GCSE Four operations and place value Practice Questions

Find the column of the $7$

Reading columns from the right they are units, tens, hundreds, thousands. The $7$ sits in the hundreds column.

Multiply the digit by its place value

The value of a digit is the digit multiplied by its column value. Here that is $7$ hundreds.

State the value

So the $7$ stands for $700$.

Add the fraction parts

The two halves combine to make one whole.

Add to the whole number

Add that new whole to the $1$ already there.

State the answer

So the answer is $2$.

Decide the order of operations

Using BIDMAS, multiplication is done before addition.

Identify the multiplication

Do the $3\times 12$ part first.

Work it out

$3$ lots of $12$ is $36$.

Now do the addition

Add $45$ to the result.

Work it out

$36+45=81$ using column addition.

State the answer

So $3\times 12+45=81$.

Label the missing digits

Let the missing units digit be a and the missing tens digit be b.

Write each number using place value

Break each number into its place-value parts.

Add the known parts

Add up everything except the unknown digits.

Form an equation

The total must equal $431$.

Rearrange

Subtract $376$ from both sides.

Use the fact that a is a single digit

Since a is one digit, $10b$ must be within $9$ of $55$.

Find $10b$

The only multiple of $10$ that leaves a single-digit a is $50$.

Find a

Then a is $5$.

Check the addition

The numbers are $275$ and $156$, and they do add to $431$.

State the answer

So both missing digits are $5$.

Understand the task

We must invent a real-life problem that uses each of the four operations exactly once, then solve it.

Choose a context

A group of friends buying event tickets is a natural setting.

Set a ticket price

Say each ticket costs £$12$.

Use multiplication

The group buys $5$ tickets, so multiply.

Work it out

Five tickets cost £$60$.

Use subtraction

They receive an £$8$ discount, so subtract.

Work it out

The bill comes down to £$52$.

Use division

The cost is split equally between $4$ friends.

Work it out

Each friend pays £$13$ for their share of tickets.

Use addition

Each friend also buys a £$3$ programme, so add.

Work it out

So each friend pays £$16$ in total.

Check all four operations appear

Multiplication, subtraction, division and addition are each used exactly once.

Write the calculation clearly

Brackets show the order the operations are applied.

Evaluate to confirm

Following the brackets gives $13+3$.

State the problem and answer

The designed problem is solved: each friend pays £$16$.