What is 3/8 plus 9/18? (Answer: 7/8)

Exact Answer

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Problem: What is 3/8 plus 9/18?
Formula / Expression: 3/8 + 9/18
Final Answer: 7/8
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 8 × 18 = 144, keeping the calculation simpler).
Working: LCD(8, 18) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 3/8 by 9, and multiply the numerator and denominator of 9/18 by 4 so both fractions share the common base 72.
Working: 3 × 9/8 × 9 = 27/72 and 9 × 4/18 × 4 = 36/72

Step 3: Add the Numerators
Now add the numerators (27 + 36 = 63) and keep the common denominator 72 unchanged.
Working: 27 + 36/72 = 63/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 72, which is 9. Divide both the numerator and denominator by 9.
Working: 63 ÷ 9/72 ÷ 9 = 7/8

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 8 yields an exact terminating decimal of 0.875 (or 87.5%).
Working: 7 ÷ 8 = 0.875 (87.5%)

Key Values:
- Simplified Fraction: 7/8
- Mixed Number Form: 7/8
- Decimal Value: 0.875
- Percentage: 87.5%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-8-plus-9-18/
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3/8 + 9/18 = 7/8

Simplified Fraction

7/8

Mixed Number

Proper (7/8)

Decimal Value

0.875

Percentage

87.5%

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Step-by-Step Solution: 3/8 + 9/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 8 × 18 = 144, keeping the calculation simpler).

LCD(8, 18) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 3/8 by 9, and multiply the numerator and denominator of 9/18 by 4 so both fractions share the common base 72.

3 × 9/8 × 9 = 27/72 and 9 × 4/18 × 4 = 36/72

Step 3

Add the Numerators

Now add the numerators (27 + 36 = 63) and keep the common denominator 72 unchanged.

27 + 36/72 = 63/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 72, which is 9. Divide both the numerator and denominator by 9.

63 ÷ 9/72 ÷ 9 = 7/8

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 8 yields an exact terminating decimal of 0.875 (or 87.5%).

7 ÷ 8 = 0.875 (87.5%)

Visual Representation

The diagram below illustrates 3/8 plus 9/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/8`
Mixed Number Form	`7/8`
Decimal Form	`0.875`
Percentage	`87.5%`

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Frequently Asked Questions

What is 3/8 plus 9/18 as a fraction?

3/8 + 9/18 in simplest fraction form is 7/8.

What is 3/8 plus 9/18 as a decimal?

3/8 + 9/18 converted to a decimal is 0.875.

What is 3/8 plus 9/18 as a percentage?

3/8 + 9/18 expressed as a percentage is 87.5%.

Does 3/8 plus 9/18 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.875) because the denominator in simplest terms contains only prime factors 2 and/or 5.