Fractions as a Multiple of Unit Fractions

Fractions as a Multiple of Unit Fractions exercise

• Help Axel and Tank to choose a whole pizza.

  Hints

  If the numerator and denominator are the same, this is equivalent to a whole. $\frac2 6$ + $\frac4 6$ = $\frac6 6$ which is 1 whole.

  Count all the slices of pizza. Is this the same as the number of portions it has been cut into?

  Solution

  • The first pizza has $\frac3 4$ in total. This is NOT equivalent to a whole.

  • The second pizza has $\frac3 3$ in total. This IS equivalent to a whole, so is CORRECT.

  • The third pizza has $\frac5 6$ in total. This is NOT equivalent to a whole.

  • The fourth pizza has $\frac8 8$ in total. This IS equivalent to a whole, so is CORRECT.

• Multiplying pizza slices.

  Hints

  Count how many pizza slices there are in total. This is the factor you are multiplying by.

  Count how many parts the pizza has been sliced into. If it has been sliced into 6, the unit fraction would be $\frac1 6$.

  Solution

  • For the first pair: There are 5 slices in total and each slice is $\mathbf{\frac{1}{4}}$, since the pizzas have been cut into 4 parts.

  • For the second pair: There are 5 slices in total and each slice is $\mathbf{\frac{1}{6}}$, since the pizzas have been cut into 6 parts.

  • For the third pair: There are 5 slices in total and each slice is $\mathbf{\frac{1}{3}}$, since the pizzas have been cut into 3 parts.

  • For the fourth pair: There are 4 slices in total and each slice is $\mathbf{\frac{1}{5}}$, since the pizzas have been cut into 5 parts.

• Cookie dough dessert.

  Hints

  How many slices do they eat in total?

  Have they eaten more than a whole cookie dough pizza?

  If they have eaten a whole cookie dough pizza plus a bit more, then the answer should be a mixed number.

  Solution

  Axel and Tank eat 7 slices. Each slice is $\mathbf{\frac{1}{6}}$ so we need to find: 7 x $\mathbf{\frac{1}{6}}$.

  Since $\mathbf{\frac{6}{6}}$ is equal to one whole, we know that they have eaten 1 whole pizza PLUS $\mathbf{\frac{1}{6}}$ of a pizza which equals: 1$\mathbf{\frac{1}{6}}$

• Multiply the unit fractions.

  Hints

  First, multiply the factor by the numerator. For example, with 5 x $\frac1 3$ solve 5 x 1. Then write this above the denominator. $\frac5 3$.

  Convert the improper fraction into a mixed number: $\frac5 3$ becomes 1 $\frac2 3$.

  Solution

  • Axel and Tank are ordering lots of pizzas for a pizza party. They order 10 x $\mathbf{\frac{1}{3}}$ veggie slices of pizza. In total they have 3 $\mathbf{\frac{1}{3}}$ veggie pizzas.

  • They order 8 x $\mathbf{\frac{1}{5}}$ anchovy slices of pizza. In total they have 1 $\mathbf{\frac{3}{5}}$ anchovy pizzas.

  • Finally, they order 9 x $\mathbf{\frac{1}{4}}$ sea supreme slices of pizza. In total they have 2 $\mathbf{\frac{1}{4}}$ sea supreme pizzas.

• What is a unit fraction?

  Hints

  Count how many parts the pizza shape has been cut into. This is the bottom part of your fraction (the denominator). For example, a pizza cut into 5 parts, would have 5 as the denominator.

  Remember that a unit fraction always has 1 as the numerator (top part of the fraction).

  Solution

  This pizza shape has been cut into three parts, so the bottom part of the fraction (denominator) is 3.

  Each slice is 1 out of 3 or $\frac1 3$. A unit fraction always has 1 as the numerator.

• Ordering fractions.

  Hints

  If the answer can be simplified, reduce it to its simplest form.

  Convert the improper fraction to a mixed number.

  First, multiply the factor by the numerator to find the improper fraction.

  Solution

  The order of the totals from smallest to largest are:

  • 10 x $\mathbf{\frac{1}{8}}$ = 1$\frac2 8$ = 1 $\mathbf{\frac{1}{4}}$

  • 6 x $\mathbf{\frac{1}{4}}$ = 1$\frac2 4$ = 1 $\mathbf{\frac{1}{2}}$

  • 14 x $\mathbf{\frac{1}{8}}$ = 1$\frac6 8$ = 1$\mathbf{\frac{3}{4}}$

  • 9 x $\mathbf{\frac{1}{4}}$ = 2$\mathbf{\frac{1}{4}}$

  • 5 x $\mathbf{\frac{1}{2}}$ = 2$\mathbf{\frac{1}{2}}$