Revision notes - Fractions, Percentages and Decimals

• Fraction - part of a whole

• Equivalent fractions - fractions which have the same value.

• Improper fraction - fraction in which numerator is greater than denominator.

• Mixed number - has a whole number and a fraction next to it.

• Converting mixed number to improper fraction -

Multiply the denominator and the whole number and add the numerator. denominator remains the same.

Example:  3 1/2

3 x 2 = 6      6 + 1 = 7     so 3 1/2 = 7/2

• Converting improper fraction to mixed number -

Divide the numerator by denominator, answer will be the whole number, remainder will be the numerator and denominator remains the same.

Example:  9/2 

9 divided by 2 is 4 remainder 1 so 9/2 = 4 1/2

• Comparing fractions:

Scenario 1: If the denominators are the same, look at the numerators.

If the numerator is a bigger, the fraction is bigger.

Example: 1/6 < 2/6 < 3/6

Scenario 2: If the denominators are different but the numerators are the same, look at the denominator. As the denominator gets bigger, fraction gets smaller.

Example: 1/7 < 1/6 < 1/5

Scenario 3: If the denominators and numerators are different, make the denominators the same(by multiplying or dividing).

Example: find out which of the following fractions is bigger.

3/5     or  1/3

You can make them both fifteenths.

In 3/5, multiply the denominator by 3(always follow rule whatever done to the denominator should be done to the numerator). So 3/5 would become 9/15.

Similarly, 1/3 would become 5/15.

Now, you have two fractions with similar denominators which are easy to compare.

9/15  > 5/15  so 3/5 > 1/3

• Adding and subtracting fractions:

Before you add or subtract fractions, you always have make their denominators the same. Remember, you can do this only by multiplying or subtracting.

• Multiplying fractions:

This is straight forward. Multiply the numerators and multiply the denominators.

3/5 x 1/2  =  3 x 1/5 x 2 = 3/10

3 x 2/3 is same as 3/1 x 2/3  = 3 x 2 /1 x 3 = 6/3 = 2

• Dividing fractions:

  3/5  ÷ 2/3   follow the rule Keep, Change and Flip.

Keep 3/5, change ÷ into x and flip 2/3

So, it would be 3/5 x 3/2 which is equal to 9/10.

• Finding half of a fraction:

Example: find half of 3/5

3/5 ÷ 2  which would be 3/5 x 1/2 which is equal to 3/10

Basically, you multiply the denominator by 2.

So, half of 3/4 is equal to 3/8 and half of 2/3 is equal to 2/6 which is equal to 1/3

• Finding fraction of an amount or quantity:

Divide by the denominator and multiply by the numerator.

So, to find 3/4 of 60, divide 60 by 4 and multiply the answer you get by 3.

When you divide 60 by 4, you are actually finding 1/4 of 60.

There are three quarters in 3/4, so  you have to multiply the answer by 3.

• Finding the original amount or quantity, when you know the fraction.

Example: If 3/4 of a number is 15, what is the number?

3/4 = 15.

So 1/4 = 5 because 15 ÷ 3 = 5

 1 whole is 5 x 4 which is 20

So the number is 20

• Fractions, Percentages and Decimals are related.

1/2 = 50% = 0.5

1/4 = 25% = 0.25

3/4 = 75% = 0.75

1/10 = 0.1 = 0.1

1/5 = 20% = 0.2

2/5 = 40% = 0.4

3/5 = 60% = 0.6

4/5 = 80% = 0.8

1/100 = 1% = 0.01

1/8 = 12.5% = 0.125

1/3 = 33 1/3% = 0.33

From the above, you can understand how to find percentages of an amount of quantity.

To find 50%, divide the amount by 2 as 50% = 1/2

To find 25%, divide the amount by 4 as 25% = 1/4

To find 75%, divide the amount by 4 and multiply the answer by 3 as 75% = 3/4

To find 10%, divide the amount by 10 as 10% = 1/10

To find 20%, divide the amount by 5 as 20% = 1/5

and so on.

If you have to find 15% of something, find 10% and 5% and add the answers together.

• Finding sale price:

Example: A scarf is sold at a discount of 20%. If the original price is £15, what is the discount and how much does it cost after discount?

Discount is 20%

20% of £15 = £15 ÷ 5 = £3 so discount = £ 3

Price after discount = £15 - £3 = £12

Remember, this type of question involves two steps.

If the question asks you to find sale price or discounted price, you have to find the sale or discount amount and take it away from the original price.

Key: Always read the question properly, make sure what has been asked and answer accordingly.

• Finding the whole amount when you know the percentage.

