Converting improper fountain to mixed numbers

In this lesson, we"re walking to focus on details kinds the fractions. We"ll begin out by talking about positive fractions, and then we’ll deal with an unfavorable fractions at the finish of the lesson.

You are watching: 1 1/7 as an improper fraction


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Up until now, many of the fountain we’ve dealt with are what we call “proper” fractions, whereby the numerator is much less than the denominator. Here are some examples of ideal fractions:


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Now we’re introducing a new kind of fraction, referred to as an “improper” fraction, wherein the numerator is greater than or equal to the denominator. In various other words, improper fractions space “top-heavy.” here are some examples of wrong fractions:


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Even despite “improper” sounds prefer a negative thing, there’s nothing bad around improper fractions. In the same way that a proper fraction represents a hopeful number much less than ???1???, one improper portion represents a number that’s better than or equal to ???1???.

For example, ???7/4??? (“seven-fourths”) way seven time ???1/4???, or ???1/4??? seven times. Each of the gray sections listed below represents ???1/4??? the a circle, and also we have actually seven the them.


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As you can see, this is the very same thing as saying the we have actually one circle add to three-fourths that a circle, because we have actually one complete circle top top the left and ???3/4??? the a circle on the right.

Now, we just said that

???frac74=1frac34???

We know ???7/4??? is an not correct fraction. And

???1frac34???

(“one and also three-fourths”) called a mixed number, because it’s a mix of the whole number ???1??? and also the fraction ???3/4???. ???1??? is the variety of complete circles us have, and also ???3/4??? is the section of a circle it is left over.

If us summarize what we know so far, we deserve to say the there are three types of fractions:


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It’s crucial to understand that we can always convert improper fractions to blended numbers, and vice versa. Because that example, you’d create “two and also three-sevenths” as

???2frac37???

Remember,


Converting blended numbers to improper fractions

If we want to convert a positive blended number to an improper fraction, we follow this steps:

Multiply the fraction’s denominator through the totality number

Add the an outcome to the fraction’s numerator

Write that result on top of the original denominator


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Convert the combined number to an improper fraction

Example

Convert the blended number to an not correct fraction.

???2frac37???

We understand that

???2??? is the totality number

???3/7??? is the fraction

???3??? is the fraction’s numerator

???7??? is the fraction’s denominator

We must multiply the fraction’s denominator (???7???) by the totality number (???2???).

???7 imes2=14???

Then we add the fraction’s molecule (???3???) to the an outcome of that multiplication (???14???).

???14+3=17???

This an outcome (???17???) will certainly be the molecule of our improper fraction, and also we’ll store the initial denominator (???7???) to obtain the last answer:

???frac177???

In various other words,

???2frac37=2+frac37=frac7 imes27+frac37=frac7 imes2+37=frac14+37=frac177???


Converting improper fountain to blended numbers

If we want to convert an improper portion to a combined number, we follow these steps:

Divide the molecule of the improper portion by the denominator.

Write down the whole number part of that result.

Write down any kind of remainder together the molecule in the portion part, above the original denominator in the portion part.

If the remainder that the division is ???0???, the just way you have the right to write the an outcome as a entirety number, instead of a combined number.


Example

Convert the improper fraction to a combined number.

???frac196???

If us look at the positive multiples of ???6???,

???6cdot1=6???

???6cdot2=12???

???6cdot3=18???

???6cdot4=24???

we have the right to see that ???6??? goes right into ???19??? three times, yet not four times, because ???6cdot3=18??? is still much less than ???19??? yet ???6cdot4=24??? isn’t.

That means that ???3??? will be the totality number in our mixed number. Because ???6cdot3=18???, we have to include ???1??? to gain from ???18??? to ???19???, which method the remainder is ???1???. Therefore, the remainder (???1???) will be the molecule of the fraction (in our mixed number), and also the denominator of the improper portion (???6???) will be the denominator that the fraction (in our mixed numbers), therefore the mixed number that’s indistinguishable to the original improper portion is

???3frac16???

In various other words,

???frac196=frac18+16=frac(6cdot3)+16=frac6cdot36+frac16=3+frac16=3frac16???


Even though “improper” sounds favor a negative thing, yes sir nothing bad around improper fractions.

See more: When Markups Are Based On The Selling Price, The:, Chapter 8 Quiz 2 Flashcards


Negative fractions

Just as there space positive suitable fractions, confident improper fractions, and also positive mixed numbers, over there are negative proper fractions, negative improper fractions, and negative mixed numbers.

You need to be careful around signs once you refer a negative mixed number together the amount of a entirety number and also a fraction. Both the whole number and also the portion must be negative. It helps to use grouping signs (such together parentheses or square brackets) in act this. Because that example,

???-2frac37??? way ???-left(2+frac37 ight)=-2-frac37???, no ???-2+frac37???

Going earlier to our examples, we find that

???-2frac37=-left(2+frac37 ight)=-left(frac7 imes27+frac37 ight)=-left=-frac177???

and

???-frac196=-left(frac18+16 ight)=-left=-left(frac6cdot36+frac16 ight)=-left(3+frac16 ight)=-3frac16???


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find out mathKrista KingJanuary 28, 2021math, discover online, virtual course, virtual math, prealgebra, pre-algebra, combined numbers, improper fractions, fractions, fundamentals, fundamentals of math
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