What is 18/56 plus 9/21? (Answer: 3/4)

Exact Answer

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Problem: What is 18/56 plus 9/21?
Formula / Expression: 18/56 + 9/21
Final Answer: 3/4
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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 9/21 by 8 so both fractions share the common base 168.
Working: 18 × 3/56 × 3 = 54/168 and 9 × 8/21 × 8 = 72/168

Step 3: Add the Numerators
Now add the numerators (54 + 72 = 126) and keep the common denominator 168 unchanged.
Working: 54 + 72/168 = 126/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 168, which is 42. Divide both the numerator and denominator by 42.
Working: 126 ÷ 42/168 ÷ 42 = 3/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).
Working: 3 ÷ 4 = 0.75 (75%)

Key Values:
- Simplified Fraction: 3/4
- Mixed Number Form: 3/4
- Decimal Value: 0.75
- Percentage: 75%

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Solved with FractionsCalc:
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18/56 + 9/21 = 3/4

Simplified Fraction

3/4

Mixed Number

Proper (3/4)

Decimal Value

0.75

Percentage

75%

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Step-by-Step Solution: 18/56 + 9/21

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 9/21 by 8 so both fractions share the common base 168.

18 × 3/56 × 3 = 54/168 and 9 × 8/21 × 8 = 72/168

Step 3

Add the Numerators

Now add the numerators (54 + 72 = 126) and keep the common denominator 168 unchanged.

54 + 72/168 = 126/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 168, which is 42. Divide both the numerator and denominator by 42.

126 ÷ 42/168 ÷ 42 = 3/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).

3 ÷ 4 = 0.75 (75%)

Visual Representation

The diagram below illustrates 18/56 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/4`
Mixed Number Form	`3/4`
Decimal Form	`0.75`
Percentage	`75%`

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Frequently Asked Questions

What is 18/56 plus 9/21 as a fraction?

18/56 + 9/21 in simplest fraction form is 3/4.

What is 18/56 plus 9/21 as a decimal?

18/56 + 9/21 converted to a decimal is 0.75.

What is 18/56 plus 9/21 as a percentage?

18/56 + 9/21 expressed as a percentage is 75%.

Does 18/56 plus 9/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.