Applying Rational Equations 1 Extra Commentary
A1 A2 B1 B2 C1 C2
for
US / fə(r) /
•UK / fɔr,fə /
- preposition
- Used to show the purpose, or need of something
time
US / taɪm /
•UK / taɪm /
- noun
- Speed at which music is played; tempo
- Point as shown on a clock, e.g. 3 p.m
- Number of hours, minutes needed to do something
- Occasion when something happens
- Period or occasion that something occurred
- Period in history or the past
- Something measured in minutes, hours, days, etc.
- How long an event takes; duration
- verb
- To check speed at which music is performed
- To choose a specific moment to do something
- To measure how long an event takes, e.g. a race
- To schedule something to occur at a specific moment
why
US / waɪ /
•UK / hwaɪ, waɪ /
- adverb
- Question word to ask for a reason
- exclamation
- (Used to express surprise or approval)
spend
US / spend /
•UK / spɛnd /
- verb
- To use money to pay for something
- To use time in order to do something
- To use up something completely
algebraic
US / ˌældʒɪ'breɪɪk /
•UK / ˌældʒəˈbreɪk /
- adjecitve
- Concerning algebra
hour
US / 'aʊə(r) /
•UK / aʊr /
- noun
- 60 minutes
- Particular time of the day
- Fixed, regularly occurring time
those
US / ðəʊz /
•UK / ðoz /
- determiner
- The people or things we are talking about
- pronoun
- The objects far from the speaker
just
US / dʒʌst /
•UK / dʒʌst /
- adjecitve
- Proper or appropriate; as is deserved
- Doing or being what is right or fair
- Legally correct; having enough evidence
- adverb
- Almost; nearly
- Exactly at the time of
- Exactly (the same as, like)
few
US / fju: /
•UK / fju /
- pronoun
- Not many, a small number
much
US / mʌtʃ /
•UK / mʌtʃ /
- adjecitve
- Very; to a high level or degree
- adverb
- A lot; large amount; a high degree of
- Nearly; basically
- On many occasions; often
- noun
- A large amount; a great quantity
ask
US / ɑ:sk /
•UK / æsk /
- verb
- To say to someone that you want something
express
US / ɪk'spres /
•UK / ɪkˈsprɛs /
- adjecitve
- Sent by a fast mail service
- Traveling at high speed
- noun
- Fast train or bus
- verb
- To send something by fast mail
- To state or show what you think or how you feel
well
US / wel /
•UK / wɛl /
- adjecitve
- Being in a fortunate, good condition or state
- Healthy and in good condition
- adverb
- In an acceptable, proper, or successful manner
- In a complete, total, or full manner
- A great and considerable degree
- In a successful way, in a good or satisfactory way
- exclamation
- Used to begin or continue a particular statement
- Used to show you want to start saying something
- Used to express that you are waiting for a reply
- You say this to change the topic of a conversation
- Used to indicate you are making a final remark
- noun
- Long deep hole in the ground to get water
- verb
- To cause your eyes to fill with tears
basis
US / ˈbeɪsɪs /
•UK / ˈbesɪs /
- noun
- Main ingredient or part of something
- Starting situation, fact, idea to develop from
arbitrarily
US / 'ɑ:bɪtrəlɪ /
•UK / ˌɑrbəˈtrɛrəlɪ /
- adverb
- Without using reason, often unfairly; on a whim
question
US / 'kwestʃən /
•UK / ˈkwɛstʃən /
- noun
- Issue or problems you are dealing with
- What you ask about; issue
- verb
- To ask for or try to get information
- To have or express concerns or uncertainty
wonder
US / 'wʌndə(r) /
•UK / ˈwʌndɚ /
- noun
- Surprise caused by experiencing something amazing
- verb
- To feel curious about something
- To think or consider about something over time
per
US / pə(r) /
•UK / pɚ /
- preposition
- In the manner directed or suggested
- For each; during each
voodoo
US / ˈvu:du: /
•UK / ˈvudu /
- noun
- Cult practiced by sorcery and spirit possession
should
US / ʃʊd /
•UK / ʃʊd /
- other
- Used to indicate what is proper or reasonable
eat
US / i:t /
•UK / it /
- verb
- To put food in your mouth
combine
US / kəmˈbaɪn /
•UK / kəmˈbaɪn /
- verb
- To mix several things together to form one thing
sure
US / ʃʊə(r) /
•UK / ʃʊr /
- adjecitve
- Having no doubts about something
- Have confidence in your own words or actions
- Firmly established or held; being firm or stable
- Being correct or true
- adverb
- What you say to agree willingly
