What is 4/10 plus 2/3? (Answer: 16/15)

Exact Answer

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Problem: What is 4/10 plus 2/3?
Formula / Expression: 4/10 + 2/3
Final Answer: 1 1/15 (16/15)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 3 = 30.
Working: LCD(10, 3) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 4/10 by 3, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.
Working: 4 × 3/10 × 3 = 12/30 and 2 × 10/3 × 10 = 20/30

Step 3: Add the Numerators
Now add the numerators (12 + 20 = 32) and keep the common denominator 30 unchanged.
Working: 12 + 20/30 = 32/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 32 ÷ 2/30 ÷ 2 = 16/15

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (16) is greater than the denominator (15), divide 16 by 15: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/15.
Working: 16/15 = 1 1/15

Step 6: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 15 produces a repeating decimal (approximately 1.066667, or 106.6667%).
Working: 16 ÷ 15 = 1.066667 (106.6667%)

Key Values:
- Simplified Fraction: 16/15
- Mixed Number Form: 1 1/15
- Decimal Value: 1.066667
- Percentage: 106.6667%

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Solved with FractionsCalc:
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4/10 + 2/3 = 16/15

Simplified Fraction

16/15

Mixed Number

1 1/15

Decimal Value

1.066667

Percentage

106.6667%

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Step-by-Step Solution: 4/10 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 3 = 30.

LCD(10, 3) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 4/10 by 3, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.

4 × 3/10 × 3 = 12/30 and 2 × 10/3 × 10 = 20/30

Step 3

Add the Numerators

Now add the numerators (12 + 20 = 32) and keep the common denominator 30 unchanged.

12 + 20/30 = 32/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 30, which is 2. Divide both the numerator and denominator by 2.

32 ÷ 2/30 ÷ 2 = 16/15

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (16) is greater than the denominator (15), divide 16 by 15: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/15.

16/15 = 11/15

Step 6

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 15 produces a repeating decimal (approximately 1.066667, or 106.6667%).

16 ÷ 15 = 1.066667 (106.6667%)

Visual Representation

The diagram below illustrates 4/10 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/15`
Mixed Number Form	`1 1/15`
Decimal Form	`1.066667`
Percentage	`106.6667%`

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Frequently Asked Questions

What is 4/10 plus 2/3 as a fraction?

4/10 + 2/3 in simplest fraction form is 16/15 (or 1 1/15 as a mixed number).

What is 4/10 plus 2/3 as a decimal?

4/10 + 2/3 converted to a decimal is 1.066667.

What is 4/10 plus 2/3 as a percentage?

4/10 + 2/3 expressed as a percentage is 106.6667%.

How do you write 4/10 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 16/15 can be written as the mixed number 1 1/15.

Does 4/10 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.066667...) because the denominator contains prime factors other than 2 and 5.