Tawa College - Junior - Number Revision

Junior Number Revision

By Lynley MacEwan

Factors, Multiples and Primes

Factors are numbers that can be evenly divided into a number

e.g the factors of 10 are 1, 2, 5 and 10​

Multiples are the numbers in the times table​

e.g. multiples of 4 are 4, 8, 12, 16, ...​

Prime numbers have exactly 2 factors (and are usually odd)

e.g. 2, 3, 5, 7, 11, 13, ....​

The LCM (Lowest common multiple) is the smallest multiple for 2 numbers​

e.g. For 8 and 12 it is 24 as 2x12 = 24 and 3x8 = 24 and its the smallest

The HCF (Highest Common Factor) is the largest factor common to 2 numbers​

e.g. For 24 and 16 it is 8 as it is the highest number that can divide into both​

Multiple Choice

List all the factors for the number 9

• 9
• 3,3
• 1,9
• 1,3,9

Multiple Choice

For the number 52; which factor or factors are missing from this list: 1, 2, 4, 26

• 52
• 12, 52
• 13, 52
• 6, 13, 52

Multiple Choice

What is the only even number that is prime?

• 1
• 2
• 4
• 10

Multiple Choice

I am a prime number between 30 and 40.  Which number could I be?

• 31
• 33
• 36
• 39

Multiple Choice

Which is a NOT a factor of 12?

• 1
• 3
• 5
• 12

Multiple Choice

Which is not a factor of 36?

• 1
• 5
• 6
• 12

Multiple Choice

Which shows ALL of the factors of 14?

• 1, 14
• 2, 7
• 1, 2, 7, 14
• 1, 28

Multiple Choice

What are the first 5 multiples of 3?

• 3, 6, 9, 12, 16
• 3, 6, 9, 13, 15
• 3, 6, 8, 12, 15
• 3, 6, 9, 12, 15

Multiple Choice

What are the multiples of 9?

• 9, 12, 15, 18, 21
• 9, 18, 27, 36, 45, 54
• 3, 6, 9, 12, 15, 18
• 9, 19, 29, 39, 49, 59

Multiple Choice

List all the factors of 12

• 1, 2, 3, 4, 6, 12
• 1, 2, 4, 12
• 1, 12
• 1, 2, 3, 4, 5, 6, 12

Multiple Choice

What is the HCF of 28 and 40?

• 2
• 4
• 7
• 8

Multiple Choice

Find the HCF of 30 and 36

• 2
• 3
• 4
• 6

Multiple Choice

Find the LCM of 12 and 16...

• 48

• 36

• 64

• 96

Multiple Choice

Find the LCM of 5 and 8...

• 40

• 80

• 20

• 60

Using your calculator correctly

Here are the buttons you need to be able to use

​

​The three buttons we are learning are the first four on the bottom line. and what is above them accessed by 2nd function.

They are ​- fractions - square root - squares - powers.

Try using them to do these first 24 questions​

​

Multiple Choice

-5 - (- 3)

• -8
• 8
• -2
• 15

Multiple Choice

$$\frac{-32}{8}$$  

• -4
• -5
• 4
• 24

Multiple Choice

3 - (-8)

• 11
• -11
• 5
• -5

Multiple Choice

-8 - (-6)

• 2
• 14
• -2
• -14

Multiple Choice

-9 x 3 =

• -27
• 27
• -28

Multiple Choice

-12 x -5 =

• -55
• 55
• 60
• -60

Multiple Choice

$$\frac{3}{6}+\frac{1}{6}=$$  

• $$\frac{4}{12}$$  

• $$\frac{2}{3}$$  

• $$\frac{3}{36}$$  

• $$\frac{1}{2}$$  

Multiple Choice

$$2\ \times\frac{5}{6}=$$  

• $$\frac{10}{6}$$  

• $$\frac{10}{12}$$  

• $$\frac{5}{6}$$  

• $$\frac{5}{12}$$  

Multiple Choice

Write the fraction in simplest form:  $$\frac{10}{12}$$  

• $$\frac{1}{2}$$  

• $$\frac{1}{12}$$  

• $$\frac{3}{8}$$  

• $$\frac{5}{6}$$  

Multiple Choice

$$\frac{2}{3}\times\frac{1}{5}=$$  Find the product:

• $$\frac{2}{15}$$  

• $$\frac{3}{8}$$  

• $$\frac{3}{10}$$  

• $$\frac{3}{4}$$  

Multiple Choice

$$\frac{2}{3}+\frac{1}{6}=$$   Find the sum. Write your answer in simplest form.

• $$\frac{3}{9}$$  

• $$\frac{1}{3}$$  

• $$\frac{5}{6}$$  

• $$\frac{7}{8}$$  

Multiple Choice

$$\frac{3}{5}-\frac{3}{10}=$$   Find the difference. Write your answer in simplest form.

• $$\frac{3}{10}$$  

• $$\frac{9}{10}$$  

• $$\frac{3}{4}$$  

• $$\frac{3}{20}$$  

Multiple Choice

$$\frac{12}{5}=$$   Write as a mixed number.

