What is 18/56 plus 8/21? (Answer: 59/84)

Exact Answer

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Problem: What is 18/56 plus 8/21?
Formula / Expression: 18/56 + 8/21
Final Answer: 59/84
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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 18/56 by 3, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.
Working: 18 × 3/56 × 3 = 54/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (54 + 64 = 118) and keep the common denominator 168 unchanged.
Working: 54 + 64/168 = 118/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/168 ÷ 2 = 59/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 84 produces a repeating decimal (approximately 0.702381, or 70.2381%).
Working: 59 ÷ 84 = 0.702381 (70.2381%)

Key Values:
- Simplified Fraction: 59/84
- Mixed Number Form: 59/84
- Decimal Value: 0.702381
- Percentage: 70.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-18-56-plus-8-21/
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18/56 + 8/21 = 59/84

Simplified Fraction

59/84

Mixed Number

Proper (59/84)

Decimal Value

0.702381

Percentage

70.2381%

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Step-by-Step Solution: 18/56 + 8/21

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 18/56 by 3, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.

18 × 3/56 × 3 = 54/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (54 + 64 = 118) and keep the common denominator 168 unchanged.

54 + 64/168 = 118/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 168, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/168 ÷ 2 = 59/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 84 produces a repeating decimal (approximately 0.702381, or 70.2381%).

59 ÷ 84 = 0.702381 (70.2381%)

Visual Representation

The diagram below illustrates 18/56 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/84`
Mixed Number Form	`59/84`
Decimal Form	`0.702381`
Percentage	`70.2381%`

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Frequently Asked Questions

What is 18/56 plus 8/21 as a fraction?

18/56 + 8/21 in simplest fraction form is 59/84.

What is 18/56 plus 8/21 as a decimal?

18/56 + 8/21 converted to a decimal is 0.702381.

What is 18/56 plus 8/21 as a percentage?

18/56 + 8/21 expressed as a percentage is 70.2381%.

Does 18/56 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.702381...) because the denominator contains prime factors other than 2 and 5.