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.

Question

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

Answer 1

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.