Question
A grocery store sells bananas, where 6 bananas cost $3. How much will 16 bananas cost at this rate? Use the scale factor to help you solve.
Start by setting up a table that could be used to find the price of 16 bananas.
Number of Bananas Price
6
$
3
16
$
?
Good work!
One way to find the cost of 16 bananas is to use the scale factor. Write a multiplication equation you could use to find the scale factor.
× ?
Number of Bananas Price
6 $3
16
6
·
?
=
16
Good work!
To help you find the scale factor, rewrite the multiplication equation as a division equation.
× ?
Number of Bananas Price
6 $3
16
6 · ? = 16
16
÷
6
= ?
Nice!
To find the scale factor, we can divide. What is 16 divided by 6?
× ?
Number of Bananas Price
6 $3
16
6 · ? = 16
16 ÷ 6 =
8
3
You got it!
What is the scale factor?
×
8
3
Number of Bananas Price
6 $3
16
6 · ? = 16
16 ÷ 6 =
6
16
Excellent!
Use the scale factor to find the price of 16 bananas. What number do you need to multiply $3 by to keep the ratio the same?
×
8
3
×
6
16
Number of Bananas Price
6 $3
16
Excellent!
To find the price of 16 bananas, you can multiply $3 by the scale factor,
6
16
. Write 3 ·
6
16
as a single fraction.
×
6
16
×
6
16
Number of Bananas Price
6 $3
16
3 ·
6
16
=
·
·
as a fraction
Start by setting up a table that could be used to find the price of 16 bananas.
Number of Bananas Price
6
$
3
16
$
?
Good work!
One way to find the cost of 16 bananas is to use the scale factor. Write a multiplication equation you could use to find the scale factor.
× ?
Number of Bananas Price
6 $3
16
6
·
?
=
16
Good work!
To help you find the scale factor, rewrite the multiplication equation as a division equation.
× ?
Number of Bananas Price
6 $3
16
6 · ? = 16
16
÷
6
= ?
Nice!
To find the scale factor, we can divide. What is 16 divided by 6?
× ?
Number of Bananas Price
6 $3
16
6 · ? = 16
16 ÷ 6 =
8
3
You got it!
What is the scale factor?
×
8
3
Number of Bananas Price
6 $3
16
6 · ? = 16
16 ÷ 6 =
6
16
Excellent!
Use the scale factor to find the price of 16 bananas. What number do you need to multiply $3 by to keep the ratio the same?
×
8
3
×
6
16
Number of Bananas Price
6 $3
16
Excellent!
To find the price of 16 bananas, you can multiply $3 by the scale factor,
6
16
. Write 3 ·
6
16
as a single fraction.
×
6
16
×
6
16
Number of Bananas Price
6 $3
16
3 ·
6
16
=
·
·
as a fraction
Answers
GPT-4o mini
To find the price of 16 bananas using the scale factor, we need to represent the scale factor as a fraction. We found that the scale factor from 6 bananas to 16 bananas is:
\[
\frac{16}{6}
\]
Now we can express the price of 16 bananas using this scale factor.
Starting with the price of 6 bananas, which is $3, we can multiply this by the scale factor:
\[
\text{Price of 16 bananas} = 3 \cdot \frac{16}{6}
\]
To rewrite \(3 \cdot \frac{16}{6}\) as a single fraction, we treat 3 as a fraction:
\[
3 = \frac{3}{1}
\]
So the multiplication can be expressed as:
\[
\frac{3}{1} \cdot \frac{16}{6}
\]
Now we multiply the numerators and the denominators:
\[
= \frac{3 \cdot 16}{1 \cdot 6} = \frac{48}{6}
\]
Now we simplify:
\[
\frac{48}{6} = 8
\]
Thus, the price of 16 bananas is **$8**.
In summary, the final computation to find the price as a single fraction is:
\[
3 \cdot \frac{16}{6} = \frac{3 \cdot 16}{1 \cdot 6} = \frac{48}{6} = 8
\]
So, you need to multiply $3 by \(\frac{16}{6}\), resulting in a single fraction of \(\frac{48}{6}\) which simplifies to $8.
\[
\frac{16}{6}
\]
Now we can express the price of 16 bananas using this scale factor.
Starting with the price of 6 bananas, which is $3, we can multiply this by the scale factor:
\[
\text{Price of 16 bananas} = 3 \cdot \frac{16}{6}
\]
To rewrite \(3 \cdot \frac{16}{6}\) as a single fraction, we treat 3 as a fraction:
\[
3 = \frac{3}{1}
\]
So the multiplication can be expressed as:
\[
\frac{3}{1} \cdot \frac{16}{6}
\]
Now we multiply the numerators and the denominators:
\[
= \frac{3 \cdot 16}{1 \cdot 6} = \frac{48}{6}
\]
Now we simplify:
\[
\frac{48}{6} = 8
\]
Thus, the price of 16 bananas is **$8**.
In summary, the final computation to find the price as a single fraction is:
\[
3 \cdot \frac{16}{6} = \frac{3 \cdot 16}{1 \cdot 6} = \frac{48}{6} = 8
\]
So, you need to multiply $3 by \(\frac{16}{6}\), resulting in a single fraction of \(\frac{48}{6}\) which simplifies to $8.