Year 6

Arithmetic Booklet

Practice

2019-2020

Week 1: Place Value partitioning

Week 2: Multiplying and dividing by 10, 100 and 1000

Week 3: Addition (including decimals)

Week 4: Subtraction (including decimals)

Week 5: Missing values

Week 6: Short multiplication (including decimals)

Week 7: Long multiplication

Week 8: Short division

Week 9: Long division

Week 10: Order of Operations

Week 11: Adding and subtracting fractions

Week 12: Adding and subtracting fractions (mixed numbers)

Week 13: Multiplying and dividing fractions

Week 14: Fractions of amounts

Week 15: Percentages

Week 1: Place Value partitioning

Partitioning is a way of working out maths problems that involve large numbers by splitting them into smaller units so they're easier to work with. EG: Seven million, five hundred thousand and seventy-two

(7, 500, 072).

Sometimes, you are given the number which is partially partitioned:

EG: 5178923 = 5,000,000 + ……….. + 70,000 + ………….. + 900 + 20 + 3

(The digit 1 is in the hundred thousands column so this would be 100,000.

The digit 8 is in the thousands column so this would be 8,000).

Commas are usually used to separate larger numbers (often punctu-ated after every three digits).

YOUR TURN:

1) 8892 = 8,000 + … + 90 + … 6) 450,245 = ?

2) 94,634 = ? 7) 342 = ?

3) 342,789 = ? 8) 311,569 = ?

4) 1,034,237 = ? 9) 76,341 = ?

5) 40,058 = ? 10) 9,994,276 = ?

Week 2: Multiplying and dividing by 10, 100 or 1000

REMEMBER! When you multiply digits in any multiple of 10 (e.g. 10, 100 or 1000) move left; when you divide, your digits move right.

Multiplying makes the number larger (multiplying by 10 means it is ten times larger). Dividing makes the number smaller (dividing by 100 means it is hundred times smaller).

The distance they move depends on the amount of zeros in your number. If you are multiplying by 100 they move left 2 spaces be-cause 100 has 2 zeros. The decimal point does not move.

EG: 27.9 ÷ 10 = 2.79 27.9 ÷ 100 = 0.279 27.9 ÷ 1000 = 0.0279

If you are multiplying by 200 etc, then you can follow the rule by multiplying by 100 first and then multiply your answer by 2.

EG: 34.5 X200 = 34.5 x 100 = 345 (then multiply your answer by 2) 345 x 2 = 690. This can also be achieved by multiplying by 2 first and then multiplying by 100.

YOUR TURN:

1) 6.9 ÷ 10 = ? 6) 0.6 x 200 = ?

2) 567 x 1000 = ? 7) 24 ÷ 200 = ?

3) 45.9 ÷ 100 = ? 8) 126.9 x 300 = ?

4) 0.9 x 10 = ? 9) 244.8 ÷ 300 = ?

5) 50 ÷ 100 = ? 10) 56 x 500 = ?

Week 3: Addition Step One: Line up the digits in the correct columns.

Step Two: Start from the ones column.

Step Three: Remember to carry over any tens e.g. 9 + 8 = 17 (carry the one over).

Step Four: Remember to add all the digits in the column.

Step Five: CHECK YOUR ANSWER!

Adding and subtracting decimals

When adding and subtracting decimals, add or subtract as normal, but make sure that the decimal points are correctly aligned.

EG: 4.27 + 2.3 =

4.27

+ 2.30

______

6.57

Remember that 2.3 is the same as 2.30 (0 hundredths).

YOUR TURN:

1) 56563 + 6529 = ? 6) 0.645 + 0.2 = ?

2) 67865 + 77453 = ? 7) 23 + 3.45 = ?

3) 56344 + 12876 + 34667 = ? 8) 126.9 + 4.599 = ?

4) 99231 + 44538 + 51221 = ? 9) 244.8 + 3.258 = ?

5) 876546 + 345897 = ? 10) 56.31 + 0.3 = ?

Week 4: Subtraction Step One: Line up the digits in the

correct columns.

Step Two: Start from the ones column.

Step Three: Remember to borrow from the column to the left if it is not possible to calculate. TIP: The top digit must be equal to or more than the digit below for it to work. If not, borrow!

Step Four: CHECK YOUR ANSWER! Have you subtracted or accidentally added?

