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Improper Fractions and Mixed Numbers

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Improper Fractions and Mixed Numbers
CCSS.MATH.CONTENT.4.NF.B.3.C

Basics on the topic Improper Fractions and Mixed Numbers

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Axel and Tank received a postcard from their friend with a recipe for snow. However, there’s just one problem: they need to convert improper fractions to mixed numbers in order to see how much of each ingredient they need. Let’s read about this improper fractions to mixed numbers video so we can help Axel and Tank with converting improper fractions to mixed numbers.

What is an improper fraction and What is a mixed number?

There are three types of fractions:

  • proper fraction- the numerator is smaller than the denominator
  • improper fraction- the numerator is larger than the denominator
  • mixed number- a combination of a whole number and a fraction

Can you convert improper fractions to mixed numbers? The answer is yes, you can change improper fractions to mixed numbers. The next section will explain how to change improper fractions to mixed numbers using simple steps.

Changing Improper Fractions to Mixed Numbers

How do you convert an improper fraction to a mixed number? We can convert, or change, improper fractions to mixed numbers so they are easier to understand. Here is an example of how to make improper fractions into mixed numbers:

  • Step 1: Represent seven-thirds using fraction bars.

seven-thirds-fraction-bars-improper-fractions-to-mixed-numbers.svg

  • Step 2: Count how many wholes we have shaded in and write the whole number.

_seven-thirds-fraction-bars-two-wholes-improper-fractions-to-mixed-numbers.svg

  • Step 3: Record the remaining part as a fraction.

seven-thirds-fraction-bars-two-wholes-one-third-improper-fractions-to-mixed-numbers.svg

If you look closely at the image above you can see how to write improper fractions as mixed numbers. You will find that the answer is the mixed number is two and one third, once you follow the steps on how to turn improper fractions into mixed numbers.

How to Convert Improper Fractions to Mixed Numbers Summary

How do you change improper fractions to mixed numbers? Remember, these steps explain how to turn improper fractions to mixed numbers:

  • Step 1: Represent seven-thirds using fraction bars.
  • Step 2: Count how many wholes we have shaded in and write the whole number.
  • Step 3: Record the remaining part as a fraction.

Now, can you change improper fractions to mixed numbers? Practice how to convert improper fractions to mixed numbers on this website with the improper fractions to mixed numbers worksheet along with other activities, and exercises.

Transcript Improper Fractions and Mixed Numbers

Axel and Tank received a postcard from their friend. "Wow Axel, check out all that snow!" "What's this?" "It looks like a recipe to make our own snow!" "Cool (...) except the ingredients are written as these special fractions!" "That can't be proper!" Let's learn about, "Improper Fractions and Mixed Numbers," so we can help Axel and Tank make snow! An improper fraction, is a fraction with a numerator that is GREATER THAN (...) the denominator. We can convert, or change, improper fractions into mixed numbers so they are easier to understand. A mixed number is a combination of a WHOLE NUMBER and a FRACTION. Let's see how to convert seven-thirds into a mixed number. The first step is to represent seven-thirds using fraction bars like THIS. Fraction bars help us because it is a visual model of our fraction. Each whole is broken up into THIRDS to match our DENOMINATOR... and we need to shade in SEVEN PARTS to match our NUMERATOR. This fraction bar has three parts (...) since we need to shade more than just three, we need another fraction bar. Now we have six parts, but we need to shade in seven parts... so we need one more fraction bar in order to represent all seven parts. The second step is to count how many WHOLES we have shaded in. Since two fraction bars have ALL parts shaded in, our whole is TWO. Finally, record the remaining part as a fraction (...) which is one-third. Seven-thirds written as a mixed number is TWO and ONE-THIRD. Now that we know how to convert an improper fraction to a mixed number, let's help Axel and Tank make snow! First, they need five-fourths cups of baking soda. You can see it's an IMPROPER FRACTION because the numerator is greater than the denominator. What is the first step to convert to a mixed number? (...) The first step is to represent five-fourths using fraction bars... so we need to shade in five parts (...) because the NUMERATOR is five. The second step is to count how many WHOLES are shaded in. How many wholes are shaded in? (...) There is one WHOLE fraction bar shaded in, so we write our whole (...) ONE. What is the third step? (...) The third step is to record the remaining fraction. What is the remaining fraction? (...) One-fourth, so Axel and Tank need ONE and ONE-FOURTH cups of baking soda. Last, they need nine-sixths cups of shaving cream. What is the first step to convert to a mixed number? (...) Represent nine-sixths using fraction bars. What is the next step? (...) Count how many WHOLES we have shaded in(...) how many wholes are shaded in? (...) One whole is shaded in (...) what is the last step? Write the remaining fraction. (...) The remaining fraction is three-sixths. What do you notice about three-sixths? (...) Three-sixths is not written in simplest form. Remember, we simplify fractions with MANY PARTS into fractions with FEWER PARTS to make them easier to understand. What is three-sixths in simplest form?(...) Three-sixths in simplest form is one-half (...) we know this because HALF of the fraction bar is shaded! The whole number stays the same so... Axel and Tank need ONE and ONE-HALF cups of shaving cream. Before we see how the snow turned out, let's summarize. Remember (...) an improper fraction is a fraction with a numerator that is GREATER THAN the denominator. A mixed number is a combination of a WHOLE NUMBER and a FRACTION. The first step is to represent the improper fraction using fraction bars. The second step is to record how many wholes are shaded in. Last, we record the remaining fraction and simplify as needed. Let's see how the snow recipe turned out! "Okay, I added all the ingredients!" "Axel! What did I tell you about forgetting your glasses (...) I don't think you measured this right!"

