Question

Kate has 3/4 ounce of lip balm. She makes 1 1/2 more ounces of lip balm. She measures 1/2 portions of lip balm and places the portions in individual containers. How many containers will Kate use? If each container hold 1/2 ounces of lip balm will she have any remaining?

Answer 1

First, let's find out how much lip balm Kate has in total after she makes more. She starts with \( \frac{3}{4} \) ounce and makes \( 1 \frac{1}{2} \) ounces more.

Converting \( 1 \frac{1}{2} \) to an improper fraction:

\[
1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
\]

Now, we combine this amount with what she already has:

\[
\frac{3}{4} + \frac{3}{2}
\]

To add these fractions, we need a common denominator. The common denominator between 4 and 2 is 4.

Convert \( \frac{3}{2} \) into a fraction with a denominator of 4:

\[
\frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4}
\]

Now, add \( \frac{3}{4} \) and \( \frac{6}{4} \):

\[
\frac{3}{4} + \frac{6}{4} = \frac{3 + 6}{4} = \frac{9}{4}
\]

Now Kate has \( \frac{9}{4} \) ounces of lip balm.

Next, we need to determine how many \( \frac{1}{2} \) ounce portions she can make. We divide \( \frac{9}{4} \) by \( \frac{1}{2} \):

\[
\frac{9}{4} \div \frac{1}{2} = \frac{9}{4} \times 2 = \frac{9 \times 2}{4 \times 1} = \frac{18}{4}
\]

Simplifying \( \frac{18}{4} \):

\[
\frac{18}{4} = \frac{9}{2}
\]

Now, \( \frac{9}{2} \) is equal to \( 4 \frac{1}{2} \), which means Kate can fill 4 full containers and has \( \frac{1}{2} \) ounces left over.

Therefore, Kate will use **4 containers**, and she will have **1/2 ounce remaining**.