What is 1/56 plus 4/21? (Answer: 5/24)

Exact Answer

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Problem: What is 1/56 plus 4/21?
Formula / Expression: 1/56 + 4/21
Final Answer: 5/24
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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 4/21 by 8 so both fractions share the common base 168.
Working: 1 × 3/56 × 3 = 3/168 and 4 × 8/21 × 8 = 32/168

Step 3: Add the Numerators
Now add the numerators (3 + 32 = 35) and keep the common denominator 168 unchanged.
Working: 3 + 32/168 = 35/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 35 and 168, which is 7. Divide both the numerator and denominator by 7.
Working: 35 ÷ 7/168 ÷ 7 = 5/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 24 produces a repeating decimal (approximately 0.208333, or 20.8333%).
Working: 5 ÷ 24 = 0.208333 (20.8333%)

Key Values:
- Simplified Fraction: 5/24
- Mixed Number Form: 5/24
- Decimal Value: 0.208333
- Percentage: 20.8333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-56-plus-4-21/
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1/56 + 4/21 = 5/24

Simplified Fraction

5/24

Mixed Number

Proper (5/24)

Decimal Value

0.208333

Percentage

20.8333%

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Step-by-Step Solution: 1/56 + 4/21

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 4/21 by 8 so both fractions share the common base 168.

1 × 3/56 × 3 = 3/168 and 4 × 8/21 × 8 = 32/168

Step 3

Add the Numerators

Now add the numerators (3 + 32 = 35) and keep the common denominator 168 unchanged.

3 + 32/168 = 35/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 35 and 168, which is 7. Divide both the numerator and denominator by 7.

35 ÷ 7/168 ÷ 7 = 5/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 24 produces a repeating decimal (approximately 0.208333, or 20.8333%).

5 ÷ 24 = 0.208333 (20.8333%)

Visual Representation

The diagram below illustrates 1/56 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/24`
Mixed Number Form	`5/24`
Decimal Form	`0.208333`
Percentage	`20.8333%`

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Frequently Asked Questions

What is 1/56 plus 4/21 as a fraction?

1/56 + 4/21 in simplest fraction form is 5/24.

What is 1/56 plus 4/21 as a decimal?

1/56 + 4/21 converted to a decimal is 0.208333.

What is 1/56 plus 4/21 as a percentage?

1/56 + 4/21 expressed as a percentage is 20.8333%.

Does 1/56 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.208333...) because the denominator contains prime factors other than 2 and 5.