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Numerator and denominator Equivalent fractions Comparing fractions Mixed number to improper fractionsHere you will learn about converting improper fractions to mixed numbers, including how to recognize improper fractions and mixed numbers.

Students will first learn about converting improper fractions to mixed numbers as part of number and operations – fractions in 4th grade.

**Improper fractions** and **mixed numbers** are both ways to show numbers that have wholes and parts. To understand improper fractions, first consider proper fractions.

A **proper fraction** is a fraction where the **numerator **(top number) is **smaller **than the **denominator **(bottom number).

For example,

\hspace{2.8cm} \cfrac{1}{2} \hspace{3.8cm} \cfrac{3}{4} \hspace{3.7cm} \cfrac{7}{12}

An **improper **fraction is a fraction where the **numerator **(top number) is **larger **than the **denominator **(bottom number).

For example,

\hspace{2.3cm} \cfrac{7}{2} \hspace{5.4cm} \cfrac{9}{4} \hspace{4.1cm} \cfrac{17}{12}

A** mixed number** has a **whole number part** and a** fractional part**.

For example,

\hspace{2.2cm} 3\cfrac{1}{2} \hspace{5.2cm} 2\cfrac{1}{4} \hspace{4cm} 1\cfrac{5}{12}

Any number greater than 1 can be shown as an improper fraction AND a mixed number.

For example,

\cfrac{7}{2} \, is 7 halves, which is three groups of \, \cfrac{2}{2} \, and a group of \, \cfrac{1}{2}.

3\cfrac{1}{2} \, is 3 and one half, which is three wholes and a group of \, \cfrac{1}{2}.

\cfrac{7}{2}=3 \cfrac{1}{2}

How does this relate to 4th grade math?

**Grade 4 – Numbers and Operations – Fractions (4.NF.B.3c)**Add and subtract mixed numbers with like denominators, example, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

**Grade 4 – Numbers and Operations in Base 10 (4.NBT.B.6)**

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

In order to convert an improper fraction to a mixed number with a model:

**Model the improper fraction.****Count the number of wholes and the fraction left over.****Write the mixed number.**

In order to convert an improper fraction to a mixed number with the algorithm:

**Divide the numerator by the denominator.****For the fraction, use the remainder as the numerator and keep the same denominator.****Write the mixed number.**

Use this worksheet to check your grade 4 to 5 students’ understanding of improper fractions to mixed numbers. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREEUse this worksheet to check your grade 4 to 5 students’ understanding of improper fractions to mixed numbers. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREEWrite the improper fraction \, \cfrac{7}{3} \, as a mixed number.

**Model the improper fraction.**

Draw 3 wholes and divide them equally into thirds. Then shade in 7 parts.

2**Count the number of wholes and the fraction left over.**

There are 2 wholes (or \cfrac{3}{3} \, ) shaded in, and there is \, \cfrac{1}{3} \, left over.

3**Write the mixed number.**

Write the improper fraction \, \cfrac{8}{5} \, as a mixed number.

**Model the improper fraction.**

Draw 2 wholes and divide them equally into fifths. Then shade in 8 parts.

**Count the number of wholes and the fraction left over.**

There is 1 whole (or \cfrac{5}{5} \, ) shaded in, and there is \, \cfrac{3}{5} \, left over.

**Write the mixed number.**

\cfrac{8}{5}=1\cfrac{3}{5}

Write the improper fraction \, \cfrac{21}{6} \, as a mixed number.

**Model the improper fraction.**

Draw 4 wholes and divide them equally into sixths. Then shade in 21 parts.

**Count the number of wholes and the fraction left over.**

There are 3 wholes (or \cfrac{6}{6} \, ) shaded in, and there is \, \cfrac{3}{6} \, left over.

**Write the mixed number.**

\cfrac{21}{6}=3 \cfrac{3}{6}

3 \cfrac{3}{6} \, can also be written as the equivalent mixed number 3 \cfrac{1}{2}.

Write the improper fraction \, \cfrac{42}{10} \, as a mixed number.

**Divide the numerator by the denominator.**

42 \div 10

You can use what you know about multiplication to solve. Since 4 \times 10=40, there will be 4 groups of 10 with 2 left over.

42 \div 10=4 \; R \, 2

**For the fraction, use the remainder as the numerator and keep the same denominator.**

**Write the mixed number.**

\cfrac{42}{10}=4 \cfrac{2}{10}

4 \cfrac{2}{10} can also be written as the equivalent mixed number 4 \cfrac{1}{5} or the decimal 4.2.

Write the improper fraction \, \cfrac{17}{9} \, as a mixed number.

**Divide the numerator by the denominator.**

17 \div 9

You can use what you know about subtraction to solve. Since 17-9 = 8, there will be 1 group of 9 with 8 left over.

17 \div 9=1 \; R \, 8

**For the fraction, use the remainder as the numerator and keep the same denominator.**

**Write the mixed number.**

\cfrac{17}{9}=1 \cfrac{8}{9}

Write the improper fraction \, \cfrac{51}{8} \, as a mixed number.

**Divide the numerator by the denominator.**

51 \div 8

You can use what you know about division to solve. Since 48 + 3 = 51 and 48 \div 8 = 6, there will be 6 groups of 8 with 3 left over.

