Rehna used $(1)/(6)$ of a packet of flour to make some muffins and $(1)/(4)$ of it to make a cake She used the remainder to make some cupcakes. She used $(1)/(12)$ of the packet of flour or each cupcake. How many cupcakes did she make?

Full solution

Q. Rehna used

(1)/(6)

of a packet of flour to make some muffins and

(1)/(4)

of it to make a cake She used the remainder to make some cupcakes. She used

(1)/(12)

of the packet of flour or each cupcake. How many cupcakes did she make?

Calculate Total Flour Used: Calculate the total amount of flour used for muffins and cake. $\newline$ Rehna used $\frac{1}{6}$ of the packet for muffins and $\frac{1}{4}$ of the packet for the cake. To find the total amount used, we add these fractions together. $\newline$ $\frac{1}{6} + \frac{1}{4} = \left(\frac{2}{12}\right) + \left(\frac{3}{12}\right) = \frac{5}{12}$
Determine Remaining Flour: Determine the amount of flour left for cupcakes. $\newline$ Since Rehna used $\frac{5}{12}$ of the packet for muffins and cake, the remainder is $1 - \frac{5}{12}$ . $\newline$ $1 - \frac{5}{12} = \frac{12}{12} - \frac{5}{12} = \frac{7}{12}$ $\newline$ This is the amount of flour left for cupcakes.
Calculate Cupcakes Quantity: Calculate the number of cupcakes Rehna can make with the remainder. $\newline$ Rehna uses $\frac{1}{12}$ of the packet for each cupcake. To find out how many cupcakes she can make with $\frac{7}{12}$ of the packet, we divide $\frac{7}{12}$ by $\frac{1}{12}$ . $\newline$ $\frac{7}{12} \div \frac{1}{12} = \frac{7}{1} = 7$ $\newline$ Rehna can make $7$ cupcakes with the remainder of the flour packet.