What is 3/8 plus 9/12? (Answer: 9/8)

Exact Answer

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Problem: What is 3/8 plus 9/12?
Formula / Expression: 3/8 + 9/12
Final Answer: 1 1/8 (9/8)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 12 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 24 (which is smaller than their product 8 × 12 = 96, keeping the calculation simpler).
Working: LCD(8, 12) = 24

Step 2: Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 3/8 by 3, and multiply the numerator and denominator of 9/12 by 2 so both fractions share the common base 24.
Working: 3 × 3/8 × 3 = 9/24 and 9 × 2/12 × 2 = 18/24

Step 3: Add the Numerators
Now add the numerators (9 + 18 = 27) and keep the common denominator 24 unchanged.
Working: 9 + 18/24 = 27/24

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 24, which is 3. Divide both the numerator and denominator by 3.
Working: 27 ÷ 3/24 ÷ 3 = 9/8

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (9) is greater than the denominator (8), divide 9 by 8: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/8.
Working: 9/8 = 1 1/8

Step 6: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 8 yields an exact terminating decimal of 1.125 (or 112.5%).
Working: 9 ÷ 8 = 1.125 (112.5%)

Key Values:
- Simplified Fraction: 9/8
- Mixed Number Form: 1 1/8
- Decimal Value: 1.125
- Percentage: 112.5%

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Solved with FractionsCalc:
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3/8 + 9/12 = 9/8

Simplified Fraction

9/8

Mixed Number

1 1/8

Decimal Value

1.125

Percentage

112.5%

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Step-by-Step Solution: 3/8 + 9/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 12 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 24 (which is smaller than their product 8 × 12 = 96, keeping the calculation simpler).

LCD(8, 12) = 24

Step 2

Convert to Equivalent Fractions with Common Denominator 24

Multiply the numerator and denominator of 3/8 by 3, and multiply the numerator and denominator of 9/12 by 2 so both fractions share the common base 24.

3 × 3/8 × 3 = 9/24 and 9 × 2/12 × 2 = 18/24

Step 3

Add the Numerators

Now add the numerators (9 + 18 = 27) and keep the common denominator 24 unchanged.

9 + 18/24 = 27/24

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 24, which is 3. Divide both the numerator and denominator by 3.

27 ÷ 3/24 ÷ 3 = 9/8

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (9) is greater than the denominator (8), divide 9 by 8: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/8.

9/8 = 11/8

Step 6

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 8 yields an exact terminating decimal of 1.125 (or 112.5%).

9 ÷ 8 = 1.125 (112.5%)

Visual Representation

The diagram below illustrates 3/8 plus 9/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/8`
Mixed Number Form	`1 1/8`
Decimal Form	`1.125`
Percentage	`112.5%`

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Frequently Asked Questions

What is 3/8 plus 9/12 as a fraction?

3/8 + 9/12 in simplest fraction form is 9/8 (or 1 1/8 as a mixed number).

What is 3/8 plus 9/12 as a decimal?

3/8 + 9/12 converted to a decimal is 1.125.

What is 3/8 plus 9/12 as a percentage?

3/8 + 9/12 expressed as a percentage is 112.5%.

How do you write 3/8 plus 9/12 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 9/8 can be written as the mixed number 1 1/8.

Does 3/8 plus 9/12 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.125) because the denominator in simplest terms contains only prime factors 2 and/or 5.