Adding and subtracting whole numbers

Mental strategies (partitioning, compensating, doubling) and the written algorithms for adding and subtracting whole numbers, with carrying and borrowing.

Mental strategies

Partitioning: split numbers into place values.

$347 + 225 = (300 + 200) + (40 + 20) + (7 + 5) = 500 + 60 + 12 = 572$

Compensating: round, then fix up.

$563 - 198 = 563 - 200 + 2 = 365$

The column method

Line up the digits by place value and work from the right.

Example 1: carrying●

Find $4768 + 2359$.

Ones: $8 + 9 = 17$. Write $7$, carry $1$.

Tens: $6 + 5 + 1 = 12$. Write $2$, carry $1$.

Hundreds: $7 + 3 + 1 = 11$. Write $1$, carry $1$. Thousands: $4 + 2 + 1 = 7$.

$4768 + 2359 = 7127$

Example 2: borrowing●●

Find $6003 - 2748$.

Rewrite $6003$ as $5$ thousands, $9$ hundreds, $9$ tens and $13$ ones.

There are no tens or hundreds to borrow from, so borrow from the thousands.

Ones $13 - 8 = 5$, tens $9 - 4 = 5$, hundreds $9 - 7 = 2$, thousands $5 - 2 = 3$.

$6003 - 2748 = 3255$. Check: $3255 + 2748 = 6003$.

Flashcards

Partitioning

Split into hundreds, tens and ones, add each part, then combine.

Compensating for 46 + 99

$46 + 100 - 1 = 145$

Check a subtraction

Add the answer back to the number you took away.

Practice

Find $347 + 225$.
Find $563 - 198$.
Find $4768 + 2359$.
Find $6003 - 2748$.
Find $52 - 38$.
Which is the best way to work out $78 + 99$ in your head?
Which statement is false?
A school has $2400$ students. On Friday, $1015$ are on an excursion. How many are at school?