Math / Numbers & Operations

Question $1.25 \times 4+3 \times 2 \div\left(\frac{1}{2}\right)^{3}$

Studdy Solution

STEP 1

What is this asking? This is asking us to calculate the result of a mixed arithmetic expression involving multiplication, addition, division, and an exponent. Watch out! Remember the order of operations—PEMDAS/BODMAS/BIDMAS—especially when dealing with the exponent and the parentheses!

STEP 2

1. Exponent
2. Multiplication and Division from Left to Right
3. Addition

STEP 3

Let's tackle that exponent first!
We have $\left(\frac{1}{2}\right)^{3}$ .
This means we multiply $\frac{1}{2}$ by itself three times.
It's like saying "half of a half of a half".

STEP 4

So, $\left(\frac{1}{2}\right)^{3} = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1 \cdot 1}{2 \cdot 2 \cdot 2} = \frac{1}{8}$ .
Awesome! We simplified the exponent to $\frac{1}{8}$ .

STEP 5

Next up, we have multiplication and division.
Remember, we do these from left to right!
First, we have $1.25 \times 4$ .
Think of it as "one and a quarter, four times."

STEP 6

So, $1.25 \times 4 = 5$ .
Great!

STEP 7

Moving on, we have $3 \times 2$ , which is $3 \times 2 = 6$ .
Easy peasy!

STEP 8

Now we have $6 \div \frac{1}{8}$ .
Dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of $\frac{1}{8}$ is $\frac{8}{1}$ or just $8$ .
So we have $6 \div \frac{1}{8} = 6 \cdot 8 = 48$ .
Fantastic!

STEP 9

Finally, we just need to add everything together.
We have $5$ and $48$ .
Adding them up, we get $5 + 48 = 53$ .

STEP 10

Our final answer is $\bf{53}$ !

Was this helpful?

Question $1.25 \times 4+3 \times 2 \div\left(\frac{1}{2}\right)^{3}$

Studdy Solution

STEP 1

What is this asking? This is asking us to calculate the result of a mixed arithmetic expression involving multiplication, addition, division, and an exponent. Watch out! Remember the order of operations—PEMDAS/BODMAS/BIDMAS—especially when dealing with the exponent and the parentheses!

STEP 2

1. Exponent
2. Multiplication and Division from Left to Right
3. Addition

STEP 3

Let's tackle that exponent first!
We have $\left(\frac{1}{2}\right)^{3}$ .
This means we multiply $\frac{1}{2}$ by itself three times.
It's like saying "half of a half of a half".

STEP 4

So, $\left(\frac{1}{2}\right)^{3} = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1 \cdot 1}{2 \cdot 2 \cdot 2} = \frac{1}{8}$ .
Awesome! We simplified the exponent to $\frac{1}{8}$ .

STEP 5

Next up, we have multiplication and division.
Remember, we do these from left to right!
First, we have $1.25 \times 4$ .
Think of it as "one and a quarter, four times."

STEP 6

So, $1.25 \times 4 = 5$ .
Great!

STEP 7

Moving on, we have $3 \times 2$ , which is $3 \times 2 = 6$ .
Easy peasy!

STEP 8

Now we have $6 \div \frac{1}{8}$ .
Dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of $\frac{1}{8}$ is $\frac{8}{1}$ or just $8$ .
So we have $6 \div \frac{1}{8} = 6 \cdot 8 = 48$ .
Fantastic!

STEP 9

Finally, we just need to add everything together.
We have $5$ and $48$ .
Adding them up, we get $5 + 48 = 53$ .

STEP 10

Our final answer is $\bf{53}$ !

Get Studdy

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.

Question1.25×4+3×2÷(12)31.25 \times 4+3 \times 2 \div\left(\frac{1}{2}\right)^{3}1.25×4+3×2÷(21​)3

Studdy Solution

STEP 1

What is this asking? This is asking us to calculate the result of a mixed arithmetic expression involving multiplication, addition, division, and an exponent. Watch out! Remember the order of operations—PEMDAS/BODMAS/BIDMAS—especially when dealing with the exponent and the parentheses!

STEP 2

1. Exponent2. Multiplication and Division from Left to Right3. Addition

STEP 3

Let's **tackle that exponent** first!We have (12)3\left(\frac{1}{2}\right)^{3}(21​)3.This means we multiply 12\frac{1}{2}21​ by itself three times.It's like saying "half of a half of a half".

STEP 4

So, (12)3=12⋅12⋅12=1⋅1⋅12⋅2⋅2=18\left(\frac{1}{2}\right)^{3} = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1 \cdot 1}{2 \cdot 2 \cdot 2} = \frac{1}{8}(21​)3=21​⋅21​⋅21​=2⋅2⋅21⋅1⋅1​=81​.Awesome! We simplified the exponent to 18\frac{1}{8}81​.

STEP 5

Next up, we have multiplication and division.Remember, we do these from left to right!First, we have 1.25×41.25 \times 41.25×4.Think of it as "one and a quarter, four times."

STEP 6

So, 1.25×4=51.25 \times 4 = 51.25×4=5.Great!

STEP 7

Moving on, we have 3×23 \times 23×2, which is 3×2=63 \times 2 = 63×2=6.Easy peasy!

STEP 8

Now we have 6÷186 \div \frac{1}{8}6÷81​.Dividing by a fraction is the same as multiplying by its reciprocal.The reciprocal of 18\frac{1}{8}81​ is 81\frac{8}{1}18​ or just 888.So we have 6÷18=6⋅8=486 \div \frac{1}{8} = 6 \cdot 8 = 486÷81​=6⋅8=48.Fantastic!

STEP 9

Finally, we just need to add everything together.We have 555 and 484848.Adding them up, we get 5+48=535 + 48 = 535+48=53.

STEP 10

Our final answer is 53\bf{53}53!

Get Studdy

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.

Question $1.25 \times 4+3 \times 2 \div\left(\frac{1}{2}\right)^{3}$

1. Exponent
2. Multiplication and Division from Left to Right
3. Addition

Let's tackle that exponent first!
We have $\left(\frac{1}{2}\right)^{3}$ .
This means we multiply $\frac{1}{2}$ by itself three times.
It's like saying "half of a half of a half".

So, $\left(\frac{1}{2}\right)^{3} = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1 \cdot 1}{2 \cdot 2 \cdot 2} = \frac{1}{8}$ .
Awesome! We simplified the exponent to $\frac{1}{8}$ .

Next up, we have multiplication and division.
Remember, we do these from left to right!
First, we have $1.25 \times 4$ .
Think of it as "one and a quarter, four times."

So, $1.25 \times 4 = 5$ .
Great!

Moving on, we have $3 \times 2$ , which is $3 \times 2 = 6$ .
Easy peasy!

Now we have $6 \div \frac{1}{8}$ .
Dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of $\frac{1}{8}$ is $\frac{8}{1}$ or just $8$ .
So we have $6 \div \frac{1}{8} = 6 \cdot 8 = 48$ .
Fantastic!

Finally, we just need to add everything together.
We have $5$ and $48$ .
Adding them up, we get $5 + 48 = 53$ .

Our final answer is $\bf{53}$ !