Math / Numbers & Operations

QuestionSUbmit Test Reader
Drag each expression to the correct location on the number line. Not all expressions will be used. Evaluate the expressions. Then, place the expressions on the corresponding locations on the number line. $\begin{array}{lllll} \frac{5}{7}+\pi & \frac{5 \pi}{5}+2 & 5 \sqrt{7}-6 & \frac{19}{\pi}-5.5 & \sqrt{5}+2 \sqrt{3} \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to calculate the value of a bunch of expressions with square roots and $\pi$ , and then place them on a number line! Watch out! Don't mix up the order of operations, especially when dealing with roots and fractions.
Also, remember that $\pi$ is approximately 3.14.

STEP 2

1. Calculate the values
2. Place on the number line

STEP 3

Let's start with $\frac{5}{7} + \pi$ .
Remember $\pi \approx 3.14$ .
Since $\frac{5}{7}$ is a little less than 1, let's say approximately 0.71.
So, $\frac{5}{7} + \pi \approx 0.71 + 3.14 = \mathbf{3.85}$ .

STEP 4

Next up: $\frac{5\pi}{5} + 2$ .
Notice that the fives cancel out by dividing to one, leaving us with $\pi + 2$ .
So, $\pi + 2 \approx 3.14 + 2 = \mathbf{5.14}$ .

STEP 5

Now for $5\sqrt{7} - 6$ .
We know that $\sqrt{7}$ is between $\sqrt{4}=2$ and $\sqrt{9}=3$ .
It's actually about 2.65.
So, $5\sqrt{7} - 6 \approx 5 \cdot 2.65 - 6 = 13.25 - 6 = \mathbf{7.25}$ .

STEP 6

Let's tackle $\frac{19}{\pi} - 5.5$ .
We can approximate this as $\frac{19}{3.14} - 5.5$ .
This gives us roughly $6.05 - 5.5 = \mathbf{0.55}$ .

STEP 7

Finally, we have $\sqrt{5} + 2\sqrt{3}$ . $\sqrt{5}$ is approximately 2.24, and $\sqrt{3}$ is approximately 1.73.
So, $\sqrt{5} + 2\sqrt{3} \approx 2.24 + 2 \cdot 1.73 = 2.24 + 3.46 = \mathbf{5.7}$ .

STEP 8

Now that we have all the approximate values, we can put them on the number line.
From smallest to largest, we have: $\frac{19}{\pi} - 5.5 \approx 0.55$ , $\frac{5}{7} + \pi \approx 3.85$ , $\sqrt{5} + 2\sqrt{3} \approx 5.7$ , $\frac{5\pi}{5} + 2 \approx 5.14$ , and $5\sqrt{7} - 6 \approx 7.25$ .

STEP 9

Place the expressions on the number line in this order from left to right: $\frac{19}{\pi} - 5.5$ , $\frac{5}{7} + \pi$ , $\frac{5\pi}{5} + 2$ , $\sqrt{5} + 2\sqrt{3}$ , and $5\sqrt{7} - 6$ .

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Studdy Solution

STEP 1

What is this asking? We need to calculate the value of a bunch of expressions with square roots and $\pi$ , and then place them on a number line! Watch out! Don't mix up the order of operations, especially when dealing with roots and fractions.
Also, remember that $\pi$ is approximately 3.14.

STEP 2

1. Calculate the values
2. Place on the number line

STEP 3

Let's start with $\frac{5}{7} + \pi$ .
Remember $\pi \approx 3.14$ .
Since $\frac{5}{7}$ is a little less than 1, let's say approximately 0.71.
So, $\frac{5}{7} + \pi \approx 0.71 + 3.14 = \mathbf{3.85}$ .

STEP 4

Next up: $\frac{5\pi}{5} + 2$ .
Notice that the fives cancel out by dividing to one, leaving us with $\pi + 2$ .
So, $\pi + 2 \approx 3.14 + 2 = \mathbf{5.14}$ .

STEP 5

Now for $5\sqrt{7} - 6$ .
We know that $\sqrt{7}$ is between $\sqrt{4}=2$ and $\sqrt{9}=3$ .
It's actually about 2.65.
So, $5\sqrt{7} - 6 \approx 5 \cdot 2.65 - 6 = 13.25 - 6 = \mathbf{7.25}$ .

STEP 6

Let's tackle $\frac{19}{\pi} - 5.5$ .
We can approximate this as $\frac{19}{3.14} - 5.5$ .
This gives us roughly $6.05 - 5.5 = \mathbf{0.55}$ .

STEP 7

Finally, we have $\sqrt{5} + 2\sqrt{3}$ . $\sqrt{5}$ is approximately 2.24, and $\sqrt{3}$ is approximately 1.73.
So, $\sqrt{5} + 2\sqrt{3} \approx 2.24 + 2 \cdot 1.73 = 2.24 + 3.46 = \mathbf{5.7}$ .

STEP 8

Now that we have all the approximate values, we can put them on the number line.
From smallest to largest, we have: $\frac{19}{\pi} - 5.5 \approx 0.55$ , $\frac{5}{7} + \pi \approx 3.85$ , $\sqrt{5} + 2\sqrt{3} \approx 5.7$ , $\frac{5\pi}{5} + 2 \approx 5.14$ , and $5\sqrt{7} - 6 \approx 7.25$ .