Adding and subtracting decimals

When adding and subtracting decimals, add or subtract as normal, but make sure that the decimal points are correctly aligned.

EG: 5—0.24 =

5.30

- 0.24

______

5.06

Note that we wrote 5 as 5.00. It is not essential to do this, but it helps.

YOUR TURN:

1) 56563—6529 = ? 6) 0.645—0.2 = ?

2) 67865—57453 = ? 7) 23— 3.45 = ?

3) 56344—12876—34667 = ? 8) 126.9— 4.599 = ?

4) 99231— 44538—51221 = ? 9) 244.8—3.258 = ?

5) 876546—345897 = ? 10) 56.31— 0.3 = ?

Week 5: Missing Values Missing values require you to think carefully about which

operation to use!

EG: ……….. + 456 = 560 or ………. - 620 = 1000

As we are working backwards from our answer, we are going to use the opposite operation (often called the inverse).

560—456 = 104 or 1000 + 620 = 1620

EG: 735 + ……… = 1035 or 346—…….. = 146

As we are finding the middle number, we are looking to find the

difference between the two numbers. Therefore, we use

subtraction.

1035—735 = 300 346—146 = 200

Sometimes, a number line can also help (particularly with

negative numbers).

To check any of these answers, complete the calculation in the

formal way to check if the answer is correct.

YOUR TURN:

1) …….. + 422 = 730 6) 409 + ………. = 56032

2) ……. + 1309 = 1320 7) 3954—………. = 2000

3) ……..—568 = 23401 8) 1,324,455 + …….. = 2,000,000

4) …….—8032 = 54555 9) 98543—………….= 23335

5) 608 + ……… = 6006 10) …………… + …………… = 3450

Week 6: Short multiplication Step One: Line up the digits in the

correct columns.

Step Two: Start from the ones column.

Step Three: Three multiplied by 9 = 27 Remember to place the 7 in the answer box and carry the ten (in this case, the 2) below the next column. Carry on as nor-mal: 3 x7 = 21 (then add the two) = 23. The three is placed in the answer box and the two tens are carried over. 3 x 1 = 3. Then add the two equals five (hundred).

Step Four: CHECK YOUR ANSWER!

MULTIPLYING DECIMALS:

• Treat decimals in the same way as whole numbers.

• Approximate first

YOUR TURN: 1) 4500 x 4 = ? 6) 7 x 3.5 = ?

2) 798 x 9 = ? 7) 5.3 x 9 = ?

3) 2337 x 7 = ? 8) 9.2 x 8 = ?

4) 1889 x 6 = ? 9) 4.6 x 3 = ?

5) 5351 x 8 = ? 10) 6.7 x 5 = ?

Week 7: Long Multiplication Step One: Line up the digits in the

correct columns.

Step Two: Start from the ones column.

Step Three: After you have completed the first ones column (6 in this instance), it’s time to complete the second column (the tens, in this example it is 2 tens).

Step Four: Begin by placing in the second row a magic zero (as this tells us that we are multiplying the tens column). Carry on as normal.

Step Five: Add up both answers.

Step Six: CHECK YOUR ANSWER!

YOUR TURN: 1) 641 x 21 = ? 6) 292 x 66= ?

2) 384 x 32 = ? 7) 5371 x 14 = ?

3) 18 x 18 = ? 8) 2377 x 36 = ?

4) 555 x 37 = ? 9) 3464 x 42 = ?

5) 2525 x 46 = ? 10) 5377 x 46 = ?

NOTE: On question three, both numbers which are multi-plied together are the same. This can also be written as 18 squared (or 18²). If there were three identical numbers multiplied, this would be known as cubed (³). More infor-mation will be provided in future weeks.

Week 8: Short Division When dividing by one digit numbers, we use the bus stop method for division.

In the example on the right, the divisor (number we are going to divide by) is placed outside the question e.g. 7. The dividend (number that is to be divided) is placed inside the question e.g. 98.

HINT:

Sometimes a number can’t be divided exactly and there is an amount left over. This is known as the remainder (r.)

Remainders can also be written as fractions—2 remaining out of a possible five means it is 2/5.

Remainders can also be written as decimals (which is important for time or money scenarios).

YOUR TURN: Questions 1-5 keep as a remainder (where appropriate).

Questions 6-10, try to convert (change) into either a fraction or decimal if you can (where appropriate).

1) 5680 ÷ 5 = ? 6) 3027 ÷ 4 = ?

