Let ‘s state you had a Super Bowl party and ordered pizzas for all your friends to eat while you watched the game. The following twenty-four hours there was one full Hawaiian pizza and half an anchovy pizza left over. You would state you had “ one and a half ” pizzas left over from the party. “ One and a half ” is the typical manner of showing verbally the sum of pizzas remnant. Written as a figure you would compose it as a assorted figure “ 1 1/2 ” .While assorted Numberss are the natural pick for verbal look every bit good as the reply to a word job, assorted Numberss are non the easiest type of fraction to cipher with.

When executing mathematical operations with fractions you will happen it easier to cover with improper fractions instead than assorted NumberssImproper Fractions [ glossary term ; a fraction where the top figure is bigger than the top figure. hypertext transfer protocol: //www.bing.com/Dictionary/search? q=define+improper+fraction & A ; FORM=DTPDIA ] and Mixed Numbers [ glossary term ; a fraction figure dwelling of a proper fraction and a whole figure together hypertext transfer protocol: //www.

bing.com/Dictionary/search? q=define+mixed+number & A ; FORM=DTPDIA ]You can utilize either an improper fraction or a assorted fraction to demo the same sum.[ Pictures may necessitate to be redone.

Taken from hypertext transfer protocol: //www.mathsisfun.com/improper-fractions.html ]1 3/4 = 7/4

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1 1/4 = 5/4

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2 3/8 = 119/8 [ Divide the two whole pizzas into 8ths ]

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What if I had multiple pieces of different pizzas left over from the party.How could I state person how much I had left over?Before we learn how to officially make operations with fractions, we need to be able to change over our assorted Numberss to improper fractions and before we can verbally discourse our consequences we need to be able to change over our improper fractions into assorted Numberss.

## Converting from Mixed to Improper

To change over a assorted figure to an improper fraction we need to retrieve what a fraction means.The numerator in a fraction tells us how many pieces of a whole we have. The denominator tells us how many pieces the whole has been broken in to.Given the assorted figure 1 A? , we see the proper fraction of A? tells us we have one of two pieces. The whole figure 1 says we have two of two pieces or 2/2. If you were given 2 of two pieces and 1 more of 2 pieces, you would hold 3 of two pieces or 3/2.

That one was easy. Let ‘s expression at the assorted figure 3 2/5.Using the logical thinking from above, we see the proper fraction of 2/5 Tells us we have two of five pieces.

The whole figure 3 says we have five of five pieces 3 times. Five of five pieces 3 times would propose we have 15 pieces of five or 15/5. If you were given 15 of five pieces and 2 more of five pieces, you would hold 17 of five pieces or 17/5.The assorted figure 3 2/5 is the same sum as 17/5[ chalk talk another illustration in words.

Do n’t make the math stairss yet. We want a true apprehension of the construct before we introduce the algorithm ][ BEGIN YOUR TURN this would be a good applet to get down before we do the algorithm of how to change over. hypertext transfer protocol: //www.visualfractions.

com/MixedFraction.html ]Once you understand the thought of assorted Numberss and improper fractions are two different ways of saying fractions more than 1, so the math related to the transition is a piece of bar, or pizza.Let ‘s expression at the assorted figure 2 5/8.To change over the assorted figure to an improper fraction foremost we must multiply the denominator by the “ whole ” figure to find how many pieces are in our wholes.2 5/8i?Y2i‚?8=16There are 16 pieces in our two whole pizzas.[ Use the image above but divide the two whole pizzas into 8ths please. ]We now see that we have 16 pieces of eight from our wholes and we have 5 more pieces of eight from our fraction.Add the numerator of the proper fraction 5/8 with our 16 pieces from our wholes.

This makes 21 pieces of eight or 21/8Mathematically it looks like this:2 5/8 i?Y 2i‚?8 = 16+5 = 21 i?Y 21/8Notice how the denominator does non alter. Merely the figure of pieces in the numerator alteration. A fraction tells us how many pieces a whole was broken into and how many pieces of a whole we have.

To change over a Assorted Number to an Improper fraction, follow these stairss:Multiply the whole by the denominator of the proper fraction.Add this merchandise to the numerator of the proper fraction.The proper fraction now becomes an improper fraction.The denominator stays the same.Let ‘s make another transition from a assorted figure, 5 2/3 to an improper fraction.5 2/3 i?Y 5i‚?3 = 15+2 = 17 i?Y 17/35 2/3 = 17/3[ YOUR TURN retarding force and bead or a, B, hundred sort of thing. replies are straight across from each other now.