• $$1\frac{1}{5}$$  

• $$3\frac{2}{10}$$  

• $$2\frac{1}{5}$$  

• $$2\frac{2}{5}$$  

Multiple Choice

What is 11 squared?

11²

• 132

• 144

• 121

• 22

Multiple Choice

What is 64 squared?

64²

• 4096

• 8

• 16

• 128

Multiple Choice

What is the square root of 36?

√ 36

• 4

• 6

• 18

• 1296

Multiple Choice

19² = _____

• 400
• 360
• 324
• 361

Multiple Choice

√196 = ______

• 14
• 14²
• 15
• 15²

Multiple Choice

Solve for x.

• x = 4/3

• x = 9/4

• x = 9/16

• x = 3/16

Multiple Choice

The result of power expression $$5^4$$ is...

• 20

• 25

• 125

• 625

Multiple Choice

• 8
• 9
• 10
• 11

Multiple Choice

Find the cube root. 

• -4
• 4
• 8
• -8

​Rounding

Decimal Places

Count from the decimal place.

Look at the next number.

If 5 or above add one to the number before.

e.g. 2.57 to 1dp is 2.6

e.g. 5.3154 to 3 dp is 5.315

e.g. 2.998 to 2 dp is 3.00​

​Significant Figures

Count from the first non zero digit.

Round up if 5 or more

Make sure the number keeps it's size​

​

e.g. 54363​ to 2 sig fig is 54000

e.g. 2176 to 3 sig fig is 2180

e.g 0.0026 to 3 sig fig is ​0.003

Multiple Choice

What is 3.4550 rounded to 1 decimal place?

• 3.4
• 3.5
• 3
• 3.46

Multiple Choice

What is 12.99 rounded to 1 decimal place?

• 13

• 13.0

• 12.9

• 12.10

Multiple Choice

Round this number to two decimal place: 35.192

• 35.1

• 35.18

• 35.2

• 35.19

Multiple Choice

Round 134.67398 to 2 decimal places

• 134.67

• 134.700

• 134.6

• 134.68

Multiple Choice

Round 46.7863 to 3 decimal places

• 46.768

• 46.786

• 46.358

• 46786

Multiple Choice

Round 9563.28 to 1 significant figure

• 9

• 9000

• 10000

• 9000.0

Multiple Choice

Round 0.05098 to 2 significant figures

• 0.050

• 0.0050

• 0.059

• 0.051

Multiple Choice

Round 808094.2 to 4 significant figures

• 808100

• 808010

• 808090

• 808000

Order of Operations

When we use BEDMAS we do

• Whats in brackets first

• anything with a power next

• then Division and multiplication equally from left to right

• then addition and subtraction equally from left to right​

• if netered correctly our calculator will do BEDMAS

​ e.g. 3 + 4 x ( 3 + 7) = 3 + 4 x 10

=​ 3 + 40

= 43​

Multiple Choice

24x(4-2)÷6

• 8
• 2
• 6
• 5

Multiple Choice

7x(7-4)÷3

• 8
• 6
• 7
• 5

Multiple Choice

40+(72÷9)÷8

• 49
• 25
• 41
• 15

Multiple Choice

Solve the following:
(2 + 7 - 1) ÷ 2²

• 16
• 2
• 72.25
• 8.75

Multiple Choice

16 - 8 ÷ 2 + 5

• 17
• 7
• 9

Multiple Choice

Solve the following:
-2 x (3 + 8 ÷ 4)²

• -16
• 1.375
• 4
• -50

Multiple Choice

Simplify:
[25-(13+4)+4] ÷ 3

• 6
• 2
• 3
• 4

Percentages to fractions to decimals

Remember to use your calculator.

Fractions to decimals use the F to D

or S to D ​ key

Multiple Choice

What is $$\frac{7}{10}$$   as a decimal?

• 0.7

• 0.1

• 0.07

• 7

Multiple Choice

Which is closest to a $$\frac{1}{3}$$   as a decimal?

• 0.3

• 0.33

• 0.34

• 0.333

Multiple Choice

What is 0.34 as a percentage?

• 0.34%

• 3.4%

• 34%

• 340%

Multiple Choice

What is 0.6 as a percentage?

• 0.6%

• 6%

• 60%

• 66%

Multiple Choice

What is 0.4% as a decimal?

• 0.4

• 0.04

• 4

• 0.004

Multiple Choice

What is 3/4 as a decimal?

• 0.25

• 0.50

• 0.75

• 0.34

Multiple Choice

What is 0.4 as a fraction?

• $$\frac{2}{5}$$  

• $$\frac{4}{5}$$  

• $$\frac{1}{4}$$  

• $$\frac{4}{1}$$  

Multiple Choice

What is $$\frac{4}{5}$$   as a percentage?