either
US / ˈaɪðə(r) /
•UK / ˈiðɚ, ˈaɪðɚ /
- adjecitve
- One of two (used when there is a choice of two)
- adverb
- (After negative statements) likewise, in addition
- conjunction
- Used as the first of two connected things
- determiner
- Used as the first of two connected things
- pronoun
- The one or the other
intuition
US / ˌɪntjuˈɪʃn /
•UK / ˌɪntuˈɪʃən, -tju- /
- noun
- Natural ability to guess or feel things
here
US / hɪə(r) /
•UK / hɪr /
- adverb
- In this place; at this location, position or time
quick
US / kwɪk /
•UK / kwɪk /
- adjecitve
- Using very little time; moving far in little time
- Learning and understanding rapidly and easily
realize
US / 'ri:əlaɪz /
•UK / ˈriəˌlaɪz /
- verb
- To become aware of or understand mentally
speak
US / spi:k /
•UK / spik /
- verb
- To be able to use a certain language
- To use words to tell information, express thoughts
write
US / raɪt /
•UK / raɪt /
- verb
- To compose letters and words on paper or a screen
- To invent or create a computer program
- To create a song or piece of music
guess
US / ɡes /
•UK / ɡɛs /
- noun
- Answer given when you don't know if it is correct
- verb
- To give an answer without knowing if it is correct
intuitive
US / ɪnˈtju:ɪtɪv /
•UK / ɪnˈtuɪtɪv, -ˈtju- /
- adjecitve
- Able to understand by feeling rather than fact
many
US / 'menɪ /
•UK / ˈmɛni /
- determiner
- Used to refer a large number of things
will
US / wɪl /
•UK / wɪl /
- noun
- Desire or choice of someone
- Document saying who gets your money when you die
- Strong desire to do something; determination
- Desire to do something; strong wish to do
- other
- Used with verbs to express the future
- verb
- To leave property to someone after your death
- To use mental effort to make something happen
- Am (is, are) likely to do
- To influence someone to do something
- To make something happen by strongly wanting it
plus
US / plʌs /
•UK / plʌs /
- noun
- A benefit or advantage
- preposition
- In addition; add
- In addition to; Indicates a number above
- Having a value greater than zero
same
US / seɪm /
•UK / sem /
- adjecitve
- Being equal in quality and amount
- Identical; not different
- Not changing; constant
good
US / ɡʊd /
•UK / ɡʊd /
- adjecitve
- Proper, appropriate or right
- (Of an amount) enough; plenty
- Excellent; high quality
- Acting well or properly; of moral character
- In a positive or happy emotional state
- noun
- Advantage or benefit
finish
US / ˈfɪnɪʃ /
•UK / ˈfɪnɪʃ /
- noun
- End of something; completion
- Final coat (of paint) applied to a surface
- verb
- To use or consume all of something
- To reach the end; to complete something
- To put a final surface (e.g. paint) on something
but
US / bət /
•UK / bʌt,bət /
- conjunction
- Used before you say something different, opposite
can
US / kæn /
•UK / kən,kæn /
- noun
- A metal container for storing food
- other
- Able to; have the skill to; have the time to
- verb
- To have permission to
- To be possible to do
- To preserve food by sealing it in a metal container
equal
US / 'i:kwəl /
•UK / ˈikwəl /
- adjecitve
- Same in shape, size, or number
- verb
- To add up or be the same as
now
US / naʊ /
•UK / naʊ /
- adverb
- At the present time or moment
- Right away or in the next possible moment
- Used to refer to something that just happened
- Time between the present and a moment in the past
- conjunction
- Resulting from or because of something
not
US / nɒt /
•UK / nɑt /
- adverb
- Word indicating the negative
- (Used to form the negative of verbs)
our
US / 'aʊə(r) /
•UK / aʊr /
- determiner
- Belonging to us
really
US / ˈri:əli /
•UK / ˈriəˌli, ˈrili /
- adverb
- Used to stress something that is said; definitely
- In a true or accurate manner
- Very
pick
US / pɪk /
•UK / pɪk /
- noun
- Sharp tool used for breaking the ground
- Item selected from a group of choices
- verb
- To take fruit or vegetables from a plant or tree
- To decide on a thing from various choices; select
- To remove (flower, etc.) with your fingers
would
US / wʊd /
•UK / wʊd /
- other
- Used to indicate something imagined
- Used to ask or request something politely
- Verb used to indicate possibility, request etc.
