Dividing Whole Numbers by Unit Fractions Using Models

Dividing Whole Numbers by Unit Fractions Using Models exercise

• What does each keyword mean?

  Hints

  A fraction contains a numerator and a denominator. Which is the top and which is the bottom?

  Examples of unit fractions are

  $\frac{1}{3} , \frac{1}{5} , \frac {1}{2} , \frac{1}{10}$

  What do you notice about these?

  A cake is split into six equal slices, the splitting is called division and the individual slices are fractions of the cake.

  Solution

  A fraction is a part of a whole.

  A numerator is the top number in a fraction.

  A denominator is the bottom number in a fraction.

  Division is sharing or splitting a number into equal parts.

  A unit fraction is a fraction where the numerator is one.

• How many quarters are there in three chocolate bars?

  Hints

  The model should represent the question. First, check how many chocolate bars are in the question.

  Next, check how many pieces each bar is cut into. The denominator of the unit fraction tells you this.

  Finally, count the number of pieces in total.

  Solution

  Here we can see the correct answer.

  There are three chocolate bars split into quarters (four pieces). Counting the pieces gives 12 pieces, therefore, the answer is $3 \div \frac{1}{4} = 12$.

• Dividing a whole number by a unit fraction.

  Hints

  The first number tells us how many items there are.

  The denominator of the unit fraction tells us how many parts the item is split into.

  Two cakes split into four equal slices would be represented by the math sentence $2 \div \frac{1}{4} = 8$

  Solution

  The image shows the correct solutions.

  Sweets: $3 \div \frac{1}{4} = 12$

  Chocolate bars: $2 \div \frac{1}{6} = 12$

  Pizza: $4 \div \frac{1}{3} = 12$

  Muffins: $6 \div \frac{1}{2} = 12$

• Divide the whole numbers by the unit fraction.

  Hints

  When dividing a whole number by a unit fraction we are counting how many times the fraction is in the whole.

  When dividing a whole number by a unit fraction the quotient will always be a number greater than the whole number you started with.

  If you have five pizzas and divide each pizza in half, how many slices would you have?

  Solution

  In the image we can see the first solution:

  $\bf{5 \div \frac{1}{2} = 10}$ because there are $2$ equal pieces in each of the $5$ wholes.

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  $\bf{4 \div \frac{1}{4} = 16}$ because there are $4$ equal pieces in each of the $4$ wholes.

  $\bf{9 \div \frac{1}{3} = 27}$ because there are $3$ equal pieces in each of the $9$ wholes.

  $\bf{6 \div \frac{1}{3} = 18}$ because there are $3$ equal pieces in each of the $6$ wholes.

• How many quarters are there in two cakes?

  Hints

  Each cake is represented by one whole. There are two whole cakes.

  The denominator tells us how many equal pieces the cakes are split into. In the image we can see that each cake has been split into four equal pieces.

  Another way to read the question is - the two cakes are divided into quarters, how many pieces are there?

  Look at the image for a similar question. There are $3$ muffins, the whole number is written first. It is divided into thirds, the fraction is written after the division sign.

  Solution

  The correct maths sentence is $2 \div \frac{1}{4}$ because there are two cakes each divided into quarters.

  There are $\bf{8}$ quarters in the two cakes.

• Five cakes are cut into thirds. How many slices are there?

  Hints

  There are five cakes, this is your whole number.

  Each cake is split into equal slices. The denominator of the unit fraction tells you how many equal slices.

  Each cake has three equal slices.

  Solution

  You have five cakes, each one is split into thirds.

  This means that each of the five cakes is split into three slices. There are $\bf{15}$ slices in total.

  $5 \div \frac{1}{3} = 15$