Transcript How to Read Basic Expressions
Meet Lucky. While on a mission, a careless mistake led to his capture by a rival hacker. I know, I know, Lucky's not lucky. Luckily for Lucky, the rival hackers kinda forgot to lock the door. Lucky takes a quick peek around and, spotting no guards, makes a run for the exit. However, this dusty labyrinth is lousy with booby traps. The way out can be reached by correctly reading the expression above each door. To find the one and only escape route, Lucky must know how to read basic math expressions.
Reading basic math expressions
Above the first door are some spikes. Yikes! Lucky had better read this correctly or else. The expression looks like this: Although there are different ways to read multiplication problems, sometimes it matters if the multiplication sign is written in the expression. In this example, since the multiplication sign is written, it's preferable to read the expression as 'two times y'. But, if you have it written like this: then you can simply read it as '2y'. Since the multiplication sign is in the expression, Lucky reads the expression as '2 times y', avoids the booby trap and moves on. Beware of alligators? There must be a trap door somewhere. Lucky's gotta be careful! Division problems, much like multiplication problems, are able to be read in a few different ways. For example, this can be read in one of three ways:
'x' divided by 2 'x' over 2 or half of 'x'.
Lucky confidently reads the equation as 'x' over 2. The door opened! Thankfully, it wasn't the trap door. Lucky doesn't want to become alligator food. Lucky was able to pass through the first few doors with no problems. But there's one door remaining. It's the toughest one yet!
Positive expressions are pretty straightforward, but what if the first term is negative? Lucky can see freedom! And a web of lasers in the hallway  no worries! Math expressions, just like English, are read lefttoright. So, we start with the fraction. The fraction is negative, so we must state this first. Then, we have to read the numerator before the denominator. Remember, it's division, so you get to choose how you read it!
negative 4x divided by 3 or negative 4x over 3
The next operater from left to right is an addition sign. The term that follows can be read as 9x. Putting this all together, Lucky enunciates each word  negative 4x over 3 plus 9x.
When reading basic math expressions, it's important to remember to read from left to right, pay attention to positive and negative, and read fractions from top to bottom.
Back to Lucky. After reading the last expression. Lucky hears a noise and all the lasers are deactivated. Just Lucky's luck, he's stepped on a twig, and here come the bad guys!
How to Read Basic Expressions Übung
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Explain how to read the expression.
Tipps
Read from left to right.
When a multiplication sign is included in an expression, it should be read out when reading that expression.
Lösung
In order to read an expression, Lucky knows that he must read from left to right.
He starts out by reading "two".
Next, he sees a multiplication sign. When a multiplication sign is included in an expression, it should be read out when reading that expression. So next, Lucky reads "times."
Last, Lucky reads "$y$."
So overall, Lucky reads the expression as "two times $y$."

Explain the rules for reading expressions.
Tipps
The numerator is the top of a fraction, and the denominator is the bottom.
Positive and negative signs don't decide the order that terms are read in.
Whether a term is large or small doesn't effect when it is read.
Lösung
There are three rules for reading expressions:
 Read from left to right.
 Pay attention to positive and negative signs.
 Read fractions from top to bottom.
You should read the top, or the numerator, first when reading fractions. So "read the denominator of a fraction before the numerator" is incorrect.

Decide how to read the expression.
Tipps
There are multiple ways to read a division expression. Two of the given answers are correct.
The numerator, or top part, is read first when reading a division expression.
Lösung
Lucky knows that division expressions are read starting on the top. He knows that he should start by reading the numerator, which in this case is $x$. Then he should read the division operator as "over" or "divided by." Lastly, he should read the denominator, which is "two."
Lucky reads the equation as "$x$ over two." He could also read it as "$x$ divided by two," or "half $x$."

Determine how to write the expressions after hearing them.
Tipps
Read from left to right.
Pay attention to positive and negative signs.
Read fractions from top to bottom.
Read the expressions slowly and carefully. There are only small differences between them.
Lösung
Gina remembers the rules for reading expressions:
 Read from left to right.
 Pay attention to positive and negative signs.
 Read fractions from top to bottom.
The first word "negative" tells her to write a negative sign. Next, she hears "two $x$", so she writes $2x$. Next she hears "over three", which tells her that $2x$ was the numerator of a fraction, and that the denominator is $3$.
She then hears "plus", which she knows means that she should write an addition sign, $+$. Lastly, she hears "four zee", which tells her that the end of the expression is $4z$. She could also write $4 \times z$, but she decides to leave out the optional $\times$ symbol.
So the full expression she writes is $\dfrac{2x}{3} + 4z$.
Similarly, when she hears "negative two over three $x$, plus four times $z$" she writes $\dfrac{2}{3x} + 4z$.
When she hears "negative two ex over three, plus four" she writes $\dfrac{2x}{3} + 4$, and when she hears "two over three $x$, plus $z$" she writes down $\dfrac{2}{3x} + z$.

Determine how to read the expression.
Tipps
Read from left to right.
Pay attention to positive and negative signs.
Read fractions from top to bottom.
Lösung
We have the expression:
$\dfrac{3x}{9} + 4x$
We read from left to right, pay close attention to positive and negative signs, and we must read fractions from top to bottom.
So we start by reading the negative sign, as "negative."
Next, we read the fraction from top to bottom. We can either say "three $x$ over nine" or "three $x$ divided by nine."
Then we read the addition operation, as "plus."
Lastly, we read the multiplication of $4$ and $x$. We can read this as "four $x$" or "four times $x$."
So the correct ways to read the expression are:
 "negative three $x$ over nine, plus four $x$."
 "negative three $x$ over nine, plus four times $x$."
 "negative three $x$ divided by nine, plus four $x$."
 "negative three $x$ divided by nine, plus four times $x$."

Identify how to read the expressions correctly.
Tipps
Read from left to right.
Pay attention to positive and negative signs.
Read fractions from top to bottom.
Lösung
Jack writes down the rules of reading expressions before he begins:
 Read from left to right.
 Pay attention to positive and negative signs.
 Read fractions from top to bottom.
Jack reads the second expression as "$y$ over five." Lucky thought that $y$ was positive, and accidentally multiplied $5$ by $x$.
Jack reads the last expression as "negative two $t$ over four, plus three $c$." He sees that Lucky accidentally switched the multiplication and division operations.
2 comments
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