What is 9/54 plus 7/21? (Answer: 1/2)

Exact Answer

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Problem: What is 9/54 plus 7/21?
Formula / Expression: 9/54 + 7/21
Final Answer: 1/2
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).
Working: LCD(54, 21) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 9/54 by 7, and multiply the numerator and denominator of 7/21 by 18 so both fractions share the common base 378.
Working: 9 × 7/54 × 7 = 63/378 and 7 × 18/21 × 18 = 126/378

Step 3: Add the Numerators
Now add the numerators (63 + 126 = 189) and keep the common denominator 378 unchanged.
Working: 63 + 126/378 = 189/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 189 and 378, which is 189. Divide both the numerator and denominator by 189.
Working: 189 ÷ 189/378 ÷ 189 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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9/54 + 7/21 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 9/54 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).

LCD(54, 21) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 9/54 by 7, and multiply the numerator and denominator of 7/21 by 18 so both fractions share the common base 378.

9 × 7/54 × 7 = 63/378 and 7 × 18/21 × 18 = 126/378

Step 3

Add the Numerators

Now add the numerators (63 + 126 = 189) and keep the common denominator 378 unchanged.

63 + 126/378 = 189/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 189 and 378, which is 189. Divide both the numerator and denominator by 189.

189 ÷ 189/378 ÷ 189 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 9/54 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 9/54 plus 7/21 as a fraction?

9/54 + 7/21 in simplest fraction form is 1/2.

What is 9/54 plus 7/21 as a decimal?

9/54 + 7/21 converted to a decimal is 0.5.

What is 9/54 plus 7/21 as a percentage?

9/54 + 7/21 expressed as a percentage is 50%.

Does 9/54 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.