]Match the assorted figure to its improper fraction equivalent.3 4/5 19/54 3/5 23/55 A? 23/47 A? 29/45 7/8 47/87 5/8 61/88 5/7 61/75 3/7 38/7[ END YOUR TURN ]

## Converting from Improper Fractions to Mixed Numbers

Looking at the left over parts of the pizza above we can state how many pieces we have left merely by numbering them. There are 17 pieces of pizza left.

Each pizza was cut into 8 every bit sized pieces. We could province our left over pizza as an improper fraction 17/8.If we were traveling to speak about the sum of left over pizza we would n’t state 17 eighths we would desire to utilize a assorted figure.How do we change over improper fractions to assorted Numberss? It would do sense to make the antonym of change overing assorted Numberss to improper fractions.To change over an improper fraction to a assorted fraction, follow these stairss:Divide the numerator by the denominator.This will assist us make up one’s mind how many wholes we have.

Write down the whole figure replyUse the balance from the division of the numerator by the denominator as the numerator of the proper fraction.The denominator stays the same.To follow the stairss for the transition of an improper fraction 17/8 to a assorted figure we foremost need to split 17 by 8.8 divides into 17 twice. This tells us we have 2 wholes.

The balance of 1 becomes the numerator of our proper fraction 1/8 and the denominator stays the same.Put it all together and 17/8 bends into 2 1/8[ Can you make an life of the pizza slices uniting to go 2 1/8 please? ]So at that place you have it. To change over from an improper fraction to a assorted figure you merely split the numerator by the denominator to find the figure of wholes. Then use the balance of that division to stand for the proper fraction part of the assorted figure.[ Chalk talk the stairss one more clip. ][ YOUR TURN this is a great game for improper fractions and calculating out what they mean in footings of a whole scoop of ice pick. hypertext transfer protocol: //www.mrnussbaum.

com/icecream/index.htmlEnd YOUR TURN ]Now that you can change over assorted and improper fractions back and forth easy, allow ‘s see if you can state their comparative size in either signifier.Position the undermentioned assorted and improper fractions on the figure line below.8 A? , 7/2, 15/2, 2 A?[ Make this 1 animated. Convert the improper fractions to Mixed Numberss so show the assorted fractions winging onto the figure line in its proper place.

]Merely as it ‘s easier for us to utilize assorted Numberss when speaking about mundane points, it ‘s easier for us to associate the size of a fraction when it ‘s in assorted figure signifier.[ BEGIN YOUR TURN create a set of 3 retarding force and beads onto the figure lines, please. ]5 3/8, 24/8, 6 5/8, 37/88 5/7, 50/7, 6 3/7, 63/73 1/5, 17/5, 15/5, 2 4/5[ END YOUR TURN ][ BEGIN REVIEW ]1. Write the improper fraction 22/5 as a assorted figure.*4 2/53 7/55 3/510 2/5Feedback: Divide the numerator by the denominator to happen the wholes. Use the balance as the numerator of the proper fraction. The denominator does non alter.2.

Write the improper fraction 25/5 as a assorted figure.*55 1/55 0/55 2/5Feedback: Divide the numerator by the denominator to happen the wholes. Use the balance as the numerator of the proper fraction in this instance there is NO balance so there is NO fractional portion of the assorted figure.

3. Write the assorted figure 3 2/3 as an improper fraction.*11/38/310/312/3Feedback: 3 2/3 i?Y 3i‚?3 = 9+2 = 11 i?Y 11/3 Multiply the whole by the denominator of the proper fraction so add this merchandise to the numerator of the proper fraction.4. Write the assorted figure 3 2/7 as an improper fraction.

*23/721/712/722/7Feedback: 3 2/7 i?Y 3i‚?7 = 21+2 = 23 i?Y 23/7 Multiply the whole by the denominator of the proper fraction so add this merchandise to the numerator of the proper fraction.5. Order the assorted and improper fractions from least to greatest.

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Feedback: Since they are equal, they are interchangeable, ,5. Order the assorted and improper fractions from greatest to least.

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Feedback: , , ,7. To change over a assorted figure to an improper fraction, multiply the whole by the denominator of the proper fraction and add this merchandise to the numerator of the proper fraction.*TrueFalse8. Choose the statement below that is wrong.The denominator ne’er alterations when you convert assorted Numberss to improper fractions.When change overing an improper fraction to a assorted fraction, use the balance as the numerator of the proper fraction.To change over the assorted figure to an improper fraction foremost we must multiply the denominator by the “ whole ” figure to find how many pieces are in our wholes.

