What is 12/56 plus 5/21? (Answer: 19/42)

Exact Answer

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Problem: What is 12/56 plus 5/21?
Formula / Expression: 12/56 + 5/21
Final Answer: 19/42
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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 12/56 by 3, and multiply the numerator and denominator of 5/21 by 8 so both fractions share the common base 168.
Working: 12 × 3/56 × 3 = 36/168 and 5 × 8/21 × 8 = 40/168

Step 3: Add the Numerators
Now add the numerators (36 + 40 = 76) and keep the common denominator 168 unchanged.
Working: 36 + 40/168 = 76/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 168, which is 4. Divide both the numerator and denominator by 4.
Working: 76 ÷ 4/168 ÷ 4 = 19/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).
Working: 19 ÷ 42 = 0.452381 (45.2381%)

Key Values:
- Simplified Fraction: 19/42
- Mixed Number Form: 19/42
- Decimal Value: 0.452381
- Percentage: 45.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-56-plus-5-21/
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12/56 + 5/21 = 19/42

Simplified Fraction

19/42

Mixed Number

Proper (19/42)

Decimal Value

0.452381

Percentage

45.2381%

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Step-by-Step Solution: 12/56 + 5/21

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 12/56 by 3, and multiply the numerator and denominator of 5/21 by 8 so both fractions share the common base 168.

12 × 3/56 × 3 = 36/168 and 5 × 8/21 × 8 = 40/168

Step 3

Add the Numerators

Now add the numerators (36 + 40 = 76) and keep the common denominator 168 unchanged.

36 + 40/168 = 76/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 168, which is 4. Divide both the numerator and denominator by 4.

76 ÷ 4/168 ÷ 4 = 19/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).

19 ÷ 42 = 0.452381 (45.2381%)

Visual Representation

The diagram below illustrates 12/56 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/42`
Mixed Number Form	`19/42`
Decimal Form	`0.452381`
Percentage	`45.2381%`

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Frequently Asked Questions

What is 12/56 plus 5/21 as a fraction?

12/56 + 5/21 in simplest fraction form is 19/42.

What is 12/56 plus 5/21 as a decimal?

12/56 + 5/21 converted to a decimal is 0.452381.

What is 12/56 plus 5/21 as a percentage?

12/56 + 5/21 expressed as a percentage is 45.2381%.

Does 12/56 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452381...) because the denominator contains prime factors other than 2 and 5.