Math / Numbers & Operations

QuestionHow many $\frac{4}{5}$ s are in 4? (f)
There are $\square$ groups of $\frac{4}{5}$ in 4.

Studdy Solution

STEP 1

What is this asking? How many times does $\frac{4}{5}$ fit into 4? Watch out! Don't accidentally multiply 4 by $\frac{4}{5}$ !
We're dividing, not multiplying!

STEP 2

1. Set up the division
2. Divide the numbers

STEP 3

We're figuring out how many times $\frac{4}{5}$ goes into 4.
This is a division problem!

STEP 4

We can write this as $4 \div \frac{4}{5}$ .

STEP 5

Dividing by a fraction is the same as multiplying by its reciprocal (that's what we call the flipped version of the fraction).
The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$ .
Remember, we flip the fraction, not the whole problem!

STEP 6

So, $4 \div \frac{4}{5}$ becomes $4 \cdot \frac{5}{4}$ .
Look at that beautiful multiplication!

STEP 7

We can write 4 as $\frac{4}{1}$ , so our problem becomes $\frac{4}{1} \cdot \frac{5}{4}$ .
Now, multiply the numerators (top numbers) together and the denominators (bottom numbers) together: $\frac{4 \cdot 5}{1 \cdot 4} = \frac{20}{4}$ .

STEP 8

Now, we simplify $\frac{20}{4}$ by dividing both the numerator and the denominator by their greatest common factor, which is 4.
So, $\frac{20}{4} = \frac{20 \div 4}{4 \div 4} = \frac{5}{1}$ .
And $\frac{5}{1}$ is the same as 5!

STEP 9

There are 5 groups of $\frac{4}{5}$ in 4.

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QuestionHow many $\frac{4}{5}$ s are in 4? (f)
There are $\square$ groups of $\frac{4}{5}$ in 4.

Studdy Solution

STEP 1

What is this asking? How many times does $\frac{4}{5}$ fit into 4? Watch out! Don't accidentally multiply 4 by $\frac{4}{5}$ !
We're dividing, not multiplying!

STEP 2

1. Set up the division
2. Divide the numbers

STEP 3

We're figuring out how many times $\frac{4}{5}$ goes into 4.
This is a division problem!

STEP 4

We can write this as $4 \div \frac{4}{5}$ .

STEP 5

Dividing by a fraction is the same as multiplying by its reciprocal (that's what we call the flipped version of the fraction).
The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$ .
Remember, we flip the fraction, not the whole problem!

STEP 6

So, $4 \div \frac{4}{5}$ becomes $4 \cdot \frac{5}{4}$ .
Look at that beautiful multiplication!

STEP 7

We can write 4 as $\frac{4}{1}$ , so our problem becomes $\frac{4}{1} \cdot \frac{5}{4}$ .
Now, multiply the numerators (top numbers) together and the denominators (bottom numbers) together: $\frac{4 \cdot 5}{1 \cdot 4} = \frac{20}{4}$ .

STEP 8

Now, we simplify $\frac{20}{4}$ by dividing both the numerator and the denominator by their greatest common factor, which is 4.
So, $\frac{20}{4} = \frac{20 \div 4}{4 \div 4} = \frac{5}{1}$ .
And $\frac{5}{1}$ is the same as 5!

STEP 9

There are 5 groups of $\frac{4}{5}$ in 4.

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QuestionHow many 45\frac{4}{5}54​ s are in 4? (f)There are □\square□ groups of 45\frac{4}{5}54​ in 4.

Studdy Solution

STEP 1

What is this asking? How many times does 45\frac{4}{5}54​ fit into 4? Watch out! Don't accidentally multiply 4 by 45\frac{4}{5}54​!We're dividing, not multiplying!

STEP 2

1. Set up the division2. Divide the numbers

STEP 3

We're figuring out how many times 45\frac{4}{5}54​ goes into 4.This is a division problem!

STEP 4

We can write this as 4÷454 \div \frac{4}{5}4÷54​.

STEP 5

Dividing by a fraction is the same as multiplying by its reciprocal (that's what we call the flipped version of the fraction).The reciprocal of 45\frac{4}{5}54​ is 54\frac{5}{4}45​.Remember, we flip the fraction, not the whole problem!

STEP 6

So, 4÷454 \div \frac{4}{5}4÷54​ becomes 4⋅544 \cdot \frac{5}{4}4⋅45​.Look at that beautiful multiplication!

STEP 7

We can write 4 as 41\frac{4}{1}14​, so our problem becomes 41⋅54\frac{4}{1} \cdot \frac{5}{4}14​⋅45​.Now, multiply the numerators (top numbers) together and the denominators (bottom numbers) together: 4⋅51⋅4=204\frac{4 \cdot 5}{1 \cdot 4} = \frac{20}{4}1⋅44⋅5​=420​.

STEP 8

Now, we simplify 204\frac{20}{4}420​ by dividing both the numerator and the denominator by their greatest common factor, which is **4**.So, 204=20÷44÷4=51\frac{20}{4} = \frac{20 \div 4}{4 \div 4} = \frac{5}{1}420​=4÷420÷4​=15​.And 51\frac{5}{1}15​ is the same as **5**!

STEP 9

There are **5** groups of 45\frac{4}{5}54​ in 4.

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QuestionHow many $\frac{4}{5}$ s are in 4? (f)
There are $\square$ groups of $\frac{4}{5}$ in 4.

What is this asking? How many times does $\frac{4}{5}$ fit into 4? Watch out! Don't accidentally multiply 4 by $\frac{4}{5}$ !
We're dividing, not multiplying!

1. Set up the division
2. Divide the numbers

We're figuring out how many times $\frac{4}{5}$ goes into 4.
This is a division problem!

We can write this as $4 \div \frac{4}{5}$ .

Dividing by a fraction is the same as multiplying by its reciprocal (that's what we call the flipped version of the fraction).
The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$ .
Remember, we flip the fraction, not the whole problem!

So, $4 \div \frac{4}{5}$ becomes $4 \cdot \frac{5}{4}$ .
Look at that beautiful multiplication!

We can write 4 as $\frac{4}{1}$ , so our problem becomes $\frac{4}{1} \cdot \frac{5}{4}$ .
Now, multiply the numerators (top numbers) together and the denominators (bottom numbers) together: $\frac{4 \cdot 5}{1 \cdot 4} = \frac{20}{4}$ .

Now, we simplify $\frac{20}{4}$ by dividing both the numerator and the denominator by their greatest common factor, which is 4.
So, $\frac{20}{4} = \frac{20 \div 4}{4 \div 4} = \frac{5}{1}$ .
And $\frac{5}{1}$ is the same as 5!

There are 5 groups of $\frac{4}{5}$ in 4.