- Used to indicate a preference
- Used to indicate a reaction
- Indicates something that occurred repeatedly
- Used to indicate willingness or ability to do
video
US / 'vɪdɪəʊ /
•UK / ˈvɪdiˌo /
- adjecitve
- Of a moving film, with sound
- noun
- Recording capturing action with sound
- verb
- To make a moving film of, with sound
want
US / wɔnt /
•UK / wɑnt, wɔnt /
- noun
- Something you desire or wish for
- State or condition of poverty
- verb
- To desire or wish for something; hope for a thing
sense
US / sens /
•UK / sɛns /
- noun
- Certain mental feeling or emotion
- Normal or clear state of mind
- Meaning of a particular word, phrase or text
- verb
- To perceive using sight, sound, taste touch etc.
- To recognize the presence of something
problem
US / ˈprɒbləm /
•UK / ˈprɑbləm /
- adjecitve
- Causing trouble
- noun
- Something difficult to deal with or causes trouble
- Question to show understanding of a math concept
ratio
US / ˈreɪʃiəʊ /
•UK / ˈreɪʃioʊ /
- noun
- The relationship in relative size, etc.
behind
US / bɪˈhaɪnd /
•UK / bɪˈhaɪnd /
- adjecitve
- Concerning a later or slower time than expected
- Being in a losing position in a sporting event
- Being in the past; old fashioned
- adverb
- Remaining
- noun
- The part of the body that one sits on
- preposition
- At or toward the back of someone or something
- Supporting or helping someone
could
US / kəd /
•UK / kʊd /
- other
- Past form of 'can' to mean have ability
- Used to ask for something politely, or to offer
have
US / həv /
•UK / hæv /
- verb
- To drink, smoke, eat or use something
- To experience the effects of something
- To organize an event, or join in an activity
- To own, possess, or hold something
- To cause to happen or produce a particular effect
unit
US / ˈju:nɪt /
•UK / ˈjunɪt /
- noun
- One apartment in a building
- Group of people, e.g. soldiers, that work together
- A chapter of a textbook
- A standard of measurement of something
- Single item made by a company
independently
US / ˌɪndɪ'pendəntlɪ /
•UK / ˌɪndɪˈpɛndəntlɪ /
- adverb
- In a manner being free from the control of another
between
US / bɪˈtwi:n /
•UK / bɪˈtwin /
- preposition
- From one person, thing, or place, to another
- In the space that separates two objects
- Among two or more people who share something
they
US / ðeɪ /
•UK / ðe /
- pronoun
- Two or more people, animals, or things
add
US / æd /
•UK / æd /
- verb
- To include as well
- To put two things or numbers together, e.g. 2+2
take
US / teɪk /
•UK / tek /
- noun
- Filming of a single scene for TV or the movies
- verb
- To accept something that is offered
- To use a method of traveling, e.g. a bus or train
- To use a camera to make (a photo)
- To pick up something and go away with it
- To study a subject in school
- To attempt to pass (an exam)
- To require a certain amount of time, money, space
both
US / bəuθ /
•UK / boθ /
- determiner
- Used to refer to two things at the same time
- pronoun
- Used to refer to two things at the same time
their
US / ðɛː /
•UK / ðer /
- determiner
- Belonging to them
way
US / weɪ /
•UK / we /
- adverb
- Used to emphasize the amount of something
- noun
- Particular aspect of something being thought about
- One of various choices that could be made
- Particular existing condition or state
- (Often long) distance or length of time
- How something is done
- Route to go to a place
- Small street
- Usual behavior, emotions or habits of someone
work
US / wɜ:k /
•UK / wɚk /
- adjecitve
- Activity completed in order to make money
- noun
- The product of some artistic or literary endeavor
- Everything created by an author, artist, musician
- Activity you do in order to make money
- Place of employment
- Final product or result of a some labor or effort
- verb
- To bring into a specific state of success
- To be functioning properly, e.g. a car
- To do your job in your company or workplace
- To make an effort to do something
- To operate a machine or device
bit
US / bɪt /
•UK / bɪt /
- noun
- Device put in a horse's mouth to control it
- Small piece of something
- verb
- (E.g. of fish) to take bait and be caught
confusing
US / kənˈfju:zɪŋ /
•UK / kənˈfjuzɪŋ /
- adjecitve
- Being hard to understand
- verb
- To make something unclear or hard to understand
all
US / ɔ:l /
•UK / ɔl /
- adverb
- Completely; totally
- determiner
- Being every one of something
- pronoun
- 100% of something; the complete amount
fast
US / fɑ:st /
•UK / fæst /
- adjecitve
- In a way that is difficult to move or change
- Moving or able to move quickly
- Showing time that is later than the actual time
- adverb
- With a great deal of speed
- noun
- Period of time when a person chooses not to eat
- verb
- To refuse food for a long time
only
US / ˈəunli /
•UK / ˈonli /
- adverb
- Just one; just that amount or thing; not more than
