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

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What number is marked on the number axis?

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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