Math / Numbers & Operations

QuestionGraph $\frac{3}{4}$ and $\frac{3}{8}$ on the number line.
Compare $\frac{3}{4}$ and $\frac{3}{8}$ .
$\frac{3}{4} < \frac{3}{8}$
$\frac{3}{4} > \frac{3}{8}$

Studdy Solution

STEP 1

What is this asking? We need to mark $\frac{3}{4}$ and $\frac{3}{8}$ on a number line, and then figure out which one is bigger! Watch out! Don't let the same numerator trick you; different denominators mean different sized pieces!

STEP 2

1. Convert to common denominator
2. Graph on number line
3. Compare fractions

STEP 3

To compare these fractions, let's make their denominators the same.
We're doing this because it's like comparing apples and oranges if the denominators are different.
We want to compare the same sized pieces!

STEP 4

Notice that $4$ goes into $8$ two times.
So, we can multiply $\frac{3}{4}$ by $\frac{2}{2}$ to get a denominator of $8$ .
Remember, multiplying by $\frac{2}{2}$ is the same as multiplying by one, so it doesn't change the value of the fraction, just how it looks!

STEP 5

$\frac{3}{4} \cdot \frac{2}{2} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8}$ So, $\frac{3}{4}$ is the same as $\frac{6}{8}$ .

STEP 6

Now, let's find $\frac{6}{8}$ (which is the same as $\frac{3}{4}$ ) and $\frac{3}{8}$ on the number line.
Each tick mark represents $\frac{1}{8}$ , so $\frac{3}{8}$ is three tick marks to the right of zero, and $\frac{6}{8}$ is six tick marks to the right of zero.

STEP 7

Since $\frac{6}{8}$ is further to the right on the number line than $\frac{3}{8}$ , we know that $\frac{6}{8}$ is greater than $\frac{3}{8}$ .

STEP 8

And since $\frac{6}{8}$ is the same as $\frac{3}{4}$ , we can say that $\frac{3}{4}$ is greater than $\frac{3}{8}$ .

STEP 9

$\frac{3}{4} > \frac{3}{8}$

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QuestionGraph $\frac{3}{4}$ and $\frac{3}{8}$ on the number line.
Compare $\frac{3}{4}$ and $\frac{3}{8}$ .
$\frac{3}{4} < \frac{3}{8}$
$\frac{3}{4} > \frac{3}{8}$

Studdy Solution

STEP 1

What is this asking? We need to mark $\frac{3}{4}$ and $\frac{3}{8}$ on a number line, and then figure out which one is bigger! Watch out! Don't let the same numerator trick you; different denominators mean different sized pieces!

STEP 2

1. Convert to common denominator
2. Graph on number line
3. Compare fractions

STEP 3

To compare these fractions, let's make their denominators the same.
We're doing this because it's like comparing apples and oranges if the denominators are different.
We want to compare the same sized pieces!

STEP 4

Notice that $4$ goes into $8$ two times.
So, we can multiply $\frac{3}{4}$ by $\frac{2}{2}$ to get a denominator of $8$ .
Remember, multiplying by $\frac{2}{2}$ is the same as multiplying by one, so it doesn't change the value of the fraction, just how it looks!

STEP 5

$\frac{3}{4} \cdot \frac{2}{2} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8}$ So, $\frac{3}{4}$ is the same as $\frac{6}{8}$ .

STEP 6

Now, let's find $\frac{6}{8}$ (which is the same as $\frac{3}{4}$ ) and $\frac{3}{8}$ on the number line.
Each tick mark represents $\frac{1}{8}$ , so $\frac{3}{8}$ is three tick marks to the right of zero, and $\frac{6}{8}$ is six tick marks to the right of zero.

STEP 7

Since $\frac{6}{8}$ is further to the right on the number line than $\frac{3}{8}$ , we know that $\frac{6}{8}$ is greater than $\frac{3}{8}$ .

STEP 8

And since $\frac{6}{8}$ is the same as $\frac{3}{4}$ , we can say that $\frac{3}{4}$ is greater than $\frac{3}{8}$ .