- Not very important or serious
- Just that type of thing, person
- Short time ago; not before a certain time
- conjunction
- Except; but
two
US / tu: /
•UK / tu /
- number
- 2
and
US / ənd /
•UK / ənd, ən,ænd /
- conjunction
- Used to refer to two or more things
- Plus; in addition; on top of that
- Used to introduce an action that follows another
incorrect
US / ˌɪnkəˈrekt /
•UK / ˌɪnkəˈrɛkt /
- adjecitve
- Being wrong or inaccurate
hopefully
US / ˈhəʊpfəli /
•UK / ˈhopfəli /
- adverb
- In a manner wishing something to happen
another
US / əˈnʌðə(r) /
•UK / əˈnʌðɚ /
- adjecitve
- One more, but not this
- determiner
- One more added
- pronoun
- One more (thing)
hey
US / heɪ /
•UK / he /
- exclamation
- What you say when you want someone's attention
dean
US / di:n /
•UK / din /
- noun
- Official in charge of one part of a university
where
US / hwɛə /
•UK / hwɛr, wɛr /
- conjunction
- At or in the place which
- In whatever place
- pronoun
- Word you use to ask the location of something
decide
US / dɪ'saɪd /
•UK / dɪˈsaɪd /
- verb
- To make a choice or choose after thinking about it
- To make a legal judgment in court
- to affect the result of something
effort
US / ˈefət /
•UK / ˈɛfət /
- noun
- Amount of work used trying to do something
literally
US / ˈlɪtərəli /
•UK / ˈlɪtərəli /
- adverb
- So as to express the exact meaning of something
- Used to say something is true, even if unlikely
think
US / θɪŋk /
•UK / θɪŋk /
- verb
- To have an idea about something without certainty
- To have an idea, opinion or belief about something
about
US / ə'baʊt /
•UK / əˈbaʊt /
- adverb
- To be ready to; going to
- Nearly; approximately; roughly
- Near; next to; close to
- In every direction; in the area of
- preposition
- Concerning or of (a topic)
like
US / laɪk /
•UK / laɪk /
- adjecitve
- Being equal in status or kind to something else
- Similar; the same
- adverb
- For example
- preposition
- Used as a filler; used to ad emphasis
- In a way similar to the way something is done
- Such as; for example
- verb
- To want to
- To find something pleasing; to prefer something
that
US / ðæt /
•UK / ðæt, ðət /
- adjecitve
- The person or thing being talked about
- Used to identify something both the speakers know
- adverb
- Used to reinforce adjectives and adverbs
- To such a degree
- conjunction
- Used to connect a noun clause
- Used to introduce an adverbial clause
- Used to introduce a noun clause
- determiner
- Used as a noun to refer to something
- pronoun
- Referring an object far away
- Used to refer to the relative pronoun ‘which’
what
US / wɒt /
•UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /
- pronoun
- Thing or things that; the same kind as
- Used to emphasize something you are about to say
- adjecitve
- Used to refer to a particular amount, or number
- Used to place emphasis on a particular quality
- adverb
- To a certain degree
- determiner
- Question words used for asking for information
- exclamation
- Used to express excitement, shock, or surprise
- Used to ask people to repeat something they said
each
US / i:tʃ /
•UK / itʃ /
- determiner
- Every one of two or more things
- pronoun
- Per one person or thing
happen
US / 'hæpən /
•UK / ˈhæpən /
- verb
- To take place or occur
language
US / ˈlæŋgwɪdʒ /
•UK / ˈlæŋɡwɪdʒ /
- noun
- Words or signs used to communicate messages
then
US / ðen /
•UK / ðɛn /
- adverb
- A time that is not now
- Following another thing in time or arrangement
- Following on reasonably from what was just stated
- At that time, not now
total
US / ˈtəʊtl /
•UK / ˈtoʊtl /
- adjecitve
- Complete
- noun
- Whole number or amount of something
- verb
- To damage a car beyond repair
type
US / taɪp /
•UK / taɪp /
- noun
- Printed letters or blocks used for printing them
- Group of things or people sharing common features
- verb
- To identify something belonging to a group
- To write by touching keys on a keyboard
number
US / ˈnʌmbə(r) /
•UK / ˈnʌmbɚ /
- noun
- Symbols such as 1, 2, 56, 793
- Particular song or dance performed during a show
- Total quantity or amount of things
- verb
- To put numbers on things
- To assign a sequence within a group, series, set
- To claim to be part of a larger group, series, set
tell
US / tel /
•UK / tɛl /
- verb
- To (strongly) advise a person to do something
- To be able to guess
- To say or communicate information to someone
- To inform, but without speaking; indicate
- To have a negative effect on someone
- To order someone to do something; command
- To recognize something based on certain signs
- To report something to an authority
- To explain something or teach someone something
get
US / ɡet /
•UK / ɡɛt /
- verb
- To become affected by illness or disease
- To begin to feel or understand an emotion or idea
- To send or bring someone or something home, etc.
