Converting the Fraction 10/3: Find the Decimal Equivalent

Q: Why can't I just divide 10 by 3 to get the answer?

You can! But understanding where the fraction falls between whole numbers helps you check if your decimal answer makes sense. $ \frac{10}{3} = 3.333... $ should fall between 3 and 4.

Q: How do I find the right fractions to compare with?

Look for multiples of the denominator in the numerator! Since we have thirds, use $ \frac{9}{3} $ and $ \frac{12}{3} $ because 9 and 12 are close multiples of 3.

Q: What if the fraction is larger than expected?

That's normal! Improper fractions (where numerator > denominator) always give values greater than 1. $ \frac{10}{3} $ is improper, so it must be bigger than 1.

Q: Is there a faster way to estimate fractions?

Yes! Divide the numerator by the denominator: $ 10 ÷ 3 = 3 $ remainder $ 1 $. This means it's 3 and something, so between 3 and 4!

Q: Why do we need to reduce fractions like 9/3?

Reducing fractions helps you see the whole number clearly. $ \frac{9}{3} = 3 $ is much easier to work with than keeping it as a fraction!

Fraction Comparison with Whole Number Bounds

The number $\frac{10}{3}$ is found...

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the range in which the number is located

00:03 Draw the number line and place the given number

00:09 Place each number in the range with a common denominator (3)

00:14 Narrow down the whole numbers and find the range

00:20 We can see that the number is in this range

00:23 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The number $\frac{10}{3}$ is found...

Step-by-step solution

Let's first try to understand what is larger and what is smaller than the number $\frac{10}{3}$ .

Since the denominator is 3, both the larger and smaller numbers will also have a denominator of 3:

$\frac{?}{3}<\frac{10}{3}<\frac{?}{3}$

Now let's complete the numerators with numbers that will help us reach round numbers in the fractions as follows:

$\frac{9}{3}<\frac{10}{3}<\frac{12}{3}$

We'll then reduce the fractions as follows:

$\frac{12:3}{3:3}=\frac{4}{1}=4$

$\frac{9:3}{3:3}=\frac{3}{1}=3$

Therefore, the answer is:

$3<\frac{10}{3}<4$

Final Answer

...between $3$ to $4$ .

Key Points to Remember

Essential concepts to master this topic

Rule: Compare fractions by finding equivalent fractions with whole numbers
Technique: Use $\frac{9}{3} = 3$ and $\frac{12}{3} = 4$ as bounds
Check: Verify $3 < 3.33... < 4$ by converting to decimal ✓

Common Mistakes

Avoid these frequent errors

Converting to decimal without understanding the fraction's position
Don't just calculate 10÷3 = 3.33... without thinking about bounds! This skips the logical reasoning step and makes you guess instead of understanding. Always find nearby whole numbers first by using equivalent fractions like 9/3 and 12/3.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

Why can't I just divide 10 by 3 to get the answer?

You can! But understanding where the fraction falls between whole numbers helps you check if your decimal answer makes sense. $\frac{10}{3} = 3.333...$ should fall between 3 and 4.

How do I find the right fractions to compare with?

Look for multiples of the denominator in the numerator! Since we have thirds, use $\frac{9}{3}$ and $\frac{12}{3}$ because 9 and 12 are close multiples of 3.

What if the fraction is larger than expected?

That's normal! Improper fractions (where numerator > denominator) always give values greater than 1. $\frac{10}{3}$ is improper, so it must be bigger than 1.

Is there a faster way to estimate fractions?

Yes! Divide the numerator by the denominator: $10 ÷ 3 = 3$ remainder $1$ . This means it's 3 and something, so between 3 and 4!

Why do we need to reduce fractions like 9/3?

Reducing fractions helps you see the whole number clearly. $\frac{9}{3} = 3$ is much easier to work with than keeping it as a fraction!

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