2) 1155 ÷ 7 = ? 7) 5000 ÷ 9 = ?

3) 3048 ÷ 6 = ? 8) 2661 ÷ 3 = ?

4) 715 ÷ 8 = ? 9) 1032 ÷ 4 = ?

5) 3567 ÷ 9 = ? 10) 985 ÷ 7 = ?

Week 9: Long Division Long division is a tricky concept and takes children (as well as adults) a long time to fully mas-ter it.

STEP ONE: List the multiples of 15 on the right. This is essential to get right, otherwise your answer will be slightly incorrect. To make life easi-er, break the number down into 10 and 5 when adding on each multiple. Work from left to right:

STEP TWO: 15 does not go into 4 (leave it blank or write a 0 above the answer). 15 into 43 goes twice. Write 2 above. The 30 then is writ-ten directly underneath the 43. We then subtract the 30 from 43 to find out the remainder, which is 13.

STEP THREE: We then ‘bring down’ the next digit from our question, which is the digit 2. So the number becomes 132. So we repeat the pro-cess. 15 into 132 goes 8 times. The ‘120’ then is written directly under-neath the 132 to find the remain-der. Subtract these numbers to find the remainder, which is 12.

STEP FOUR: Again we ‘bring down’ the next digit of 9 to make it 124. 15 goes into 124 8 times. Write the 8 into the answer above and we are left with a remainder of 4, which can be written in the answer box. For those questions which require an exact answer, the remainder can be converted into a fraction as 4/15 (4 being the remainder out of a pos-sible 15).

YOUR TURN:

1) 915 ÷ 14 =

2) 2091 ÷ 17 =

3) 1250 ÷ 26 =

4) 1448 ÷ 32 =

5) 2366 ÷ 23 =

Week 10: Order of Operations

BIDMAS is an acronym or mnemonic used to help remember the correct order to complete mathematical calculations in (this called ‘order of operations’).

When you complete a mathematical number sentence involving sever-al different operations, then BIDMAS helps you to know which or-der to complete them in. Anything in Brackets should be completed first, then the indices (squared or cubed numbers), followed by any division or multiplication and finally addition or subtraction.

Division and Multiplication have been grouped together as they are of the same level; this means that if you have a calculation involving division and multiplication then you complete them as they appear from left to right. This is the same for addition and subtraction; they are completed as they appear from left to right.

YOUR TURN:

1) 7 + 8 x 3 5) (3 + 2) x 4

2) 23 – 18 ÷ 3 6) 5 – 22 x 2

3) 8 + 3 x 2 - 4 7) 102 – 5 x 2

4) 14 ÷ 2 – 10 ÷ 5 8) (8 – 4) x 32

Week 11 & 12: Adding & Subtracting Fractions

YOURTURN:

1) 4/5 - 2/10 = ? 4) 12/24 + 3/6 = ? 7) 2 & 1/2 + 5/8 = ?

2) 3/9 + 1/6 = ? 5) 8/10—5/20 = ? 8) 1 & 1/8 + 1 & 1/3 = ?

3) 7/8—3/16 = ? 6) 2 & 2/3 + 2 & 5/6 = ? 9) 2 & 1/6 + 7/18 = ?

Week 13: Multiplying & Dividing Fractions

Multiply the numerators together; then multiply the denominators together. Now you have your answer!

YOUR TURN:

1) 3/5 X 1/3 = ? 6) 1/4 ÷ 4 = ?

2) 5/6 X 3/5 = ? 7) 4/5 ÷ 6 = ?

3) 2/3 X 2 & 1/4 = ? 8) 2/5 ÷ 4 = ?

4) 4/6 X 2/3 = ? 9) 5/8 ÷ 9 = ?

5) 6 & 2/3 X 3/5 = ? 10) 2/3 ÷ 7 = ?

Week 14: Fractions of amounts

To find the amount, you need to divide the whole number by the denominator.

EG: 76 divided by 4 = 19

19 would equal 1/4, but we are looking to find 3/4.

You then need to multiply your answer by 3 (which is the nu-merator).

EG: 19 x 3 = 57

HINTS:

If you are finding half of a number, divide by two.

If you are finding a quarter of a number, halve the number

YOUR TURN:

Week 15: Percentages A percentage is a number or ratio expressed as a fraction of 100. When we talk about percentages, we imagine that 'a whole' has been divided into 100 equal parts.

