Math / Algebra

QuestionSolve: $\frac{2}{3} t=6$ $\mathrm{t}=$

Studdy Solution

STEP 1

What is this asking? Find out what number $t$ must be so that when you multiply it by $\frac{2}{3}$ , you get $6$ . Watch out! Don't forget to multiply by the reciprocal to isolate $t$ !

STEP 2

1. Understand the equation
2. Isolate $t$
3. Solve for $t$

STEP 3

Alright, let's break this down!
We have the equation $\frac{2}{3} \cdot t = 6$ .
This means that $\frac{2}{3}$ of some number $t$ gives us $6$ .
Our mission is to find out what that number $t$ is!

STEP 4

To get $t$ by itself, we need to "undo" the multiplication by $\frac{2}{3}$ .
The best way to do this is by multiplying both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
This will help us "add to one" on the left side, leaving $t$ all alone!

STEP 5

Let's do the math!
Multiply both sides by $\frac{3}{2}$ :
$\frac{3}{2} \cdot \left(\frac{2}{3} \cdot t\right) = \frac{3}{2} \cdot 6$

STEP 6

On the left side, the $\frac{3}{2}$ and $\frac{2}{3}$ multiply to make 1:
$\left(\frac{3 \cdot 2}{2 \cdot 3}\right) \cdot t = 1 \cdot t = t$

STEP 7

Now, let's handle the right side:
$\frac{3}{2} \cdot 6 = \frac{3 \cdot 6}{2} = \frac{18}{2} = 9$
So, $t = 9$ .

STEP 8

The value of $t$ is $\boxed{9}$ .

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QuestionSolve: $\frac{2}{3} t=6$ $\mathrm{t}=$

Studdy Solution

STEP 1

What is this asking? Find out what number $t$ must be so that when you multiply it by $\frac{2}{3}$ , you get $6$ . Watch out! Don't forget to multiply by the reciprocal to isolate $t$ !

STEP 2

1. Understand the equation
2. Isolate $t$
3. Solve for $t$

STEP 3

Alright, let's break this down!
We have the equation $\frac{2}{3} \cdot t = 6$ .
This means that $\frac{2}{3}$ of some number $t$ gives us $6$ .
Our mission is to find out what that number $t$ is!

STEP 4

To get $t$ by itself, we need to "undo" the multiplication by $\frac{2}{3}$ .
The best way to do this is by multiplying both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
This will help us "add to one" on the left side, leaving $t$ all alone!

STEP 5

Let's do the math!
Multiply both sides by $\frac{3}{2}$ :
$\frac{3}{2} \cdot \left(\frac{2}{3} \cdot t\right) = \frac{3}{2} \cdot 6$

STEP 6

On the left side, the $\frac{3}{2}$ and $\frac{2}{3}$ multiply to make 1:
$\left(\frac{3 \cdot 2}{2 \cdot 3}\right) \cdot t = 1 \cdot t = t$

STEP 7

Now, let's handle the right side:
$\frac{3}{2} \cdot 6 = \frac{3 \cdot 6}{2} = \frac{18}{2} = 9$
So, $t = 9$ .

STEP 8

The value of $t$ is $\boxed{9}$ .

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QuestionSolve: 23t=6\frac{2}{3} t=632​t=6 t=\mathrm{t}=t=

Studdy Solution

STEP 1

What is this asking? Find out what number t t t must be so that when you multiply it by 23\frac{2}{3}32​, you get 666. Watch out! Don't forget to multiply by the reciprocal to isolate t t t!

STEP 2

1. Understand the equation2. Isolate t t t3. Solve for t t t

STEP 3

Alright, let's break this down!We have the equation 23⋅t=6\frac{2}{3} \cdot t = 632​⋅t=6.This means that 23\frac{2}{3}32​ of some number t t t gives us 666.Our mission is to find out what that number t t t is!

STEP 4

To get t t t by itself, we need to "undo" the multiplication by 23\frac{2}{3}32​.The best way to do this is by multiplying both sides of the equation by the **reciprocal** of 23\frac{2}{3}32​, which is 32\frac{3}{2}23​.This will help us "add to one" on the left side, leaving t t t all alone!

STEP 5

Let's do the math!Multiply both sides by 32\frac{3}{2}23​:32⋅(23⋅t)=32⋅6\frac{3}{2} \cdot \left(\frac{2}{3} \cdot t\right) = \frac{3}{2} \cdot 623​⋅(32​⋅t)=23​⋅6

STEP 6

On the left side, the 32\frac{3}{2}23​ and 23\frac{2}{3}32​ multiply to make **1**:(3⋅22⋅3)⋅t=1⋅t=t\left(\frac{3 \cdot 2}{2 \cdot 3}\right) \cdot t = 1 \cdot t = t(2⋅33⋅2​)⋅t=1⋅t=t

STEP 7

Now, let's handle the right side:32⋅6=3⋅62=182=9\frac{3}{2} \cdot 6 = \frac{3 \cdot 6}{2} = \frac{18}{2} = 923​⋅6=23⋅6​=218​=9So, t=9 t = 9 t=9.

STEP 8

The value of t t t is 9\boxed{9}9​.

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QuestionSolve: $\frac{2}{3} t=6$ $\mathrm{t}=$

What is this asking? Find out what number $t$ must be so that when you multiply it by $\frac{2}{3}$ , you get $6$ . Watch out! Don't forget to multiply by the reciprocal to isolate $t$ !

1. Understand the equation
2. Isolate $t$
3. Solve for $t$

Alright, let's break this down!
We have the equation $\frac{2}{3} \cdot t = 6$ .
This means that $\frac{2}{3}$ of some number $t$ gives us $6$ .
Our mission is to find out what that number $t$ is!

To get $t$ by itself, we need to "undo" the multiplication by $\frac{2}{3}$ .
The best way to do this is by multiplying both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
This will help us "add to one" on the left side, leaving $t$ all alone!

Let's do the math!
Multiply both sides by $\frac{3}{2}$ :
$\frac{3}{2} \cdot \left(\frac{2}{3} \cdot t\right) = \frac{3}{2} \cdot 6$

On the left side, the $\frac{3}{2}$ and $\frac{2}{3}$ multiply to make 1:
$\left(\frac{3 \cdot 2}{2 \cdot 3}\right) \cdot t = 1 \cdot t = t$

Now, let's handle the right side:
$\frac{3}{2} \cdot 6 = \frac{3 \cdot 6}{2} = \frac{18}{2} = 9$
So, $t = 9$ .

The value of $t$ is $\boxed{9}$ .