Example. A scarf was sold at a discount of 20%. After discount, it costs £24. What was the original price or the price before discount?

Discount is 20%. So, price after discount would be 80% because price after discount = original price - discount

price after discount = 100% - 20% = 80%

So, according to the question, 80% = £24

        you can work out 10%, 10% = £24 ÷ £8 = £3

original price which is 100% = £3 x 10 = £30

• Decoding pie charts

Hint: 90 degrees represent 1/4

Example: 60 children were asked what their favourite flavour of ice-cream was. 30 said vanilla, 10 said chocolate and mint, 5 said chocolate and 15 said toffee ice-cream. If you show the results in a pie-chart, what angle would represent number of children who liked a) vanilla, b) chocolate and mint, c) chocolate and d) toffee ice-cream?

 Work out the fraction first.

Fraction of children who liked vanilla = 30/60 = 1/2

There are 360 degrees in a circle, so would be represented by 180 degrees.

Fraction of children who liked chocolate and mint = 10/60 = 1/6

1/6 of 360 degrees = 360 ÷ 6 = 60 degrees

Fraction of children who liked chocolate = 5/60 = 1/12

1/12 of 360 degrees = 360 ÷ 12 = 30 degrees

• Multiplying decimals by 10, 100, 1000 etc.

When you multiply, the numbers move left. Number of places depend on the zeros in the multiplying number.

So 2.5 x 10 = 25

When you multiply a number by 10, the number becomes 10 times bigger and 25 is 10 times bigger than 2.5

2.5 x 100 = 250

250 is 100 times bigger than 2.5

• Dividing decimals by 10, 100, 1000 etc.

When you divide, the numbers move right. Number of places depend on the number of zeros the divisor has

 25 ÷ 10 = 2.5

2.5 ÷ 10 = 0.25

 When you divide a number by 10, it becomes 10 times smaller. So, 2.5 is 10 times smaller than 25.

• Multiplying decimals:

2.5 x 3.1 = 7.75

because 25 x 31 =775 and 2.5 is 10 times smaller than 25 and 3.1 is 10 times smaller than 31, so the answer will be 100 times smaller than 775 which is 7.75

25 x 31 = 775

2.5 x 3.1 = 7.75

 Also, 25 x 0.31 = 7.75 because 25 has not changed and 31 has become 100 times smaller, so the answer will be 100 times smaller than 775 which is 100 times smaller than 775

• Dividing decimals:

The idea is that the number with which you are dividing can not be a decimal. So, try to make it a whole number by multiplying by 10, 100, 1000 etc.

Example: 25 ÷ 0.5

multiply 0.5 by 10 to make it 5

You have to multiply 25 by 10 also because you are multiplying 0.5 by 10

25 x 10 ÷ 0.5 x 10 = 250 ÷ 5 = 50

The answer is 50

Revision - Fractions

Write two equivalent fractions for the following fractions:

a) 1/2          f) 2/5          k)  5/6

b) 1/3          g) 3/5         l)   7/8

c) 1/4          h) 4/5         m)  1/10

d) 3/4          i) 1/5          n)   7/10

e) 2/3          j)  1/6         o)   3/10

Reduce the following fractions to lowest terms:

1) 12/36            6) 6/78

2) 15/60            7) 18/24

3) 32/40            8) 45/50

4) 24/60            9) 45/70

5) 36/60           10) 21/30

Which of the following fractions add up to 1? Out of the five fractions listed in each question, pick two that add up to1:

Hint: reduce them to lowest terms to find out

1)  2/3 , 3/4, 2/6, 1/2, 1/5

2)  4/5, 1/3, 1/4, 1/6, 2/10

3)  2/8, 3/4, 1/8, 1/6, 1/2

4)  3/8, 1/3, 3/4, 5/6, 5/8

5)  3/10, 1/3, 3/5, 1/5, 2/5

Match the following fractions in column A with that in column B that add up to 1:

             A                                          B

           1/6                                         4/5

           2/3                                         1/4

           1/5                                         1/2

           3/4                                         5/6

           1/2                                         1/3

Arrange the following fractions from smallest to biggest:

1)    1/2, 1/4, 1/6, 1/5, 1/3

2)     1/15, 3/5, 2/3, 2/5, 1/3

3)     1/2, 1/3, 5/6, 2/3,  1/6

4)    3/5, 3/4, 3/8, 3/7, 3/10

5)    3/10,  1/5,  7/10,  3/5, 3/15

Which of the following fractions is bigger?

