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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 15 is an exact multiple of 3 (3 × 5 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.
Working: LCD(3, 15) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 2/3 by 5, and multiply the numerator and denominator of 10/15 by 1 so both fractions share the common base 15.
Working: 2 × 5/3 × 5 = 10/15 and 10 × 1/15 × 1 = 10/15

Step 3: Add the Numerators
Now add the numerators (10 + 10 = 20) and keep the common denominator 15 unchanged.
Working: 10 + 10/15 = 20/15

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 15, which is 5. Divide both the numerator and denominator by 5.
Working: 20 ÷ 5/15 ÷ 5 = 4/3

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (4) is greater than the denominator (3), divide 4 by 3: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/3.
Working: 4/3 = 1 1/3

Step 6: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 3 produces a repeating decimal (approximately 1.333333, or 133.3333%).
Working: 4 ÷ 3 = 1.333333 (133.3333%)

Key Values:
- Simplified Fraction: 4/3
- Mixed Number Form: 1 1/3
- Decimal Value: 1.333333
- Percentage: 133.3333%

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

Simplified Fraction

4/3

Mixed Number

1 1/3

Decimal Value

1.333333

Percentage

133.3333%

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Step-by-Step Solution: 2/3 + 10/15

Step 1

Find the Least Common Denominator (LCD)

Notice that 15 is an exact multiple of 3 (3 × 5 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.

LCD(3, 15) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

Multiply the numerator and denominator of 2/3 by 5, and multiply the numerator and denominator of 10/15 by 1 so both fractions share the common base 15.

2 × 5/3 × 5 = 10/15 and 10 × 1/15 × 1 = 10/15

Step 3

Add the Numerators

Now add the numerators (10 + 10 = 20) and keep the common denominator 15 unchanged.

10 + 10/15 = 20/15

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 20 and 15, which is 5. Divide both the numerator and denominator by 5.

20 ÷ 5/15 ÷ 5 = 4/3

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (4) is greater than the denominator (3), divide 4 by 3: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/3.

4/3 = 11/3

Step 6

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 3 produces a repeating decimal (approximately 1.333333, or 133.3333%).

4 ÷ 3 = 1.333333 (133.3333%)

Visual Representation

The diagram below illustrates 2/3 plus 10/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/3`
Mixed Number Form	`1 1/3`
Decimal Form	`1.333333`
Percentage	`133.3333%`

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Frequently Asked Questions

What is 2/3 plus 10/15 as a fraction?

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

What is 2/3 plus 10/15 as a decimal?

2/3 + 10/15 converted to a decimal is 1.333333.

What is 2/3 plus 10/15 as a percentage?

2/3 + 10/15 expressed as a percentage is 133.3333%.

How do you write 2/3 plus 10/15 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 4/3 can be written as the mixed number 1 1/3.

Does 2/3 plus 10/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.333333...) because the denominator contains prime factors other than 2 and 5.