*The numerator in a fraction tells us how many pieces a whole is broken into. The denominator tells us how many pieces we have of the whole.Feedback: The numerator in a fraction tells us how many pieces of a whole we have. The denominator tells us how many pieces the whole has been broken in to.[ END REVIEW ][ BEGIN QUIZ ]1.

Write the improper fraction 37/6 as a assorted figure.*6 1/76 2/75 6/75 5/7Feedback: Divide the numerator by the denominator to happen the wholes. Use the balance as the numerator of the proper fraction. The denominator does non alter.2. Write the improper fraction 49/7 as a assorted figure.*77 1/76 6/76 7/7Feedback: Divide the numerator by the denominator to happen the wholes.

Use the balance as the numerator of the proper fraction in this instance there is NO balance so there is NO fractional portion of the assorted figure.3. Write the assorted figure 10 2/5 as an improper fraction.

*52/517/522/557/5Feedback: 10 2/5 i?Y 10i‚?5 = 50+2 = 52 i?Y 52/5 Multiply the whole by the denominator of the proper fraction so add this merchandise to the numerator of the proper fraction.4. Write the assorted figure 3 2/7 as an improper fraction.*23/721/712/722/7Feedback: 3 2/7 i?Y 3i‚?7 = 21+2 = 23 i?Y 23/7 Multiply the whole by the denominator of the proper fraction so add this merchandise to the numerator of the proper fraction.5. Order the Numberss from least to greatest.

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Feedback: , , ,5. Order the assorted and improper fractions from greatest to least.

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Feedback:7. To change over an improper fraction to a assorted figure, multiply the whole by the denominator of the proper fraction and add this merchandise to the numerator of the proper fraction.True*FalseFeedback: To change over an improper fraction to a assorted fraction, follow these stairss:Divide the numerator by the denominator.This will assist us make up one’s mind how many wholes we have.Write down the whole figure replyUse the balance from the division of the numerator by the denominator as the numerator of the proper fraction.

The denominator stays the same.8. Choose the statement below that is wrong.The denominator ne’er alterations when you convert assorted Numberss to improper fractions.*When change overing an improper fraction to a assorted fraction, use the balance as the denominator of the proper fraction.To change over the assorted figure to an improper fraction foremost we must multiply the denominator by the “ whole ” figure to find how many pieces are in our wholes.The numerator in a fraction tells us how many pieces of a whole we have. The denominator tells us how many pieces the whole has been broken in to.

Feedback: When change overing an improper fraction to a assorted fraction, use the balance as the numerator of the proper fraction.[ END QUIZ ][ BEGIN TEST ]1. Write the improper fraction 25/6 as a assorted figure.*4 1/64 2/63 6/63 5/6Feedback: Divide the numerator by the denominator to happen the wholes. Use the balance as the numerator of the proper fraction.

The denominator does non alter.2. Write the improper fraction 121/11 as a assorted figure.*1110 10/1111 1/1110 9/11Feedback: Divide the numerator by the denominator to happen the wholes. Use the balance as the numerator of the proper fraction in this instance there is NO balance so there is NO fractional portion of the assorted figure.3.

Write the assorted figure 9 3/8 as an improper fraction.*75/820/835/827/8Feedback: 9 3/8 i?Y 9i‚?8 = 72+3 = 75 i?Y 75/8 Multiply the whole by the denominator of the proper fraction so add this merchandise to the numerator of the proper fraction.4. Write the assorted figure 8 1/6 as an improper fraction.*49/69/68/648/6Feedback: 8 1/6 i?Y 6i‚?8 = 48+1 = 49 i?Y 49/6 Multiply the whole by the denominator of the proper fraction so add this merchandise to the numerator of the proper fraction.

5. Order the Numberss from least to greatest.

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Feedback:5. Order the assorted and improper fractions from greatest to least.

Feedback:7. To change over an improper fraction to a assorted fraction, split the numerator by the denominator, write down the whole figure reply so utilize the balance from the division of the numerator by the denominator as the numerator of the proper fraction.*TrueFalse8. Choose the statement below that is wrong.*The denominator ever alterations when you convert assorted Numberss to improper fractions.When change overing an improper fraction to a assorted fraction, use the balance from the division of the numerator by the denominator as the numerator of the proper fraction.

To change over the assorted figure to an improper fraction foremost we must multiply the denominator by the “ whole ” figure to find how many pieces are in our wholes.The numerator in a fraction tells us how many pieces of a whole we have. The denominator tells us how many pieces the whole has been broken in to.Feedback: The denominator ever stays the same.[ END Trial ]

## Decision:

You can utilize either an improper fraction or a assorted fraction to demo the same sum.