1)      3/5     or        4/5

2)     1/6      or        2/3

3)     4/5      or       3/15

4)     2/3      or       4/5

5)     1/3      or       3/10

6)     3/7      or       2/5

7)     2/15    or       1/5

8)     4/5      or       3/10

9)     9/10    or       1/3

10)   3/4      or       2/8

How many halves are there in 1?

How many thirds are there in 1?

How many tenths are there in 1?

How many thirds are there in 5?

How many fifths are there in 3?

How many tenths are there in 4?

How many sixths are there in  6?

How many halves are there in 2 1/2?

How many quarters are there in 2  1/2?

How many quarters are there in 3  3/4?

1)  4/5    =   ?/20

2)   ?/6   =   5/30

3)  4/7    =   16/?

4)  3/10   =   ?/30

5)   5/8    =   ?/48

Add the following fractions:

1/2 +  3/4  = ----------

3/4  +  3/4  = ----------

2  1/4  +  3  1/2  = ---------

5  1/2  +  6  3/4  = ----------

7  1/4   +  7  1/2 = ------------

3  1/6  +   4  3/6 = ----------

2  7/8  +   3  1/8 = -----------

4  5/6   +   5  3/6 = ------------

7  1/2  +   3  3/4 = ----------

9 1/4  +   4  3/4 = ----------

KS2 Spelling list 3

Words ending in e - drop e and add 'ing':

give             giving
hope            hoping
lose             losing
share           sharing
shake           shaking
take             taking
write           writing
make           making

smile           smiling

make           making

raise            raising

escape         escaping

range           ranging

combine      combining

divide          dividing

include        including

exclude       excluding

challenge    challenging

survive        surviving

serve           serving

examine      examining

investigate investigating

Now it's your turn to add more words to the above list.

Words ending in vowel and consonant - double the consonant when adding 'ing' or 'ed':

plan      planning     planned
stop      stopping     stopped
drop     dropping     dropped
hop      hopping       hopped
grip      gripping      gripped
grab     grabbing      grabbed
occur    occurring    occurred
slip      slipping        slipped
chat     chatting
sit        sitting
hit        hitting
begin   beginning
swim   swimming

KS2 Spelling List 2

Plural words:

Words ending in y:

Rule: If the word ends in vowel and y, add s

Example:

key           keys                  

monkey    monkeys

valley       valleys

boy           boys

toy            toys

day           days

holiday     holidays

survey      surveys

delay        delays

journey    journeys

trolley      trolleys

way          ways

tray           trays

turkey       turkeys

delay         delays

You can add similar words to the above list.

If the words end in a consonant and y, remove y and add -ies:

spy              spies                     sky            skies

baby            babies                  berry         berries

story            stories                  jelly          jellies

city              cities                    canary      canaries

library          libraries               lady          ladies

dictionary    dictionaries          ability      abilities

delivery       deliveries             difficulty  difficulties

enquiry        enquiries              similarity  similarities

query           queries                 activity     activities

pharmacy    pharmacies           variety     varieties

injury          injuries                 diary       diaries

colony         colonies               enemy    enemies

cavity          cavities                

You can add similar words to the above list

Verbs ending in consonant and y: remove y and -ies(some of the following words are nouns also)

cry      cries           try        tries

reply   replies        study    studies

carry   carries        reply    replies

marry  marries      

fly       flies

Verbs ending in vowel and y: add s

play     plays

pray     prays

buy      buys

enjoy   enjoys

spray   sprays

stay     stays

Words ending in f:

Remove f and -ves

leaf       leaves            shelf   shelves

loaf       loaves            hoof   hooves

scarf     scarves

thief      thieves

wolf      wolves

half        halves

calf        calves

elf          elves

Exceptions:  chief    chiefs

                     chef     chefs

                     roof     roofs

Words ending in -fe:

knife  knives

life     lives

wife   wives

Words ending in o:

Rule: If the words end in a vowel and o, add s.

        

radio         radios

video        videos

studio       studios

igloo         igloos

kangaroo   kangaroos

If the words end in a consonant and o, add s or -es.

piano    pianos

photo   photos

zero     zeros

hero       heroes

tomato   tomatoes

potato    potatoes

echo       echoes

Words ending in -ch, -sh, s, -ss or -x:

If a word ends in ch or x, add -es.

church   churches        bench       benches

watch      watches        torch        torches

inch         inches          branch     branches

peach       peaches       coach       coaches

beach       beaches        sandwich  sandwiches

batch       batches        match        matches

bus     buses             dress       dresses

gas      gases            address   addresses

                                    glass       glasses

                                    class       classes

bush      bushes

wish      wishes

brush     brushes

dash       dashes

flash       flashes

dish        dishes

box       boxes

fox       foxes

tax        taxes

Other words

foot       feet           door     doors

tooth     teeth          moose   moose

goose    geese        deer      deer

                              sheep   sheep

mouse      mice          house   houses

louse        lice

ox          oxen             cactus    cacti

child      children        radius    radii

man        men             antenna  antennae

woman   women

  

