Calculations
Addition, subtraction, multiplication and division
Addition
Subtraction
Multiplication
Division
Addition Learning objective: Can I add numbers without using a calculator?
Split the numbers up! The art of this is to split the numbers up into units, tens, hundreds etc. Add each “bit” separately then join them together at the end. If you are asked to find the “sum” of some numbers, add them.
An example of this: Calculate 34 + 55 Split it up into tens and units: Tens: 30 + 50 = 80 Units: 4 + 5 = 9 Final answer: 89
Another example of this: Calculate 187 + 264 Split it up into tens and units: Hundreds: 100 + 200 = 300 Tens: 80 + 60 = 140 Units: 7 + 4 = 11 Final answer: 451
Try these: 1.
2.
3.
4.
26 + 53 = 79 57 + 35 98 + 57 365 + 478
= 92 = 155 = 843
Subtraction Learning objective: Can I subtract numbers without using a calculator?
The key to subtracting is… …to estimate an answer first Perform the subtraction in stages If you are asked to find the “difference” between two numbers, subtract them
What does this mean? Calculate 72 – 38
Firstly take subtract 30
Make it easier: 72 – 30 Answer: 42 42 - 8 Answer: 34
Then subtract 8
A different method: Calculate 72 – 38 Make it easier:
+2 to the number you are subtracting
72 – 40 Answer: 32 Actual answer: 34
+2 to your answer
Another example: Calculate 91 – 23
Subtract 20
Make it easier: 91 – 20 Answer: 71 71 - 3 Actual answer: 68
Subtract 3
Try these: 1.
85 - 36
= 49
2.
52 - 25
= 27 = 38
3.
96 - 58
= 35 4.
124 - 89
Multiplication Learning objective: Can I multiply numbers without using a calculator?
First things first: You need to learn your tables! Every multiplication problem can be broken down into simple tables calculations When you are asked to find the “product� of some numbers, that means multiply them
Do you know these?
Calculate 23 × 8 This is 2 × 8 with a zero on the end
Split the large number up: 20 × 8 3×8
= 160 = 24
Add the answers together as you have a total of 23 eights Answer: 184
Have a go at these: 1.
2.
3.
17 × 6
= 102
26 × 4
= 104
43 × 7
= 301 = 576
4.
64 × 9
When they get a bit tougher: You have a few options They all work just as well as each other Choose the one that works for you
Have a go at calculating 21 × 32 Do it in as many ways possible‌
Which of these did you use to calculate 21 Ă— 32? 30 2
20
1
600
30
40
2
Answer: 672
32 Ă— 21 32 + 640 Answer: 672
2 0
0 0
6 7
1 6 4
0 0
3
3
2
2
2
Answer: 672
Are there any other methods?
Choose a method to calculate 43 Ă— 17? 10 7
40
3
400
30
280
21
Answer: 731
43 Ă— 17 301 + 430 Answer: 731
4 0
0 2
7 13
3 4 8
0 2
3
1
1
7
1
Answer: 731
Are there any other methods?
Multiply these using whichever method you like (no calculators!): 1.
26 × 14
= 364
2.
74 × 39
= 2886
3.
4.
124 × 16 249 × 179
= 1984 = 44571
Division Learning objective: Can I divide numbers without using a calculator?
We can use our tables – how? 300 ÷ 6 is easy because we already know 30 ÷ 6 30 ÷ 6 = 5 So 300 ÷ 6 =50 2800 ÷ 4 is easy because we know 28 ÷ 4 28 ÷ 4 = 7 So 2800 ÷ 4 = 700
Have a go at these: 1.
2.
3.
2000 รท 5
= 400
320 รท 4
= 80
33,000 รท 3
= 11,000 = 6,000,000
4.
42,000,000 รท 7
Sometimes the division problems are a little tougher‌
The “bus stop” method You do need to know your tables! The most common method is called “the bus stop”, because it looks like the numbers are waiting in a bus stop The divisor goes outside the “bus stop” You can also add multiples of your divisor, but this will take you longer!
Calculate 135 ÷ 3 Bus Stop Draw the bus stop:
Divisor
0 3
1
4 1
3
5 1
5
Divide each value by 3, not forgetting to carry any remainders.
Multiples We need to do the following calculations: 10 × 3 = 30
Total so far: 30
10 × 3 = 30
Total so far: 60
10 × 3 = 30
Total so far: 90
10 × 3 = 30
Total so far: 120
5 × 3 = 15
Total so far: 135
The answer is on top! How many 3s in total?
Answer: 45
Answer: 45
What about 322 ÷ 14 Bus Stop Draw the bus stop:
Divisor
0
14
3
2
3
2
3
4
2
Multiples We need to do the following calculations: 10 × 14 = 140 10 × 14 = 140
Divide each value by 14, not forgetting to carry any remainders.
Total so far: 140 Total so far: 280 Total so far: 322
3 × 14 = 42
The answer is on top!
How many 14s in total? Answer: 23
Answer: 23
Calculate these, without a calculator! 1.
2.
3.
168 รท 7 222 รท 6 384 รท 12
= 24 = 37 = 32 = 56
4.
952 รท 17
Test Your Powers! Find as many way as possible of achieving the following numbers‌
How many different calculations can you come up with that have the answer below?
128
How many different calculations can you come up with that have the answer below?
369
How many different calculations can you come up with that have the answer below?
729
How many different calculations can you come up with that have the answer below?
2048
How many different calculations can you come up with that have the answer below?
7776