Dividing with whole numbers always results in a quotient that is smaller than the amount being divided. When it is time to divide a whole number by a fraction, it can be very confusing that the quotient can now be a number greater than the starting amount. Using number lines to show this concept makes the concept visual and concrete.
Build on the Familiar
Number lines can be used to make sense of dividing whole numbers. This number line shows 20/4. We can think of it as how many groups of 4 will fit into 20. We end up with 5 groups, so the quotient is 5.
How Do You Divide A Whole Number By A Fraction?
The same ideas can be applied to a problem like 4 ➗ 1 / 3. We can think of this as how many groups that are ⅓ in size can fit into 4. First, represent the whole number using a number line.
Then think about what the fraction ⅓ means. The denominator tells us that the whole is divided into 3 equal parts. So we can divide each whole on the number line into 3 parts. Each part represents ⅓.
Finally, we can count the number of groups that are each ⅓ in size, just as we did with the whole numbers. We end up with 12 groups, so 4 divided by ⅓ = 12.
Seeing the whole number being broken up into smaller parts and then counting the number of smaller parts helps students make sense of the larger quotient.
Also read: Modelling Equations With Hangers
Frequently Asked Questions on Dividing Whole Numbers By Fractions
How do you divide a whole number by a fraction?
As mentioned above, by using numbers lines one can divide whole fractions by dividing them into equal numbers of groups.
What does it mean to divide a fraction?
In simple words, the division of fractions refers to division of a fraction into equal parts.
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How are number lines helpful in dividing whole numbers by fractions?
Number lines are horizontal lines that are represented by positive and negative integers at equal intervals. Students can better understand division of whole numbers of fractions by number lines, since they give a more visual and concrete understanding.
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