You might not establish it, yet you"re currently pretty good at recognizing a selection of various symbols that all stand for the very same number or concept. Because that example, the point in clip (4) isn"t *actually* the number four. It"s simply a symbol the represents the *concept* that the number four. To further illustrate this point, take a gander at this symbols:

4-(-4)(8 ÷ 2)(2)(2)

Each of these symbols is different, yet they"re every symbolic representations of the number four. Same deal with the Roman numeral IV. They"re just different ways of saying the same thing.

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Along the very same lines, one amount have the right to be expressed by either a fraction, decimal or percentage. Because that example, we"re yes, really saying the exact same thing whether we write

?No prob: main point the numerator and denominator by 4 to obtain

.### Sample Problem

What"s a portion equivalent come

with a denominator the 121?Multiply the top and also bottom through 11 to gain

.Wanna confuse your friends? Tell lock you"re headed to 77-121 to gain a Slurpee.

We"ve seen a bunch of instances of fractions so far, but what happens as soon as we mix them increase with entirety numbers?

As a fast reminder, a fraction whose molecule is smaller than its denominator is referred to as a suitable fraction. The point of suitable fractions is the if friend look at them top top the number line, they all live in between -1 and also 1.

Let"s revisit improper fractions because that a sec. Since it can be tough to imagine just just how much something prefer 354/22 is, we deserve to represent it together a **mixed number**, i beg your pardon is a entirety lot simpler to wrap her head around. A combined number is expressed as a whole number adhered to by a fraction. Who knows why the portion is adhering to the whole number? probably it"s lost. It is quite maze-y in here.

For example,. In other words, 5 halves is the same thing as two wholes plus an additional half. Visual help time:

Since mathematicians favor to abbreviation things, us leave the end the addition symbol and also just write.

To rotate an improper portion into a combined number, let"s think around the brownies again. Might as well get as lot use the end of lock as possible before they walk stale.

### Sample Problem

Write the fractionas a blended number.

What this number is saying is the each pan of brownies is reduced into 7 same pieces, and we have actually 22 full pieces. That way we have actually 3 full trays that brownies (3 × 7 = 21), add to 1 single, lonely brownie left over.

Therefore, .

To turn an improper portion into a mixed number without drawing pictures (although that *does* take all the fun out that it), us perform lengthy division. Remember the a portion *is* a division problem in i beg your pardon we just haven"t excellent the actual dividing. However, if we carry out that here and divide 22 by 7, using the remainder as the fractional part of our mixed number, we acquire the following:

Therefore, . Whaddaya know: that"s the exact same answer we got when us did it the various other way. It"s choose we"re caught in a wormhole of perfect logic.

We"re sure you"re dying to learn exactly how to carry out this in reverse: how to turn a blended number ago into an not correct fraction. As a magician, it"s one thing to reduced your assistant in half, yet it"s constantly nice to be able to put her back together again as well. We"ll spend some quality time converting combined numbers right into fractions as soon as we gain to the ar on including fractions. After all, the blended numberis really just, or. However, if you"ve acquired ants in her pants and absolutely can"t wait, check out the section below for a sneak peak. If you"re a sucker because that suspense, you can skip it and come ago after you"ve learned all around adding fractions.

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Okay, below we go. Come turn mixed numbers back into not correct fractions, psychic that mixed numbers are covertly abbreviated addition problems v the plus sign surgically removed.

### Sample Problem

Since we"re going come be speak the language the halves, we want to translate every little thing into those terms. How countless 1/2"s does 6 equal? Remember critical night once you overheard your mom swearing that she would only eat 1/2 the a coco chip cookie (hey, at least we"re turn off brownies), and also then she preserved going ago to the tin until she"d spend 6 whole cookies? that was 12 halves, if you"ll recall. If girlfriend don"t recall, you can additionally get there this way:

You have actually 6 × 2 = 12 half-cookies plus another half-cookie, because that a total of thirteen halves, or.