed Number

Proper (73/168)

Decimal Value

0.434524

Percentage

43.4524%

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Step-by-Step Solution: 3/56 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 56 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 56 × 21 = 1176, keeping the calculation simpler).

LCD(56, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 3/56 by 3, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.

3 × 3/56 × 3 = 9/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (9 + 64 = 73) and keep the common denominator 168 unchanged.

9 + 64/168 = 73/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 168 is 1, confirming that 73/168 cannot be reduced further—it is already in its simplest irreducible form.

73/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 168 produces a repeating decimal (approximately 0.434524, or 43.4524%).

73 ÷ 168 = 0.434524 (43.4524%)

Visual Representation

The diagram below illustrates 3/56 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/168`
Mixed Number Form	`73/168`
Decimal Form	`0.434524`
Percentage	`43.4524%`

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Frequently Asked Questions

What is 3/56 plus 8/21 as a fraction?

3/56 + 8/21 in simplest fraction form is 73/168.

What is 3/56 plus 8/21 as a decimal?

3/56 + 8/21 converted to a decimal is 0.434524.

What is 3/56 plus 8/21 as a percentage?

3/56 + 8/21 expressed as a percentage is 43.4524%.

Does 3/56 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.434524...) because the denominator contains prime factors other than 2 and 5.