Improper Fractions and Mixed Numbers exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Improper Fractions and Mixed Numbers.
  • What are improper fractions?

    Hints

    The numerator is the top part of the fraction, the denominator is the bottom part of the fraction.

    Here is an example of a mixed number. What do you notice about it?

    Solution
    • An improper fraction is a fraction with a numerator that is greater than the denominator.
    • A mixed number has a combination of a whole number and a fraction.
    • 3$\frac3 4$ is a mixed number because it has a whole number and a fraction.
    • $\frac8 3$ is an improper fraction because the numerator is greater than the denominator.
  • Sea stew ingredients.

    Hints

    Convert the improper fraction by drawing a fraction bar. The denominator is how many parts the whole is broken in to.

    Count up the whole fraction bars that have been completely shaded, this is the whole number part of your mixed number.

    After you have counted the whole bars, how many extra parts are shaded? This will be your numerator.

    Solution

    $\frac7 5$ is equal to 1$\frac2 5$

    $\frac5 3$ is equal to 1$\frac2 3$

    $\frac{12} {5}$ is equal to 2$\frac2 5$

    $\frac7 3$ is equal to 2$\frac1 3$

  • Where are the errors?

    Hints

    Try drawing each improper fraction using fraction bars. Remember that the denominator shows how many parts each bar should have.

    If all the parts of a fraction bar have been shaded, this is equal to one whole.

    Solution

    Here are the numbers that you should have highlighted.

    The correct answers to each are shown.

  • Ordering fractions and mixed numbers.

    Hints

    Begin by converting the improper fractions to mixed numbers. Or convert all the fractions to the same denominator, like fourths.

    Can your fraction be simplified for example, $\frac3 6$ is equal to $\frac1 3$?

    When using a fraction bar, remember that the denominator tells you how many parts the fraction bar is split into.

    Solution

    The fractions in order of size from smallest to greatest are:

    • $\frac{10} {8}$ (This is equivalent to $\frac5 4$ which is 1$\frac1 4$)
    • 1$\frac1 2$ (This is equivalent to 1$\frac2 4$)
    • $\frac7 4$ (This is equivalent to 1$\frac3 4$)
    • $\frac9 4$ (This is equivalent to 2$\frac1 4$)
    • $\frac6 2$ (This is equivalent to 3)
  • Using fraction bars.

    Hints

    Look at the denominator (the bottom part of the fraction), this tells you how many parts the fraction is split into.

    Look at the numerator (the top part of the fraction), this tells you how many parts are shaded in.

    Solution

    Here are the correct answers.

  • Improper, mixed and whole numbers.

    Hints

    Can the fraction be simplified, for example, $\frac3 6$ can be simplified to $\frac1 2$.

    Convert the improper fractions to mixed numbers by drawing a fraction bar, use the denominator to decide how many parts the bar needs.

    Count how many parts are shaded in total, this is the numerator.

    Solution

    Here are the correct answers.