• 45%

• 40%

• 90%

• 80%

​Writing as a percentage

Fill in the Blank

Express 38 as a percentage of 200

Fill in the Blank

Express 60 as a percentage of 80

Fill in the Blank

100 pupils entered a drawing competition. 58 of them were girls. What percentage of the pupils who entered the competition were girls?

Fill in the Blank

A jogging route is 10km long. Zaman has jogged 4km. What percentage of the route has Zaman jogged?

Fill in the Blank

Jasman finished $$\frac{3}{5}$$  of his homework. What percentage of his homework did he finish?

Fill in the Blank

Ali was asked to paint a wall of area $$84cm^2$$  . In one hour, he finished painting  $$21cm^2$$  of the wall. What percentage of the wall was painted?

A percentage of ...

Multiple Choice

Calculate 25% of 80

• 20
• 80
• 48
• 95

Multiple Choice

What is 30% of 50?

• 16
• 16.3
• 17.4
• 15

Multiple Choice

Today, you have a 20% off of the price coupon for Best Buy. If you buy an XBox game that costs $65.00, how much money will you be saving by using your coupon?

• $13.00
• $15.00
• $7.00
• $42.00

Multiple Choice

Mandy bought Halloween decorations from Amazon.com for $90.  Shipping and handling are an additional 20% of the price.  How much shipping and handling will Mandy pay?

• $19
• $17
• $20
• $18

Multiple Choice

Co went to Denny's for breakfast today.  He ordered a Grand Slam for $7.95 and an orange juice for $2.05.  He left the waitress a tip worth 10% of the total bill. How much money did he leave the waitress?

• $1.50
• $2.00
• $3.00
• $1.00

Multiple Choice

Carter made 27 of the 30 conversions he attempted in one season. What percent of the conversion attempts did he make?

• 15%

• 90%

• 10%

• 5%

Increasing and decreasing

Multiple Choice

Increase $50 by 90%

• $70

• $90

• $95

• $100

Multiple Choice

Increase $20 by 30%

• $22

• $24

• $26

• $28

Multiple Choice

Decrease $80 by 30%

• $56

• $50

• $60

• $70

Multiple Choice

The population of a town is 45 000.

The population is expected to rise by 15% in the next ten years.

Estimate the population in ten years’ time

• 6 750

• 38 250

• 51 750

Multiple Choice

A metal bar is 1.8 metres long.

It is heated and the length increases by 0.5%.

How long is the bar now?

• 9

• 1 809

• 1 791

Multiple Choice

Caleb is interested in a jacket that is $245 with a sale price of 30% off.

How much will the jacket cost ?

• $275

• $171.50

• $318.50

• $350

Multiple Choice

GST is 15%. If a pair of jeans is $120 before GST is added on, How much will it cost after GST is included?

• $135

• $138

• $18

• $15

​Ratios

Simplifying Ratios is like simplifying fractions.

​e.g. Simplify 12 : 24 = 1 : 2

​or Simplify 18 : 16 : 24 = 9 : 8 : 12​

​Splitting in a ratio has a number of steps

1. How many parts?

2. ​Whats a part worth?

3. What is each share worth?​

Multiple Choice

A class has 15 boys and 20 girls. What is the boy:girl ratio in simplest form?

• 4 : 5

• 10 : 13

• 3:4

• 3:5

Multiple Choice

The Northwestern huskies had a record of 25 wins and 45 losses.  What was the ratio of wins to losses?

• 9:5
• 5:9
• 5:3
• 3:5

Multiple Choice

What is the ratios of cats to dogs if there are 28 cats and 70 dogs?

• 2:5
• 5:2
• 70:28
• 98

Multiple Choice

Simplify the ratio of
35 : 14

• 5 : 2
• 2 : 5
• 3 : 1
• No Option is Correct

Multiple Choice

Express the following ratio in simplest form:

20:45

• 10:22.5

• 4:9

• 40:90

• 5:9

Multiple Choice

Share 40 sweets between Saja and Keeley in the ratio 5 : 3

• 25 : 15 sweets

• 15 : 25 sweets

• 30 : 10 sweets

• 5 : 3 sweets

Multiple Choice

Share 21kg in the ratio 3 : 4

• 9kg : 12kg

• 12kg : 9kg

• 8kg : 12kg

• 7kg : 14kg

Multiple Choice

Share 60 litres in the ratio 7 : 5

• 35L : 25L

• 25L : 35L

• 7L : 5L

• 35kg: 25kg

Multiple Choice

Share 66ml in the ratio 2 : 4 : 5

• 12ml : 24ml : 30ml

• 12g: 24g : 30g

• 2ml : 4ml : 5ml

• 30ml : 12ml : 24ml

Multiple Choice

$360 is shared among Thomas, Daniel, and Harrison in the ratio 2:3:5. How much is the largest amount received?

• $108

• $72

• $180

• $164

Multiple Choice

A tin of biscuits contains shortbread, fruit, and chocolate biscuits in the ratio 3:1:4.

The tin contains 56 chocolate biscuits.

How many biscuits in the box are fruits?

• 21

• 28

• 7

• 14