- To go somewhere to obtain something
- To (cause to) do a particular thing
- To obtain, receive or be given something
- To currently have
- To prepare for use
- To understand something being said or read
answer
US / 'ɑ:nsə(r) /
•UK / ˈænsɚ /
- noun
- Reply to a question someone asks
- Solution to a problem or test question
- verb
- To reply to a question someone asks
- To solve a test question or a problem
less
US / les /
•UK / lɛs /
- adjecitve
- Smaller in amount or degree
- adverb
- To a smaller degree
- noun
- A smaller amount
- preposition
- With the subtraction of
make
US / meɪk /
•UK / mek /
- noun
- Product made by a particular company; brand
- verb
- To arrange or prepare something e.g. dinner
- To get to (a place) on time
- To gain the status of (teacher, lawyer, etc.)
- To create something by putting things together
- To earn a certain amount of money at a job
- To cause or force a person to do something
- To cause something to happen or be formed
one
US / wʌn /
•UK / wʌn /
- pronoun
- You; we; people in general; someone
- The thing or person previously referred to
- adjecitve
- Used to refer to people generally
- Being a strong example of (something mentioned)
- number
- Number 1
other
US / 'ʌðə(r) /
•UK / ˈʌðər /
- adjecitve
- A thing different from that mentioned
- determiner
- (Something) else; not the first (one)
- pronoun
- Being the one and only thing of that category
than
US / ðən /
•UK / ðən /
- conjunction
- Used to compare two things that are not equal
how
US / haʊ /
•UK / haʊ /
- adjecitve
- To what degree? in what amount?
- adverb
- (Used to explain the way to do something)
- exclamation
- For what purpose or reason?
- (Used to ask someone or something's condition)
sal
US / sæl /
•UK / sæl /
- noun
- A North Indian tree that yields hard, durable timber and dammar resin.
you
US / jʊ /
•UK / ju /
- pronoun
- Person someone is speaking or writing to
- Person or people in general
flip
US / flɪp /
•UK / flɪp /
- noun
- Act of turning your body in the air; somersault
- Movement of something from one position to another
- verb
- To turn your body in the air, as in gymnastics
- To move into a different position quickly
- To move a button or switch to turn on or off
this
US / ðɪs /
•UK / ðɪs /
- adjecitve
- Used to indicate something already been discussed
- Used to indicate something happening around now
- adverb
- An indication by a physical motion or gesture
- A specific amount of
- determiner
- Person, thing, or idea near you
- pronoun
- Person, thing that has already been discussed
term
US / tɜ:m /
•UK / tɚm /
- noun
- Conditions applying to an agreement, contract
- Length of time something is expected to happen
- Fixed period of weeks for learning at school
- The (precise) name given to something
- verb
- To call; give a name to
half
US / hɑ:f /
•UK / hæf, hɑf /
- adjecitve
- Not complete
- adverb
- Partly; somewhat
- noun
- One of two equal periods of game time in a sport
- The part you get when one is divided into two;
little
US / 'lɪtl /
•UK / ˈlɪtl /
- adjecitve
- Being short in length of time
- Not great in size, amount, or degree; small
- Being very young or younger than others
- adverb
- By an amount or degree that is not very much
- Not often; rarely
- noun
- A person's name
let
US / let /
•UK / lɛt /
- verb
- To allow someone to do something
- Introducing a suggestion to do something together
- To rent a house, etc. to others
might
US / maɪt /
•UK / maɪt /
- other
- Used to politely request an action
- Used to express that something could happen
- Power, strength, force or influence
rate
US / reɪt /
•UK / ret /
- noun
- Current price or cost of something
- Speed or frequency of events over time
- verb
- To assess something or consider its qualities
the
US / ðə /
•UK / ðə /
- article
- Used to refer to something already mentioned
- Used to show there is only one of something
- determiner
- Used to describe all of a family