What is 3/8 plus 4/5? (Answer: 47/40)

Exact Answer

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Problem: What is 3/8 plus 4/5?
Formula / Expression: 3/8 + 4/5
Final Answer: 1 7/40 (47/40)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.
Working: LCD(8, 5) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 3/8 by 5, and multiply the numerator and denominator of 4/5 by 8 so both fractions share the common base 40.
Working: 3 × 5/8 × 5 = 15/40 and 4 × 8/5 × 8 = 32/40

Step 3: Add the Numerators
Now add the numerators (15 + 32 = 47) and keep the common denominator 40 unchanged.
Working: 15 + 32/40 = 47/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 40 is 1, confirming that 47/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (47) is greater than the denominator (40), divide 47 by 40: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/40.
Working: 47/40 = 1 7/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 40 yields an exact terminating decimal of 1.175 (or 117.5%).
Working: 47 ÷ 40 = 1.175 (117.5%)

Key Values:
- Simplified Fraction: 47/40
- Mixed Number Form: 1 7/40
- Decimal Value: 1.175
- Percentage: 117.5%

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Solved with FractionsCalc:
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3/8 + 4/5 = 47/40

Simplified Fraction

47/40

Mixed Number

1 7/40

Decimal Value

1.175

Percentage

117.5%

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Step-by-Step Solution: 3/8 + 4/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.

LCD(8, 5) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

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

3 × 5/8 × 5 = 15/40 and 4 × 8/5 × 8 = 32/40

Step 3

Add the Numerators

Now add the numerators (15 + 32 = 47) and keep the common denominator 40 unchanged.

15 + 32/40 = 47/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 40 is 1, confirming that 47/40 cannot be reduced further—it is already in its simplest irreducible form.

47/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (47) is greater than the denominator (40), divide 47 by 40: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/40.

47/40 = 17/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 40 yields an exact terminating decimal of 1.175 (or 117.5%).

47 ÷ 40 = 1.175 (117.5%)

Visual Representation

The diagram below illustrates 3/8 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/40`
Mixed Number Form	`1 7/40`
Decimal Form	`1.175`
Percentage	`117.5%`

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Frequently Asked Questions

What is 3/8 plus 4/5 as a fraction?

3/8 + 4/5 in simplest fraction form is 47/40 (or 1 7/40 as a mixed number).

What is 3/8 plus 4/5 as a decimal?

3/8 + 4/5 converted to a decimal is 1.175.

What is 3/8 plus 4/5 as a percentage?

3/8 + 4/5 expressed as a percentage is 117.5%.

How do you write 3/8 plus 4/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 47/40 can be written as the mixed number 1 7/40.

Does 3/8 plus 4/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.175) because the denominator in simplest terms contains only prime factors 2 and/or 5.