NOTE:

Q1-5 from long division and long multiplication taken from GCSE maths course – these are Q1-10 here.

Q11-20 are new.

My attempt to make a nice bus stop method in latex:

\def\arraystretch{1.5} \begin{array}{cc|ccccc} &  & 0 & 1 & 2 & . & 5\\ \hline 4 & 2 & 5 & ^{5}2 & ^{10}5 & . & ^{21}0\end{array}

QUESTIONS 11-15 – LONG DIVISION WITH DECIMALS


Question 11

LEVEL 4

Using long division, calculate the following:

125\div 4.2

Select the correct answer from the options below:

A: 125

B: 115

C: 105

D: 135

 

CORRECT ANSWER:  125

WORKED SOLUTION:

First, multiply the value of 4.2 by 10 to get 42, then calculate 525 \div 42

\;\;\;\;\;0\;\;\;1\;\;\;2\;.\;\;5\\42\overline{\left)5\;{}^5 2\;{}^{10} 5\;.{}^21 0\right.}

 

This gives a value of 12.5.

Finally, multiply 12.5 by 10 to get 125


Question 12

LEVEL 4

Using long division, calculate the following:

72\div 4.5

Select the correct answer from the options below:

A: 16

B: 20

C: 22

D: 12

 

CORRECT ANSWER:  16

WORKED SOLUTION:

First, multiply the value of 4.5 by 10 to get 45, then calculate 72 \div 4.5

\;\;\;\;\;0\;\;1\;.\;\;6 \\45\overline{\left)7{} ^7\; 2{}\;. ^{27} 0{}\right.}

 

This gives a value of 1.6.

Finally, multiply 1.6 by 10 to get 16


Question 13

LEVEL 4

Using long division, calculate the following:

186\div 2.4

Select the correct answer from the options below:

A: 77.5

B: 80.5

C: 75.5

D: 70.5

 

CORRECT ANSWER:  77.5

WORKED SOLUTION:

First, multiply the value of 2.4 by 10 to get 24, then calculate 186 \div 24

\;\;\;\;\;0\;\;0\;\;7\;\;.\;\;\;7\;\;\;5 \\24 \overline{\left)1{} ^1\; 8{} ^{18} 6{}\; . \; ^{18} 0\; ^{12}0\right.}

 

This gives a value of 1.6.

Finally, multiply 1.6 by 10 to get 16


Question 14

LEVEL 4

Using long division, calculate the following:

96.5\div 8

Select the correct answer from the options below:

A: 12.0625

B: 15.005

C: 14.05

D: 15.50

 

CORRECT ANSWER:  12.0625

WORKED SOLUTION:

Use the bus stop method:

\;\;\;1\;\;2\;\;.\;\;0\;\;6\;\;2\;\;5 \\8 \overline{\left)9{}\; ^1 6{}\;.  \;5{} \; ^5 0{} \;^{2}0\; ^{4}0\right.}

So the answer is 12.0625


Question 15

LEVEL 4

Using long division, calculate the following:

654.5\div 4

Select the correct answer from the options below:

A: 163.625

B: 165.75

C: 170.25

D: 155.5

 

CORRECT ANSWER:  163.625

WORKED SOLUTION:

Use the bus stop method:

\;\;\;1\;\;6\;\;\;3\;\;.\;\;6\;\;\;2\;\;5 \\4 \overline{\left)6{}\; ^2 5{}\; ^1 4{}\; \;.  ^2 5{}\; ^1 0{}\; ^{2}0 \right.}

So the answer is 163.625


QUESTIONS 16-20 – LONG MULTIPLICATION WITH DECIMALS


Question 16

LEVEL 4

Using long multiplication, calculate the following:

27.3\times12

Select the correct answer from the options below:

A: 327.6

B: 324.6

C: 342.6

D: 367.6

CORRECT ANSWER: 327.6

WORKED SOLUTION:

First, multiply 27.3 by 10 (we will divide by 10 at the end) and then calculate 273\times12

We can split the calculation up into steps, so

200\times12=2400

70\times12=840

3\times12=36

Adding together the results

2400+840+36=3276

Finally, dividing by 10 gives 327.6


Question 17

LEVEL 4

Using long multiplication, calculate the following:

103\times8.2

Select the correct answer from the options below:

A: 844.6

B: 895.2

C: 873.2

D: 824.6

CORRECT ANSWER: 844.6

WORKED SOLUTION:

First, multiply 8.2 by 10 (we will divide by 10 at the end) and then calculate 103\times 82

We can split the calculation up into steps, so

100\times 82=8200

3\times 82= 246

Adding together the results

8200+246=8446

Finally, dividing by 10 gives 844.6


Question 18

LEVEL 4

Using long multiplication, calculate the following:

97\times3.24

Select the correct answer from the options below:

A: 314.28

B: 320.32

C: 300.82

D: 322.2

CORRECT ANSWER: 314.28

WORKED SOLUTION:

First, multiply 3.24 by 100 (we will divide by 100 at the end) and then calculate 324\times 97

We can split the calculation up into steps, so

300\times 97=29100

20\times 97= 1940

4\times 97 = 388

Adding together the results

29100+1940+388=31428

Finally, dividing by 100 gives 314.28


Question 19

LEVEL 4

Using long multiplication, calculate the following:

18.2\times15

Select the correct answer from the options below:

A: 273

B: 287

C: 275

D: 282

CORRECT ANSWER: 273

WORKED SOLUTION:

First, multiply 18.2 by 10 (we will divide by 10 at the end) and then calculate 182\times 15

We can split the calculation up into steps, so

100\times 15=1500

80\times 15= 1200

2\times 15 = 30

Adding together the results

1500+1200+30=2730

Finally, dividing by 10 gives 273


Question 20

LEVEL 4

Using long multiplication, calculate the following:

39.3\times 6

Select the correct answer from the options below:

A: 235.8

B: 245.8

C: 247.8

D: 232.8

CORRECT ANSWER: 235.8

WORKED SOLUTION:

First, multiply 39.3 by 10 (we will divide by 10 at the end) and then calculate 393\times 6

We can split the calculation up into steps, so

300\times 6=1800

90\times 6= 540

3\times 6 = 18

Adding together the results

1800+540+18=2358

Finally, dividing by 10 gives 235.8