STEP 9

$\frac{3}{4} > \frac{3}{8}$

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QuestionGraph 34\frac{3}{4}43​ and 38\frac{3}{8}83​ on the number line.Compare 34\frac{3}{4}43​ and 38\frac{3}{8}83​.34<38\frac{3}{4} < \frac{3}{8}43​<83​34>38\frac{3}{4} > \frac{3}{8}43​>83​

Studdy Solution

STEP 1

What is this asking? We need to mark 34\frac{3}{4}43​ and 38\frac{3}{8}83​ on a number line, and then figure out which one is bigger! Watch out! Don't let the same numerator trick you; different denominators mean different sized pieces!

STEP 2

1. Convert to common denominator2. Graph on number line3. Compare fractions

STEP 3

To compare these fractions, let's make their denominators the same.We're doing this because it's like comparing apples and oranges if the denominators are different.We want to compare the same sized pieces!

STEP 4

Notice that 444 goes into 888 **two** times.So, we can multiply 34\frac{3}{4}43​ by 22\frac{2}{2}22​ to get a denominator of 888.Remember, multiplying by 22\frac{2}{2}22​ is the same as multiplying by **one**, so it doesn't change the *value* of the fraction, just how it looks!

STEP 5

34⋅22=3⋅24⋅2=68\frac{3}{4} \cdot \frac{2}{2} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8}43​⋅22​=4⋅23⋅2​=86​ So, 34\frac{3}{4}43​ is the same as 68\frac{6}{8}86​.

STEP 6

Now, let's find 68\frac{6}{8}86​ (which is the same as 34\frac{3}{4}43​) and 38\frac{3}{8}83​ on the number line.Each tick mark represents 18\frac{1}{8}81​, so 38\frac{3}{8}83​ is **three** tick marks to the right of zero, and 68\frac{6}{8}86​ is **six** tick marks to the right of zero.

STEP 7

Since 68\frac{6}{8}86​ is further to the right on the number line than 38\frac{3}{8}83​, we know that 68\frac{6}{8}86​ is **greater than** 38\frac{3}{8}83​.

STEP 8

And since 68\frac{6}{8}86​ is the same as 34\frac{3}{4}43​, we can say that 34\frac{3}{4}43​ is **greater than** 38\frac{3}{8}83​.

STEP 9

34>38\frac{3}{4} > \frac{3}{8}43​>83​

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionGraph $\frac{3}{4}$ and $\frac{3}{8}$ on the number line.
Compare $\frac{3}{4}$ and $\frac{3}{8}$ .
$\frac{3}{4} < \frac{3}{8}$
$\frac{3}{4} > \frac{3}{8}$

What is this asking? We need to mark $\frac{3}{4}$ and $\frac{3}{8}$ on a number line, and then figure out which one is bigger! Watch out! Don't let the same numerator trick you; different denominators mean different sized pieces!

1. Convert to common denominator
2. Graph on number line
3. Compare fractions

To compare these fractions, let's make their denominators the same.
We're doing this because it's like comparing apples and oranges if the denominators are different.
We want to compare the same sized pieces!

Notice that $4$ goes into $8$ two times.
So, we can multiply $\frac{3}{4}$ by $\frac{2}{2}$ to get a denominator of $8$ .
Remember, multiplying by $\frac{2}{2}$ is the same as multiplying by one, so it doesn't change the value of the fraction, just how it looks!

$\frac{3}{4} \cdot \frac{2}{2} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8}$ So, $\frac{3}{4}$ is the same as $\frac{6}{8}$ .

Now, let's find $\frac{6}{8}$ (which is the same as $\frac{3}{4}$ ) and $\frac{3}{8}$ on the number line.
Each tick mark represents $\frac{1}{8}$ , so $\frac{3}{8}$ is three tick marks to the right of zero, and $\frac{6}{8}$ is six tick marks to the right of zero.

Since $\frac{6}{8}$ is further to the right on the number line than $\frac{3}{8}$ , we know that $\frac{6}{8}$ is greater than $\frac{3}{8}$ .

And since $\frac{6}{8}$ is the same as $\frac{3}{4}$ , we can say that $\frac{3}{4}$ is greater than $\frac{3}{8}$ .

$\frac{3}{4} > \frac{3}{8}$