6th grade Q1

A mixed number is a combination of a whole number and a proper fraction.

For example, $6\frac{1}{4}$ means 6 whole pizzas and $\frac{1}{4}$ of another pizza.

Example: Let’s solve this task: $6\frac{1}{4}-2\frac{3}{4}$

This is what it looks like when you remove $2\frac{3}{4}$ pizzas from the $6\frac{1}{4}$ pizzas you start off with. Notice that you have to slice one of the whole pizzas and give parts of it away. This is called regrouping.

Now let's see how it's done with numbers!

Step 1: Subtract the whole numbers

6 - 2 = 4

Step 2: Subtract the fractions

$\frac{1}{4}-\frac{3}{4}$

But $\frac{1}{4}$ is smaller than $\frac{3}{4}$, so you need to regroup.

You can divide 1 pizza into $\frac{4}{4}$. So, 6 pizzas become $5+\frac{4}{4}$ pizzas. Then

$6\frac{1}{4}=5+\frac{4}{4}+\frac{1}{4}=5+\frac{5}{4}=5\frac{5}{4}$

So the original $6\frac{1}{4}-2\frac{3}{4}$ becomes $5\frac{5}{4}-2\frac{3}{4}$

Step 3: After regrouping subtract again

$5\frac{5}{4}-2\frac{3}{4}$

First, subtract the whole numbers:

$5-2=3$

Next, subtract the fractions:

$\frac{5}{4}-\frac{3}{4}=\frac{2}{4}$

Step 4: Combine the results

Now, combine the whole number and the fraction:

$3+\frac{2}{4}$

Step 5: Simplify the fraction

Simplify $\frac{2}{4}$ by dividing both the numerator and denominator by 2:

$\frac{2}{4}=\frac{1}{2}$

So, $3\frac{2}{4}$ becomes $3\frac{1}{2}$

You’re Done!

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

This means you have 3 whole and $\frac{1}{2}$ of another pizza.

Important:

• Regrouping is needed when the fraction you subtract is greater than the fraction you subtract from, like when $\frac{3}{4}$ is greater than $\frac{1}{4}$ in this example.