What is 1/2 times 2/3? (Answer: 1/3)

Exact Answer

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Problem: What is 1/2 times 2/3?
Formula / Expression: 1/2 × 2/3
Final Answer: 1/3
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Step-by-Step Solution:

Step 1: Multiply the Numerators Together
Multiply the top numbers (numerators) of both fractions: 1 × 2 = 2.
Working: 1 × 2 = 2

Step 2: Multiply the Denominators Together
Multiply the bottom numbers (denominators) of both fractions: 2 × 3 = 6.
Working: 1 × 2/2 × 3 = 2/6

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 2 and 6, which is 2. Divide both the numerator and denominator by 2.
Working: 2 ÷ 2/6 ÷ 2 = 1/3

Step 4: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).
Working: 1 ÷ 3 = 0.333333 (33.3333%)

Key Values:
- Simplified Fraction: 1/3
- Mixed Number Form: 1/3
- Decimal Value: 0.333333
- Percentage: 33.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-times-2-3/
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1/2 × 2/3 = 1/3

Simplified Fraction

1/3

Mixed Number

Proper (1/3)

Decimal Value

0.333333

Percentage

33.3333%

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Step-by-Step Solution: 1/2 × 2/3

Step 1

Multiply the Numerators Together

Multiply the top numbers (numerators) of both fractions: 1 × 2 = 2.

1 × 2 = 2

Step 2

Multiply the Denominators Together

Multiply the bottom numbers (denominators) of both fractions: 2 × 3 = 6.

1 × 2/2 × 3 = 2/6

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 2 and 6, which is 2. Divide both the numerator and denominator by 2.

2 ÷ 2/6 ÷ 2 = 1/3

Step 4

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).

1 ÷ 3 = 0.333333 (33.3333%)

Visual Representation

The diagram below illustrates 1/2 times 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/3`
Mixed Number Form	`1/3`
Decimal Form	`0.333333`
Percentage	`33.3333%`

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Frequently Asked Questions

What is 1/2 times 2/3 as a fraction?

1/2 × 2/3 in simplest fraction form is 1/3.

What is 1/2 times 2/3 as a decimal?

1/2 × 2/3 converted to a decimal is 0.333333.

What is 1/2 times 2/3 as a percentage?

1/2 × 2/3 expressed as a percentage is 33.3333%.

Does 1/2 times 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.333333...) because the denominator contains prime factors other than 2 and 5.