Finding the Exact Value: Locating 7/5 in Number Systems

Q: How do I know where a fraction belongs on the number line?

Convert the fraction to a decimal or mixed number! For example, $ \frac{7}{5} = 1.4 $ or $ 1\frac{2}{5} $, so it's clearly between 1 and 2.

Q: What if the fraction looks bigger than it actually is?

Don't be fooled by large numerators! Always divide to get the actual value. $ \frac{7}{5} = 7 ÷ 5 = 1.4 $, which is much smaller than 7.

Q: Can I use benchmark fractions to help?

Yes! Use fractions you know well: $ \frac{5}{5} = 1 $, $ \frac{10}{5} = 2 $. Since \( \frac{5}{5} , we know \( 1 .

Q: What's the fastest way to place any fraction?

Divide the numerator by the denominator! This gives you the decimal value instantly, making placement on the number line super easy.

Q: Why can't I just compare the top numbers?

Because the denominator matters! $ \frac{7}{5} $ and $ \frac{7}{10} $ have the same numerator but completely different values: 1.4 vs 0.7.

Fraction Placement with Number Line Positioning

The number $\frac{7}{5}$ 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 where the number is located

00:03 We'll draw the number line and place the given number

00:12 We'll place every number in the range with the common denominator (5)

00:25 We can see that the number is in this range

00:31 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 $\frac{7}{5}$ is found...

Step-by-step solution

Let's first try to understand what is greater and what is smaller than the number $\frac{7}{5}$ .

Since the denominator is 5, both the larger and smaller numbers will also have a denominator of 5:

$\frac{?}{5}<\frac{7}{5}<\frac{?}{5}$

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

$\frac{5}{5}<\frac{7}{5}<\frac{10}{5}$

We'll reduce the fractions as follows:

$\frac{5:5}{5:5}=\frac{1}{1}=1$

$\frac{10:5}{5:5}=\frac{2}{1}=2$

Therefore, the answer is:

$1<\frac{7}{5}<2$

Final Answer

...between $1$ and $2$ .

Key Points to Remember

Essential concepts to master this topic

Convert: Change improper fractions to mixed numbers or decimals
Technique: Find reference fractions like $\frac{5}{5} = 1$ and $\frac{10}{5} = 2$
Check: Verify that $1 < 1.4 < 2$ makes sense on number line ✓

Common Mistakes

Avoid these frequent errors

Comparing only numerators instead of actual fraction values
Don't just look at 7 and think it's bigger than 3 or 4 = wrong placement! This ignores the denominator completely. Always convert fractions to decimals or find equivalent fractions with same denominators to compare properly.

Practice Quiz

Test your knowledge with interactive questions

What number is marked on the number axis?

FAQ

Everything you need to know about this question

How do I know where a fraction belongs on the number line?

Convert the fraction to a decimal or mixed number! For example, $\frac{7}{5} = 1.4$ or $1\frac{2}{5}$ , so it's clearly between 1 and 2.

What if the fraction looks bigger than it actually is?

Don't be fooled by large numerators! Always divide to get the actual value. $\frac{7}{5} = 7 ÷ 5 = 1.4$ , which is much smaller than 7.

Can I use benchmark fractions to help?

Yes! Use fractions you know well: $\frac{5}{5} = 1$ , $\frac{10}{5} = 2$ . Since $\frac{5}{5} < \frac{7}{5} < \frac{10}{5}$ , we know $1 < \frac{7}{5} < 2$ .

What's the fastest way to place any fraction?

Divide the numerator by the denominator! This gives you the decimal value instantly, making placement on the number line super easy.

Why can't I just compare the top numbers?

Because the denominator matters! $\frac{7}{5}$ and $\frac{7}{10}$ have the same numerator but completely different values: 1.4 vs 0.7.

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