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Find four rational numbers between 1 and 2.

To find four rational numbers between 1 and 2, we can express them as fractions with a common denominator.
Since we need to find $n=4$ rational numbers, we multiply the numerator and denominator by $(n+1)=5$ .
$1 = \frac{1 \times 5}{5} = \frac{5}{5}$ $2 = \frac{2 \times 5}{5} = \frac{10}{5}$
Now, we can easily find four rational numbers between $\frac{5}{5}$ and $\frac{10}{5}$ .
$\frac{6}{5}, \frac{7}{5}, \frac{8}{5}, \frac{9}{5}$
Answer: $\boxed{\frac{6}{5}, \frac{7}{5}, \frac{8}{5}, \frac{9}{5}}$
1. Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ .
To find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ , we express them as fractions with a common denominator.
Since we need to find $n=5$ rational numbers, we multiply the numerator and denominator by $(n+1)=6$ .
$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$ $\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}$
Now, we can easily find five rational numbers between $\frac{18}{30}$ and $\frac{24}{30}$ .
$\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}$
Answer: $\boxed{\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}}$
1. Locate $\sqrt{3}$ on the number line.
Draw a number line.
Mark point O at 0 and point A at 1.
At point A, draw a perpendicular line segment AB of length 1 unit.
Join O and B.
By the Pythagorean theorem, the length of OB is $\sqrt{OA^2 + AB^2} = \sqrt{1^2 + 1^2} = \sqrt{2}$ .
At point B, draw a perpendicular line segment BC of length 1 unit to OB.
Join O and C.
By the Pythagorean theorem, the length of OC is $\sqrt{OB^2 + BC^2} = \sqrt{(\sqrt{2})^2 + 1^2} = \sqrt{2+1} = \sqrt{3}$ .
With O as the center and OC as the radius, draw an arc that intersects the number line.
This intersection point represents $\sqrt{3}$ .

Answer: $\boxed{\text{Follow the steps above to locate } \sqrt{3} \text{ on the number line.}}$

Questions and answers in english

Step-by-step solution

To find four rational numbers between 1 and 2, we can express them as fractions with a common denominator.

Now, we can easily find four rational numbers between $\frac{5}{5}$ and $\frac{10}{5}$ .

To find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ , we express them as fractions with a common denominator.

Now, we can easily find five rational numbers between $\frac{18}{30}$ and $\frac{24}{30}$ .

Draw a number line.

At point A, draw a perpendicular line segment AB of length 1 unit.

Join O and B.

At point B, draw a perpendicular line segment BC of length 1 unit to OB.

Join O and C.

With O as the center and OC as the radius, draw an arc that intersects the number line.

Still stuck on this one?

More English Questions

Questions and answers in english

Step-by-step solution

To find four rational numbers between 1 and 2, we can express them as fractions with a common denominator.

Now, we can easily find four rational numbers between 55\frac{5}{5}55​ and 105\frac{10}{5}510​.

To find five rational numbers between 35\frac{3}{5}53​ and 45\frac{4}{5}54​, we express them as fractions with a common denominator.

Now, we can easily find five rational numbers between 1830\frac{18}{30}3018​ and 2430\frac{24}{30}3024​.

Draw a number line.

At point A, draw a perpendicular line segment AB of length 1 unit.

Join O and B.

At point B, draw a perpendicular line segment BC of length 1 unit to OB.

Join O and C.

With O as the center and OC as the radius, draw an arc that intersects the number line.

Still stuck on this one?

More English Questions

Now, we can easily find four rational numbers between $\frac{5}{5}$ and $\frac{10}{5}$ .

To find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ , we express them as fractions with a common denominator.

Now, we can easily find five rational numbers between $\frac{18}{30}$ and $\frac{24}{30}$ .