KS2 Spelling List 1

Adverbs with two 'l's:

Note: If an adverb is derived from an adjective ending with an 'l', then it has two 'l's.

thankful     thankfully

hopeful      hopefully

cheerful     cheerfully

careful       carefully

graceful     gracefully

painful       painfully

colourful    colourfully

beautiful     beautifully

playful        playfully

usual          usually

final           finally

brutal          brutally

original       originally

eventual      eventually

general        generally

ideal            ideally

normal         normally

partial          partially

real              really

actual          actually

KS2 Grammar Revision

Noun

It is a place, person or thing.

Types of Nouns:

1. Common noun: things that are around us.

Examples: table, chair, board

2. Proper noun: name of a place or person. It always start with a capital letter.

Examples: London, England, Sam

3. Collective noun: word that refers to groups

Examples: team, herd, flock, pack, bunch

4. Abstract noun: word that refer to ideas, concepts and feelings.

Examples: happiness, wisdom, courage

Pronoun

Words that are used to replace nouns.

Subject pronoun: used to replace subjects in a sentence.

Examples: I, He, She, It, They, We, You.

Object pronoun: used to replace objects in a sentence.

Examples: me, him, her, it, them, us, you

Possessive pronoun: used to refer something belongs to someone.

Examples: my, her, his, their, our, your

Relative pronoun: comes in the beginning of a relative clause. It is usually used to connect clauses.

Examples: that, who, whose, which, whom

Clause:
Group of words which includes verb.

Example: As I walked to the bus stop - This is a clause as it has a verb - walked.

Phrase:

Group of words with no verb among them.

Example: in the morning, after two hours, into the woods

Noun phrase

A group of words that act as a noun is a noun phrase.

Examples: The big, blue balloon popped.

                  The long, winding road was lined by thick bushes         

                  on either side.

Adjectives

Words that describe nouns

Examples: beautiful, hideous, generous, miserly

Adverbs

Words that describe verbs, adjectives or other adverbs. They usually end with '-ly', but not always.

Some examples:
adverbs used to describe quantity: many, much, more, lot, few, less, little

adverbs used to describe frequency and time: often, never, once, daily, monthly, now, soon, later, always

other examples: far, fast, rather, very


Relative clause:

A clause that begins with a relative pronouns such as that, which, when, whose, where.

This clause describes the noun that comes before it.

Examples:

I went to the park that is next to my house.

The underlined clause is the relative clause. It starts with a relative pronoun and it describes the noun, in this case, the park, that comes before it.

1 step and 2 step word problems - finding fraction of amounts

Finding fraction of amounts - 1 step problems:
(Show the working out)

1. Sam has 42 marbles. He gave 5/7 of the marbles to Anna. How many marbles did he gave to Anna?

2.  Sam has £360. He lent 3/5 of the money he has to Anna. How much money did he give to Anna?

3. A cake weighs 375 grams. Sam ate 3/5 of the cake. How many grams did he ate?

4. A juice carton has 150 ml of juice. Anna drank 4/5 of juice in the carton. How much juice did Anna drink?

5. There were 56 balloons in a bunch. 7/8 of the balloons were blue. How many balloons were blue?

6. A bouquet has 25 flowers. 3/5 of the flowers in the bouquet are roses. How many roses are there in the bouquet?

7. A dog weighs 15 kg. It gained 1/5 of its weight in a month, how many kilograms did it gain?

8. A school library has 500 books. 3/10 of the books are non fiction. How many non fiction books are in the library?

9. Anna had 39 stickers. She gave 2/13 of her stickers to Sam. How many stickers did she give to Sam?

10. There are 30 children in Year 4. 7/10 of the children are girls. How many girls are there in Year 4?

2 step problems:

(Show the working out)

1. There are 30 children in Year 4. 3/5 of the children had school dinner. Rest brought packed lunch. how many children brought packed lunch?

2. Anna had 78 stickers. She gave 1/6 of her stickers to Sam. How many stickers did she have left?

3. Sam had £45. He spent 4/9 of the money he had. How much money did he have left?

4. Anna blew 27 balloons. 1/9 of the balloons popped. How many balloons remained without being popped?

5. Sam had 63 stamps. He stuck 7/9 of the stamps in an album. How many stamps were not stuck in the album?