What is 3/10 plus 3/8? (Answer: 27/40)

Exact Answer

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Problem: What is 3/10 plus 3/8?
Formula / Expression: 3/10 + 3/8
Final Answer: 27/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 10 × 8 = 80, keeping the calculation simpler).
Working: LCD(10, 8) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 3/10 by 4, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.
Working: 3 × 4/10 × 4 = 12/40 and 3 × 5/8 × 5 = 15/40

Step 3: Add the Numerators
Now add the numerators (12 + 15 = 27) and keep the common denominator 40 unchanged.
Working: 12 + 15/40 = 27/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 27 and 40 is 1, confirming that 27/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 27/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 40 yields an exact terminating decimal of 0.675 (or 67.5%).
Working: 27 ÷ 40 = 0.675 (67.5%)

Key Values:
- Simplified Fraction: 27/40
- Mixed Number Form: 27/40
- Decimal Value: 0.675
- Percentage: 67.5%

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Solved with FractionsCalc:
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3/10 + 3/8 = 27/40

Simplified Fraction

27/40

Mixed Number

Proper (27/40)

Decimal Value

0.675

Percentage

67.5%

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Step-by-Step Solution: 3/10 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 10 × 8 = 80, keeping the calculation simpler).

LCD(10, 8) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 3/10 by 4, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.

3 × 4/10 × 4 = 12/40 and 3 × 5/8 × 5 = 15/40

Step 3

Add the Numerators

Now add the numerators (12 + 15 = 27) and keep the common denominator 40 unchanged.

12 + 15/40 = 27/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 27 and 40 is 1, confirming that 27/40 cannot be reduced further—it is already in its simplest irreducible form.

27/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 40 yields an exact terminating decimal of 0.675 (or 67.5%).

27 ÷ 40 = 0.675 (67.5%)

Visual Representation

The diagram below illustrates 3/10 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/40`
Mixed Number Form	`27/40`
Decimal Form	`0.675`
Percentage	`67.5%`

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Frequently Asked Questions

What is 3/10 plus 3/8 as a fraction?

3/10 + 3/8 in simplest fraction form is 27/40.

What is 3/10 plus 3/8 as a decimal?

3/10 + 3/8 converted to a decimal is 0.675.

What is 3/10 plus 3/8 as a percentage?

3/10 + 3/8 expressed as a percentage is 67.5%.

Does 3/10 plus 3/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.675) because the denominator in simplest terms contains only prime factors 2 and/or 5.