STEP 9

Place the expressions on the number line in this order from left to right: $\frac{19}{\pi} - 5.5$ , $\frac{5}{7} + \pi$ , $\frac{5\pi}{5} + 2$ , $\sqrt{5} + 2\sqrt{3}$ , and $5\sqrt{7} - 6$ .

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Studdy Solution

STEP 1

What is this asking? We need to calculate the value of a bunch of expressions with square roots and π\piπ, and then place them on a number line! Watch out! Don't mix up the order of operations, especially when dealing with roots and fractions.Also, remember that π\piπ is approximately 3.14.

STEP 2

1. Calculate the values2. Place on the number line

STEP 3

Let's **start** with 57+π\frac{5}{7} + \pi75​+π.Remember π≈3.14\pi \approx 3.14π≈3.14.Since 57\frac{5}{7}75​ is a little less than 1, let's say approximately 0.71.So, 57+π≈0.71+3.14=3.85\frac{5}{7} + \pi \approx 0.71 + 3.14 = \mathbf{3.85}75​+π≈0.71+3.14=3.85.

STEP 4

Next up: 5π5+2\frac{5\pi}{5} + 255π​+2.Notice that the fives **cancel out** by dividing to one, leaving us with π+2\pi + 2π+2.So, π+2≈3.14+2=5.14\pi + 2 \approx 3.14 + 2 = \mathbf{5.14}π+2≈3.14+2=5.14.

STEP 5

Now for 57−65\sqrt{7} - 657​−6.We know that 7\sqrt{7}7​ is between 4=2\sqrt{4}=24​=2 and 9=3\sqrt{9}=39​=3.It's actually about 2.65.So, 57−6≈5⋅2.65−6=13.25−6=7.255\sqrt{7} - 6 \approx 5 \cdot 2.65 - 6 = 13.25 - 6 = \mathbf{7.25}57​−6≈5⋅2.65−6=13.25−6=7.25.

STEP 6

Let's tackle 19π−5.5\frac{19}{\pi} - 5.5π19​−5.5.We can approximate this as 193.14−5.5\frac{19}{3.14} - 5.53.1419​−5.5.This gives us roughly 6.05−5.5=0.556.05 - 5.5 = \mathbf{0.55}6.05−5.5=0.55.

STEP 7

Finally, we have 5+23\sqrt{5} + 2\sqrt{3}5​+23​. 5\sqrt{5}5​ is approximately 2.24, and 3\sqrt{3}3​ is approximately 1.73.So, 5+23≈2.24+2⋅1.73=2.24+3.46=5.7\sqrt{5} + 2\sqrt{3} \approx 2.24 + 2 \cdot 1.73 = 2.24 + 3.46 = \mathbf{5.7}5​+23​≈2.24+2⋅1.73=2.24+3.46=5.7.

STEP 8

STEP 9

Place the expressions on the number line in this order from left to right: 19π−5.5\frac{19}{\pi} - 5.5π19​−5.5, 57+π\frac{5}{7} + \pi75​+π, 5π5+2\frac{5\pi}{5} + 255π​+2, 5+23\sqrt{5} + 2\sqrt{3}5​+23​, and 57−65\sqrt{7} - 657​−6.

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What is this asking? We need to calculate the value of a bunch of expressions with square roots and $\pi$ , and then place them on a number line! Watch out! Don't mix up the order of operations, especially when dealing with roots and fractions.
Also, remember that $\pi$ is approximately 3.14.

1. Calculate the values
2. Place on the number line

Let's start with $\frac{5}{7} + \pi$ .
Remember $\pi \approx 3.14$ .
Since $\frac{5}{7}$ is a little less than 1, let's say approximately 0.71.
So, $\frac{5}{7} + \pi \approx 0.71 + 3.14 = \mathbf{3.85}$ .

Next up: $\frac{5\pi}{5} + 2$ .
Notice that the fives cancel out by dividing to one, leaving us with $\pi + 2$ .
So, $\pi + 2 \approx 3.14 + 2 = \mathbf{5.14}$ .

Now for $5\sqrt{7} - 6$ .
We know that $\sqrt{7}$ is between $\sqrt{4}=2$ and $\sqrt{9}=3$ .
It's actually about 2.65.
So, $5\sqrt{7} - 6 \approx 5 \cdot 2.65 - 6 = 13.25 - 6 = \mathbf{7.25}$ .

Let's tackle $\frac{19}{\pi} - 5.5$ .
We can approximate this as $\frac{19}{3.14} - 5.5$ .
This gives us roughly $6.05 - 5.5 = \mathbf{0.55}$ .

Finally, we have $\sqrt{5} + 2\sqrt{3}$ . $\sqrt{5}$ is approximately 2.24, and $\sqrt{3}$ is approximately 1.73.
So, $\sqrt{5} + 2\sqrt{3} \approx 2.24 + 2 \cdot 1.73 = 2.24 + 3.46 = \mathbf{5.7}$ .

Place the expressions on the number line in this order from left to right: $\frac{19}{\pi} - 5.5$ , $\frac{5}{7} + \pi$ , $\frac{5\pi}{5} + 2$ , $\sqrt{5} + 2\sqrt{3}$ , and $5\sqrt{7} - 6$ .