Lesson 23: Subtracting Mixed Numbers with Regrouping

New Concept

Regrouping mixed numbers means borrowing from the whole number to increase the fraction, making subtraction possible when the top fraction is smaller than the bottom.

In regrouping, we exchange a value for an equal amount. For example, 1 ten for 10 ones, or 1 whole for $\frac{7}{7}$.

What’s next

Now, let’s explore worked examples showing visual breakdowns and problems that involve percentages and whole numbers to solidify your understanding.

Property

In regrouping, we exchange a value for an equal amount, like 1 whole for $\frac{5}{5}$. To subtract mixed numbers when the top fraction is smaller than the bottom one, you must rename the first number.

Examples

$3\frac{1}{5} - 1\frac{2}{5} \rightarrow 2\frac{6}{5} - 1\frac{2}{5}$
$5\frac{1}{6} - 1\frac{5}{6} \rightarrow 4\frac{7}{6} - 1\frac{5}{6}$

Explanation

Can't subtract a big fraction from a tiny one? No worries! Just 'borrow' 1 from the whole number next door, turn it into a fraction that matches the denominator, and add it to your fraction. Now you have enough to subtract!

Property

To subtract a mixed number from a whole number, you first need to rewrite the whole number as a mixed number with a common denominator.

Examples

$6 - 1\frac{3}{4} \rightarrow 5\frac{4}{4} - 1\frac{3}{4} = 4\frac{1}{4}$
$7 - 2\frac{1}{3} \rightarrow 6\frac{3}{3} - 2\frac{1}{3} = 4\frac{2}{3}$

Explanation

Taking a fraction from a whole number is like making change for a pie. You have to slice one of your whole pies! Convert '1' from your whole number into a full fraction with the denominator you need.