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