What is 1/4 plus 9/18? (Answer: 3/4)

Exact Answer

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Problem: What is 1/4 plus 9/18?
Formula / Expression: 1/4 + 9/18
Final Answer: 3/4
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 4 × 18 = 72, keeping the calculation simpler).
Working: LCD(4, 18) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 1/4 by 9, and multiply the numerator and denominator of 9/18 by 2 so both fractions share the common base 36.
Working: 1 × 9/4 × 9 = 9/36 and 9 × 2/18 × 2 = 18/36

Step 3: Add the Numerators
Now add the numerators (9 + 18 = 27) and keep the common denominator 36 unchanged.
Working: 9 + 18/36 = 27/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 36, which is 9. Divide both the numerator and denominator by 9.
Working: 27 ÷ 9/36 ÷ 9 = 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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1/4 + 9/18 = 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: 1/4 + 9/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 4 × 18 = 72, keeping the calculation simpler).

LCD(4, 18) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 1/4 by 9, and multiply the numerator and denominator of 9/18 by 2 so both fractions share the common base 36.

1 × 9/4 × 9 = 9/36 and 9 × 2/18 × 2 = 18/36

Step 3

Add the Numerators

Now add the numerators (9 + 18 = 27) and keep the common denominator 36 unchanged.

9 + 18/36 = 27/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 36, which is 9. Divide both the numerator and denominator by 9.

27 ÷ 9/36 ÷ 9 = 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 1/4 plus 9/18 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 1/4 plus 9/18 as a fraction?

1/4 + 9/18 in simplest fraction form is 3/4.

What is 1/4 plus 9/18 as a decimal?

1/4 + 9/18 converted to a decimal is 0.75.

What is 1/4 plus 9/18 as a percentage?

1/4 + 9/18 expressed as a percentage is 75%.

Does 1/4 plus 9/18 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.