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In today's lesson, we're going to look at some expressions that are used in everyday
English, but they come from math.
So, if you know some math terminology, you'll understand these a little bit easier.
We also have...
I have a video about math words, you can check that out as well, but let's start with some
"Plus" and "minus" or "pluses" and "minuses".
Now, in math, we use: "One plus one equals", so "plus", there, is more like a verb, but
it's more of an equation; it makes the equation move.
Here, we're using them as nouns.
So, that's a key feature you have to remember - they are nouns.
And, basically, synonyms to "pluses" and "minuses" are "pros" and "cons".
So, when you're looking at a situation, or an action, or an idea, you have to look at
the good and the bad side; you have to look at the pros and the cons; you have to look
at the pluses and the minuses; the advantages and disadvantages; the positives and the negatives.
So, "plus" and "minuses" work the same way, so these give you a little bit of an extra
synonym; an extra choice, especially in writing, but also in speaking.
So, if we're looking at...
We're looking at this person, this candidate's presidency, and we're trying to debate: "What
are the good points?
What are the bad points?"
So, some of the pluses of his potential presidency are that he will help the economy.
The one big minus, though, is that he's a racist and he might destroy harmony in society,
I'm not mentioning any names; I'll leave that to you, but we'll leave it at that as well.
So, he has...
There are several pluses to his potential presidency; there's one big minus that might
outweigh all those pluses.
"Exponential" comes from "exponent".
Now, you might know this as, like...
This is an exponent.
But when we talk about "exponential", we're talking about it to a very large degree.
To a large degree or to a large extent; something that is significant.
We're talking about growth, so exponential growth; or the opposite, exponential decline;
or an exponential spread.
So, it means it's going to...
Something is going to increase by many times, or decrease by many times, or spread very
Now, when we say: "exponential", there's no number to it.
We don't actually have this number, here; we're just saying that it's going to be very
fast, very large, etc.
So, after World War II, the economies of most western nations grew exponentially.
In this case, I'm using the adverb.
"Exponential" is an adjective; "exponentially" is an adverb.
And most of the countries witnessed exponential growth.
The use of the internet has spread exponentially around the globe - it means it spread very
fast and all over the place.
So, there's no number; just very quickly, very fast.
Now, parallel lines are lines that run along the same path in the same direction, but never
So, we say: "It's in line with" or "on a similar path"; these are synonyms to "parallel".
So, the FBI is conducting an investigation into the event, but the local police department,
although they're going to cooperate with the FBI, are going to run a parallel investigation
on their own.
So they're going to help the FBI, but they're also going to have their own investigation
that's going to go along the same path; a parallel investigation, meaning in the same
"A fraction of".
So, a "fraction" is, for example, number over a number - that's a fraction.
When we say: "A fraction of", we're saying a small amount of or a partial amount.
So, if you're looking at two companies who create software, let's say...
So, this company creates very good software, but my company creates equally good software,
but at a fraction of the cost; means much cheaper, much lower.
A smaller or a partial.
So, they charge 1000 bucks; I charge only 600.
It's a partial; it's a fraction of their price; much, much lower.
So, so far we have four.
Let's look at four more.
Okay, let's look at a few more.
So, if you're talking about lines or triangles especially, this is the angle.
For example: This is a 90-degree angle.
But when we talk about "angle" in everyday life, we're talking about perspective; the
way we view something.
So, you can view it from this angle, you can view it from this angle, you can view it from
this angle - you're going to have a different perspective; a different way of seeing something
from every different angle.
And it's also a different approach.
The way we want to accomplish something, we approach it from different angles, we're going
to have different results.
So, if we want to solve this problem, we can't just look at it straight on; we have to look
at it from different angles.
Now, a more slang use...
If you ever hear the expression: "Hmm.
What's his angle?"
When we use this, it means we...
We're suspicious; we don't trust the person.
"What's his angle?
What's he trying to accomplish?"
So, we're not sure about his approach to something and we don't trust it.
We think he's trying to go this way, so really he can go this way.
He has a different target in mind than what we can see.
So, we don't trust his angle because we know later he'll come in from this angle and do
So, it's a bit of a slang use, but again, it basically means the approach or the perspective
that someone is taking.
"Go off on a tangent".
Now, if you think about math, again, here's a circle, and you want to maybe measure a
point or you might want to measure something, and you think about a line touching the circle...
It touches it on one point; not like the way I drew it.
It touches on one point, and then continues off in the distance; it doesn't go into the
So, this line is called the tangent.
So, if somebody goes off on a tangent, it means they're getting away from the central
point; they're getting away from the circle and going on to something else.
So, if we have an interview with a politician and we ask him a very direct question, a lot
of them will, you know...
They'll touch on the topic, and then they'll just go off on a tangent and talk about something
So, the politician started to answer the question, but then he went off on a tangent and started
talking about his dogs, and basically avoided answering the question.
So, go off...
Now, we also use this about, like, people who daydream.
We ask them a question and they start to answer it; they legitimately want to give you an
answer, but then they mention a word and that gets their mind going, and then they start
following that tangent and then they just go off with that tangent, and talk about something
completely different and unrelated to the original question.
So, they lose focus; they lose track of what they were saying originally.
Now, if something "adds up"...
If it adds up, it makes sense.
If it doesn't add up, it doesn't make sense.
So, we're talking about somebody giving you a story.
For example, the police are interviewing a witness or they're interviewing a suspect,
and the suspect or the witness are saying: "Oh, this happened, and this happened, and
this happened", and the police are going: "Hmm.
This doesn't add up."
So, this part of the story, plus this part of the story, plus this part of the story
does not equal this part of the story; something doesn't add up.
Either you're lying, or you missed something, or we missed something in the questions, so
it doesn't add up; it doesn't make sense.
Last: "The lowest common denominator".
So, again, we're talking about fractions - this is the numerator; this is the denominator.
Now, when we want to add fractions...
For example, if I want to say...
I want to add one...
One quarter and two-fifths.
So, I can't add one...
It's not three over nine; it doesn't work that way.
I need to find a common denominator - one that both of these can go into, and I think
the lowest is 20, so you get whatever, 5 over 20 and 10 over...
8 over 20, and then you make the addition.
So, "the lowest common denominator" in everyday English means the lowest level or the base.
Now, generally when we talk about the lowest level, we mean the lowest level people; we're
talking about an audience or consumers.
So, there are very good newspapers in this country, let's say.
In Canada, we have some very good newspapers, but we also have some not so good newspapers.
These not so good newspapers, they cater to or they target the lowest common denominator,
so they give them very sensationalist headlines, because why?
Don't say: "Because why?"
Because they want to sell newspapers.
So, they... they create a newspaper, and they target the lowest common denominator with
their sensationalist headlines.
They want to sell more papers to the people who don't really read too much or who don't
care about very good reporting.
So that's: "the lowest common denominator".
So, there you go: Eight expressions from math.
So, it's good to learn math, it's good to learn English, it's good to learn them together.
You can use these in everyday English.
I wouldn't necessarily use these in writing; more for speaking, etc.
But if you have any questions about these, please go to www.engvid.com and join the forum,
and you can ask the questions; I'll be very happy to help you out with these.
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