Interpreting Fractions as Division

Interpreting Fractions as Division exercise

• What are the fraction parts?

  Hints

  The top of the fraction is called the numerator and is how many parts of the whole we have. For example, if we had one slice of this pizza we would put $1$ on the top of the fraction.

  The bottom of the fraction is called the denominator.

  Solution

  • $a$ is the numerator and is how many parts of the whole we have
  • $b$ is the denominator and is how many equal parts the whole is divided into

  For example, one slice of this pizza is $1$ out of $6$ equal parts, so we write $\dfrac{1}{6}$, where $1$ is the numerator and $6$ is the denominator.

• Convert division to a fraction.

  Hints

  • The top (numerator) of the fraction is how many parts we have.
  • The bottom (denominator) of the fraction is how many equal parts the whole is divided into.

  The numerator $a$, is the number of slices we have and the denominator $b$ is the number of equal slices the pizza is cut into. For example, one slice of this pizza is $1\div5 = \frac{1}{5}$.

  Solution

  $1\div10 = \frac{1}{10}$

  One slice of pizza out of a total of $10$ equal slices.

• Using division to represent a fraction of chocolate.

  Hints

  Each chocolate bar should be split into $4$, as there are $4$ people to share the chocolate.

  Use bars to split it.

  When the chocolate is split into $4$, each person gets $1$ out of $4$.

  We do this $3$ times as there are $3$ bars of chocolate.

  We are sharing $3$ chocolate bars with $4$ people.

  $3\div4$

  Solution

  Each person gets $3\div4 = \frac{3}{4}$ of a bar of chocolate.

• Using division to represent a fraction of cola.

  Hints

  Each bottle should be shared into $7$.

  There are $5$ bottles, each shared into $7$. Each friend would get $\frac{1}{7}$ from each bottle, so we multiply this by $5$ (bottles).

  Solution

  $\frac{5}{7} = 5\div7$

  There are $5$ bottles each shared into $7$, that is $5\div7$.

• Convert the fractions to division.

  Hints

  • The top (numerator) of the fraction is how many parts we have.
  • The bottom (denominator) of the fraction is how many equal parts the whole is divided into.
  • As a division sentence we would write ${numerator}\div{denominator}$.

  $\frac{numerator}{denominator} = {numerator}\div{denominator}$

  For example, one slice of this cake could be written as $\frac{1}{8} = 1\div8$.

  Solution

  • $\frac{2}{3} = 2\div3$

  • $\frac{1}{2} = 1\div2$

  • $\frac{1}{3} = 1\div3$

  • $\frac{1}{5} = 1\div5$

  • $\frac{3}{5} = 3\div5$

  ${}$

  $\dfrac{numerator}{denominator} = {numerator}\div{denominator}$.

  For example, one slice from two is $\dfrac{1}{2} = 1\div2$ as above.

• Determine the fraction when dividing pizza.

  Hints

  Each pizza should be split into the number of friends. For example, if there were $8$ friends the pizza would be split into $8$.

  When the pizza has been split into the number of friends we multiply the fraction by $4$, as we have $4$ pizzas.

  For example, $\frac{1}{13}\times4 = \frac{4}{13}$

  Solution

  • $5$ friends $= 4\div5 = \frac{4}{5}$
  • $6$ friends $= 4\div6 = \frac{4}{6}$
  • $12$ friends $= 4\div12 = \frac{4}{12}$
  • $9$ friends $= 4\div9 = \frac{4}{9}$