What is 1/56 plus 3/21? (Answer: 9/56)

Exact Answer

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Problem: What is 1/56 plus 3/21?
Formula / Expression: 1/56 + 3/21
Final Answer: 9/56
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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 1/56 by 3, and multiply the numerator and denominator of 3/21 by 8 so both fractions share the common base 168.
Working: 1 × 3/56 × 3 = 3/168 and 3 × 8/21 × 8 = 24/168

Step 3: Add the Numerators
Now add the numerators (3 + 24 = 27) and keep the common denominator 168 unchanged.
Working: 3 + 24/168 = 27/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 27 ÷ 3/168 ÷ 3 = 9/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 56 produces a repeating decimal (approximately 0.160714, or 16.0714%).
Working: 9 ÷ 56 = 0.160714 (16.0714%)

Key Values:
- Simplified Fraction: 9/56
- Mixed Number Form: 9/56
- Decimal Value: 0.160714
- Percentage: 16.0714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-56-plus-3-21/
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1/56 + 3/21 = 9/56

Simplified Fraction

9/56

Mixed Number

Proper (9/56)

Decimal Value

0.160714

Percentage

16.0714%

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Step-by-Step Solution: 1/56 + 3/21

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 1/56 by 3, and multiply the numerator and denominator of 3/21 by 8 so both fractions share the common base 168.

1 × 3/56 × 3 = 3/168 and 3 × 8/21 × 8 = 24/168

Step 3

Add the Numerators

Now add the numerators (3 + 24 = 27) and keep the common denominator 168 unchanged.

3 + 24/168 = 27/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 168, which is 3. Divide both the numerator and denominator by 3.

27 ÷ 3/168 ÷ 3 = 9/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 56 produces a repeating decimal (approximately 0.160714, or 16.0714%).

9 ÷ 56 = 0.160714 (16.0714%)

Visual Representation

The diagram below illustrates 1/56 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/56`
Mixed Number Form	`9/56`
Decimal Form	`0.160714`
Percentage	`16.0714%`

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Frequently Asked Questions

What is 1/56 plus 3/21 as a fraction?

1/56 + 3/21 in simplest fraction form is 9/56.

What is 1/56 plus 3/21 as a decimal?

1/56 + 3/21 converted to a decimal is 0.160714.

What is 1/56 plus 3/21 as a percentage?

1/56 + 3/21 expressed as a percentage is 16.0714%.

Does 1/56 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.160714...) because the denominator contains prime factors other than 2 and 5.