Finding the Fraction 7/8: Number Identification Problem

Q: How do I know where 7/8 fits on the number line?

Think of 7/8 as 7 pieces out of 8 total pieces. Since you have almost all the pieces (7 out of 8), it's very close to 1 whole, so it falls between $ \frac{1}{2} $ and 1.

Q: Why can't 7/8 be between 0 and 1/2?

Because $ \frac{7}{8} $ is much larger than $ \frac{1}{2} $! Convert to see: $ \frac{1}{2} = \frac{4}{8} $, and clearly $ \frac{7}{8} > \frac{4}{8} $.

Q: What's the easiest way to compare fractions to 1/2?

Convert 1/2 to have the same denominator! For example, $ \frac{1}{2} = \frac{4}{8} $. Now compare numerators: since 7 > 4, we know $ \frac{7}{8} > \frac{1}{2} $.

Q: How close is 7/8 to 1?

$ \frac{7}{8} $ is very close to 1! It's only $ \frac{1}{8} $ away from 1 whole. Think of it as missing just 1 piece out of 8.

Q: Can I use decimals to check my answer?

Absolutely! Convert to decimals: $ \frac{1}{2} = 0.5 $, $ \frac{7}{8} = 0.875 $, and 1 = 1.0. Clearly 0.5

Fraction Ordering with Benchmark Comparisons

The number $\frac{7}{8}$ 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

00:04 Draw the number line and place the given number

00:09 Place each number in the range with common denominator (8)

00:14 Reduce the whole numbers and find the range

00:23 We can see that the number is in this range

00:29 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 $\frac{7}{8}$ is found...

Step-by-step solution

Since the denominator is 8, both the larger and smaller numbers will also have a denominator of 8:

$\frac{?}{8}<\frac{7}{8}<\frac{?}{8}$

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

$\frac{4}{8} < \frac{7}{8} < \frac{8}{8}$

Next, we will simplify the fractions as follows:

$\frac{4:4}{8:4}=\frac{1}{2}$

$\frac{8:8}{8:8}=\frac{1}{1}=1$

Therefore, the answer is:

$\frac{1}{2}<\frac{7}{8}<1$

Final Answer

...between $\frac{1}{2}$ to $1$ .

Key Points to Remember

Essential concepts to master this topic

Rule: Compare fractions to benchmark values like 1/2 and 1
Technique: Convert 4/8 = 1/2 and 8/8 = 1 to find boundaries
Check: Verify 1/2 < 7/8 < 1 by cross-multiplying: 4 < 7 < 8 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators without considering denominators
Don't just look at 7 and think it's close to whole numbers = wrong placement! The denominator 8 matters just as much. Always consider the fraction as 7 parts out of 8 total parts.

Practice Quiz

Test your knowledge with interactive questions

What are the missing numbers (?) on the numer line below?

FAQ

Everything you need to know about this question

How do I know where 7/8 fits on the number line?

Think of 7/8 as 7 pieces out of 8 total pieces. Since you have almost all the pieces (7 out of 8), it's very close to 1 whole, so it falls between $\frac{1}{2}$ and 1.

Why can't 7/8 be between 0 and 1/2?

Because $\frac{7}{8}$ is much larger than $\frac{1}{2}$ ! Convert to see: $\frac{1}{2} = \frac{4}{8}$ , and clearly $\frac{7}{8} > \frac{4}{8}$ .

What's the easiest way to compare fractions to 1/2?

Convert 1/2 to have the same denominator! For example, $\frac{1}{2} = \frac{4}{8}$ . Now compare numerators: since 7 > 4, we know $\frac{7}{8} > \frac{1}{2}$ .

How close is 7/8 to 1?

$\frac{7}{8}$ is very close to 1! It's only $\frac{1}{8}$ away from 1 whole. Think of it as missing just 1 piece out of 8.

Can I use decimals to check my answer?

Absolutely! Convert to decimals: $\frac{1}{2} = 0.5$ , $\frac{7}{8} = 0.875$ , and 1 = 1.0. Clearly 0.5 < 0.875 < 1.0 ✓

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