51 \div 8=6 \; R \, 3

**For the fraction, use the remainder as the numerator and keep the same denominator.**

**Write the mixed number.**

\cfrac{51}{8}=6 \cfrac{3}{8}

- In the beginning, choose worksheets that allow students a lot of space to solve. There are many different ways that students can go about converting from improper fractions to mixed numbers based on their own understanding. They can draw different types of models (including area models and number lines) or explore different operations and equations to solve. It is important that students have space to show all this thinking on paper.

- Start by letting students explore this topic through models and their own understanding of improper fractions and mixed numbers. The division algorithm becomes a logical solving strategy once students really understand how improper fractions show equal groups of the denominator.

**Drawing unclear models**

Models can be a useful tool to solve fractions problems, but only if they are drawn correctly. Models also tend to work better with smaller fractions. The more drawing that has to be done, the more room for error. Also consider giving students access to a digital model that creates the fraction pieces for them.

**Not keeping the denominator the same**

The improper fraction and the mixed number of the same number both have the same value. This means the denominator should be the same, because the size of the parts in a fraction does not change when converting from improper fractions to mixed numbers. However, note that the denominator can change when simplifying, but this does not change the overall value of the improper fraction or mixed number.

For example,

**Dividing incorrectly**

When converting, most division equations will involve quotients with remainders. Making a division error will cause the mixed number to be incorrect.

**Including an improper fraction within a mixed number**

Once a number is converted to a mixed number, the fractional part should be proper. If the fraction is improper, it means that another whole can be created.

For example,

Write the improper fraction \, \cfrac{71}{9} \, as a mixed number.

1. Write the following improper fraction as a mixed number: \, \cfrac{5}{4}

1\cfrac{1}{4}

\cfrac{4}{5}

1\cfrac{1}{5}

1\cfrac{3}{4}

Draw 2 wholes and divide them equally into fourths. Then shade in 5 parts.

There is 1 whole (or \cfrac{4}{4} \, ) shaded in, and there is \, \cfrac{1}{4} \, left over.

\cfrac{5}{4}=1 \cfrac{1}{4}

2. Write the following improper fraction as a mixed number: \, \cfrac{8}{3}

1\cfrac{2}{3}

2\cfrac{1}{3}

2\cfrac{2}{3}

\cfrac{3}{8}

Draw 3 wholes and divide them equally into thirds. Then shade in 8 parts.

There are 2 wholes (or \cfrac{3}{3} \, ) shaded in, and there is \, \cfrac{2}{3} \, left over.

\cfrac{8}{3}=2 \cfrac{2}{3}

3. Write the following improper fraction as a mixed number: \, \cfrac{23}{5}

\cfrac{5}{23}

2\cfrac{3}{5}

3\cfrac{4}{5}

4\cfrac{3}{5}

Draw 5 wholes and divide them equally into fifths. Then shade in 23 parts.

There are 4 wholes (or \cfrac{5}{5} \, ) shaded in, and there is \, \cfrac{3}{5} \, left over.

\cfrac{23}{5}=4 \cfrac{3}{5}

4. Write the following improper fraction as a mixed number: \, \cfrac{43}{12}

3\cfrac{7}{12}

\cfrac{12}{43}

4\cfrac{1}{12}

3\cfrac{1}{7}

Divide the numerator by the denominator.

43 \div 12

You can use what you know about division to solve.

Since 36 + 7 = 43 and 36 \div 3=12, there will be 3 groups of 12 with 7 left over.

43 \div 12=3 \; R \, 7

\cfrac{43}{12}=3 \cfrac{7}{12}

5. Write the following improper fraction as a mixed number: \, \cfrac{41}{6}

6\cfrac{6}{5}

5\cfrac{5}{6}

6\cfrac{5}{6}

\cfrac{5}{6}

Divide the numerator by the denominator.

41 \div 6

You can use what you know about subtraction to solve:

\begin{aligned} &41-6 = 35\\ &35-6 = 29\\ &29-6 = 23\\ &23-6 = 17\\ &17-6 = 11\\ &11-6 = 5 \end{aligned}

There will be 6 groups of 6 with 5 left over.

41 \div 6=6 \; R \, 5

\cfrac{41}{6}=6 \cfrac{5}{6 }

6. Write the following improper fraction as a mixed number: \, \cfrac{67}{5}

13\cfrac{7}{10}

12\cfrac{7}{5}

\cfrac{5}{67}

13\cfrac{2}{5}

Divide the numerator by the denominator.

67 \div 5

You can use what you know about division to solve.

Since 5 \times 12=60, then 5 \times 13=65. There will be 13 groups of 5 with 2 left over.

67 \div 5=13 \; R \, 2

\cfrac{67}{5}=13 \cfrac{2}{5}

Yes, this is also common. For example, \frac{16}{2}=8 and \frac{55}{11}=5. Any time the numerator is a multiple of the denominator, the improper fraction will convert to a whole number without a fractional part.

No, students can master this skill without converting to the lowest terms (as known as the simplest form). However, there may be some instances where students are expected to record an answer in lowest terms. Check your state’s standards for specific guidelines.

A mixed number is sometimes also referred to as a mixed fraction. They have the same meaning.

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