What is 4/56 plus 4/21? (Answer: 11/42)

Exact Answer

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Problem: What is 4/56 plus 4/21?
Formula / Expression: 4/56 + 4/21
Final Answer: 11/42
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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 4/56 by 3, and multiply the numerator and denominator of 4/21 by 8 so both fractions share the common base 168.
Working: 4 × 3/56 × 3 = 12/168 and 4 × 8/21 × 8 = 32/168

Step 3: Add the Numerators
Now add the numerators (12 + 32 = 44) and keep the common denominator 168 unchanged.
Working: 12 + 32/168 = 44/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 44 and 168, which is 4. Divide both the numerator and denominator by 4.
Working: 44 ÷ 4/168 ÷ 4 = 11/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 42 produces a repeating decimal (approximately 0.261905, or 26.1905%).
Working: 11 ÷ 42 = 0.261905 (26.1905%)

Key Values:
- Simplified Fraction: 11/42
- Mixed Number Form: 11/42
- Decimal Value: 0.261905
- Percentage: 26.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-56-plus-4-21/
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4/56 + 4/21 = 11/42

Simplified Fraction

11/42

Mixed Number

Proper (11/42)

Decimal Value

0.261905

Percentage

26.1905%

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Step-by-Step Solution: 4/56 + 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 4/56 by 3, and multiply the numerator and denominator of 4/21 by 8 so both fractions share the common base 168.

4 × 3/56 × 3 = 12/168 and 4 × 8/21 × 8 = 32/168

Step 3

Add the Numerators

Now add the numerators (12 + 32 = 44) and keep the common denominator 168 unchanged.

12 + 32/168 = 44/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 44 and 168, which is 4. Divide both the numerator and denominator by 4.

44 ÷ 4/168 ÷ 4 = 11/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 42 produces a repeating decimal (approximately 0.261905, or 26.1905%).

11 ÷ 42 = 0.261905 (26.1905%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/42`
Mixed Number Form	`11/42`
Decimal Form	`0.261905`
Percentage	`26.1905%`

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Frequently Asked Questions

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

4/56 + 4/21 in simplest fraction form is 11/42.

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

4/56 + 4/21 converted to a decimal is 0.261905.

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

4/56 + 4/21 expressed as a percentage is 26.1905%.

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

It results in a repeating decimal (approximately 0.261905...) because the denominator contains prime factors other than 2 and 5.