Lesson 36: Subtracting Fractions and Mixed Numbers from Whole Numbers

New Concept

To subtract a fraction from a whole number, we rewrite the whole number as a mixed number. We accomplish this by 'borrowing' 1 from the whole number part.

What’s next

This card is just the beginning. Next, you’ll apply this concept through worked examples and word problems to solidify your understanding.

Property

To subtract, you must rename the whole number by "borrowing" one whole and converting it into a fraction with a matching denominator.

Examples

$3 - 1\frac{1}{4} = 2\frac{4}{4} - 1\frac{1}{4} = 1\frac{3}{4}$
$6 - 2\frac{3}{10} = 5\frac{10}{10} - 2\frac{3}{10} = 3\frac{7}{10}$
$5 - \frac{5}{12} = 4\frac{12}{12} - \frac{5}{12} = 4\frac{7}{12}$

Explanation

You can't take a fraction from a whole number without some creative regrouping! Think of it like this: you have four whole pies and need to give away two and one-sixth pies. You must slice one of the whole pies into sixths first. Now you have three whole pies and six-sixths, making the subtraction a piece of cake!

Property

To solve $5 - 1\frac{1}{3}$, you must understand why 5 is changed to $4\frac{3}{3}$. This is because a whole number doesn't have a fraction part to subtract from, so you must create one by regrouping. $5 = 4 + 1 = 4 + \frac{3}{3} = 4\frac{3}{3}$.

Examples

For $5 - 1\frac{1}{3}$, you must change 5 into $4\frac{3}{3}$ to enable subtraction.
When calculating $8 - 3\frac{2}{5}$, the first step is to rewrite 8 as $7\frac{5}{5}$.
To solve $2 - \frac{3}{8}$, you have to think of 2 as $1\frac{8}{8}$ before you can subtract.

Explanation

Why can't we just subtract 1 from 5 and leave the fraction? Imagine having five dollar bills and needing to pay someone one dollar and twenty-five cents. You can't just hand over a quarter from nowhere! You have to break one of your dollars into four quarters first. Renaming a whole number is just like making change for fractions.