Calculate the Fraction: Converting 2 ÷ 3 to Standard Form

Q: Why does 2 ÷ 3 become 2/3 and not 3/2?

Think of division as sharing! When you divide 2 by 3, you're asking "how much is 2 when shared among 3 parts?" The answer is $ \frac{2}{3} $ of one whole part.

Q: How do I remember which number goes where?

Use this memory trick: "First over Second" - the first number (before ÷) goes on top, the second number (after ÷) goes on bottom!

Q: Is 2/3 the same as 0.666...?

Yes! $ \frac{2}{3} $ equals 0.666... (repeating). The fraction form is exact, while the decimal is an approximation.

Q: Can I simplify 2/3 further?

$ \frac{2}{3} $ is already in simplest form because 2 and 3 share no common factors other than 1. It cannot be reduced further!

Division to Fractions with Standard Form

What fraction results from dividing 2 by 3?

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Step-by-step video solution

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00:00 Find the fraction

00:03 Write division as a fraction

00:12 And this is the solution to the question

Step-by-step written solution

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Understand the problem

What fraction results from dividing 2 by 3?

Step-by-step solution

First, let's write the division exercise:

$2:3$

Now let's write it as a simple fraction, remembering that the numerator is on top and the denominator is on the bottom:

$\frac{2}{3}$

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division a ÷ b equals fraction a/b directly
Technique: Place dividend 2 as numerator, divisor 3 as denominator
Check: Verify $\frac{2}{3} \times 3 = 2$ matches original dividend ✓

Common Mistakes

Avoid these frequent errors

Flipping the numerator and denominator positions
Don't write 2 ÷ 3 as $\frac{3}{2}$ = wrong fraction! This reverses the division and gives 1.5 instead of 0.67. Always remember: dividend becomes numerator, divisor becomes denominator.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

Why does 2 ÷ 3 become 2/3 and not 3/2?

Think of division as sharing! When you divide 2 by 3, you're asking "how much is 2 when shared among 3 parts?" The answer is $\frac{2}{3}$ of one whole part.

How do I remember which number goes where?

Use this memory trick: "First over Second" - the first number (before ÷) goes on top, the second number (after ÷) goes on bottom!

Is 2/3 the same as 0.666...?

Yes! $\frac{2}{3}$ equals 0.666... (repeating). The fraction form is exact, while the decimal is an approximation.

Can I simplify 2/3 further?

$\frac{2}{3}$ is already in simplest form because 2 and 3 share no common factors other than 1. It cannot be reduced further!

What if I get a whole number when dividing?

If division results in a whole number (like 6 ÷ 3 = 2), you can write it as a fraction $\frac{6}{3}$ or simplify to the whole number 2. Both are correct!

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