EG: 50% OF 456 = Half of 456 = 228

EG: 25% OF 3000 = 3000 divided by 4 = 750

EG: 20% OF 620 = 620 divided by 5 = 124

EG: 10% OF 890 = 890 divided by 10 = 89

To find other percentages, find 10% and 1% of a number FIRST.

EG: 21% OF 720

Find 10% of 720 (720 divided by 10) = 72

Find 1% of 720 = (720 divided by 100) = 7.2

20% is double 10% so 20% of 720 = 72 x 2 = 144

20% = 144

1% = 7.2

(20% + 1% = 21% 144 + 7.2 = 151.2)

YOUR TURN:

1) 30% of 30 2) 55% of 120 3) 18% of 150 4) 65% of 26

5) 96% of 1000 6) 25% of 44 7) 15% of 60 8) 50% of 428

9) 75% of 416 10) 5% of 680

ANSWERS

Week 1:

1) 8,000 + 800 + 90 + 2

2) 90,000 + 4,000 + 600 + 30 + 4

3) 300,000 + 40,000 + 2,000 + 700 + 80 + 9

4) 1,000,000 + 30,000 + 4,000 + 200 + 30 + 7

5) 40,000 + 500 + 8

6) 400,000 + 50,000 + 200 + 40 + 5

7) 300 + 40 + 2

8) 300,000 + 10,000 + 1,000 + 500 + 60 + 9

9) 70,000 + 6,000 + 300 + 40 + 1

10) 9,000,000 + 900,000 + 90,000 + 4,000 + 200 + 70 + 6

Week 2:

1) 0.69

2) 567,000

3) 0.459

4) 9

5) 0.50

6) 120

7) 0.12

8) 38,070

9) 0.816

10) 28,000

Week 3:

1) 63,092

2) 145,318

3) 103,887

4) 194,990

5) 1,222,443

6) 0.845

7) 26.45

8) 131.499

9) 248.058

10) 56.61

Week 4:

1) 50,034

2) 10,412

3) 8,801

4) 3,472

5) 530,649

6) 0.445

7) 19.55

8) 122.301

9) 241.542

10) 56.01

Week 5:

1) 308

2) 11

3) 23,969

4) 62,587

5) 5,398

6) 55,623

7) 1,954

8) 675,545

9) 75,208

10) Combination of numbers. Ex-ample: 3,000 + 450 = 3,450

Week 6:

1) 18,000

2) 7,182

3) 16,359

4) 11,334

5) 42,808

6) 24.5

7) 47.7

8) 73.6

9) 13.8

10) 33.5

Week 7:

1) 13,461

2) 12,288

3) 324

4) 20,535

5) 116,150

6) 19,272

7) 75,194

8) 85,572

9) 145,488

10) 247,342

Week 8:

1) 1,136

2) 165

3) 508

4) 89.375 or 89 r 3

5) 396.33 or 396 r3

6) 756.75 or 756 r3

7) 555.55 or 555 r 5

8) 887

9) 258

10) 140.71 or 140 r 5

Week 9:

1) 65 and 5/14 or 65 r5

2) 123

3) 48 and 1/13 or 48 r2

4) 45 and 1/4 or 45 r 8

5) 102 and 20/23 or 102 r 20

Week 10:

1) 31

2) 17

3) 10

4) 5

5) 20

6) -3

7) 90

8) 36

Weeks 11 and 12:

1) 6/10 or 3/5

2) 9/18 or 1/2

3) 11/16

4) 24/24 or 1 whole

5) 11/20

6) 5 and 3/6 or 5 and 1/2

7) 3 and 1/8

8) 2 and 11/24

9) 2 and 10/18 or 2 and 5/9

Week 13:

1) 3/15 or 1/5

2) 15/30 or 1/2

3) 18/12 or 1 & 6/12

4) 8/18

5) 60/15 or 4

6) 1/18

7) 4/30

8) 2/20 or 1/10

9) 5/72

10) 2/21

Week 14:

1) 57

2) 21

3) 9

4) 5

5) 15

6) 32

7) 60

8) 11

9) 4

10) 10

11) 15

12) 10

13) 9

14) 180

15) 4

Week 15:

1) 9

2) 66

3) 27

4) 16 and 9/10 or 16.9

5) 960

6) 11

7) 9

8) 214

9) 312

10) 34