What is 3/56 plus 7/21? (Answer: 65/168)

Exact Answer

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Problem: What is 3/56 plus 7/21?
Formula / Expression: 3/56 + 7/21
Final Answer: 65/168
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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 7/21 by 8 so both fractions share the common base 168.
Working: 3 × 3/56 × 3 = 9/168 and 7 × 8/21 × 8 = 56/168

Step 3: Add the Numerators
Now add the numerators (9 + 56 = 65) and keep the common denominator 168 unchanged.
Working: 9 + 56/168 = 65/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 168 is 1, confirming that 65/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 168 produces a repeating decimal (approximately 0.386905, or 38.6905%).
Working: 65 ÷ 168 = 0.386905 (38.6905%)

Key Values:
- Simplified Fraction: 65/168
- Mixed Number Form: 65/168
- Decimal Value: 0.386905
- Percentage: 38.6905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-56-plus-7-21/
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3/56 + 7/21 = 65/168

Simplified Fraction

65/168

Mixed Number

Proper (65/168)

Decimal Value

0.386905

Percentage

38.6905%

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Step-by-Step Solution: 3/56 + 7/21

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 7/21 by 8 so both fractions share the common base 168.

3 × 3/56 × 3 = 9/168 and 7 × 8/21 × 8 = 56/168

Step 3

Add the Numerators

Now add the numerators (9 + 56 = 65) and keep the common denominator 168 unchanged.

9 + 56/168 = 65/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 168 is 1, confirming that 65/168 cannot be reduced further—it is already in its simplest irreducible form.

65/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 168 produces a repeating decimal (approximately 0.386905, or 38.6905%).

65 ÷ 168 = 0.386905 (38.6905%)

Visual Representation

The diagram below illustrates 3/56 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/168`
Mixed Number Form	`65/168`
Decimal Form	`0.386905`
Percentage	`38.6905%`

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Frequently Asked Questions

What is 3/56 plus 7/21 as a fraction?

3/56 + 7/21 in simplest fraction form is 65/168.

What is 3/56 plus 7/21 as a decimal?

3/56 + 7/21 converted to a decimal is 0.386905.

What is 3/56 plus 7/21 as a percentage?

3/56 + 7/21 expressed as a percentage is 38.6905%.

Does 3/56 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.386905...) because the denominator contains prime factors other than 2 and 5.