Comparing Mixed Numbers and Improper Fractions

Compare Improper Fractions to Mixed Numbers

4th grade - 5th grade

Improper Fraction

• A fraction where the numerator (top number) is larger than the denominator (bottom number}.

• Examples

•  $\frac{4}{3}$   $\frac{6}{4}$   $\frac{12}{5}$  

Mixed Number

• Composed of  a whole number and a fraction

• Examples

•  $1\ \frac{1}{4}$   $3\ \frac{2}{5}$   $7\ \frac{2}{3}$  
  

Let's review how to convert

both improper fractions and mixed numbers

Multiple Choice

Convert the improper fraction

$$\frac{7}{4}$$  to a mixed number

• $$1\ \frac{3}{7}$$  

• $$1\ \frac{3}{4}$$  

• $$1\ \frac{1}{4}$$  

Multiple Choice

Convert the improper fraction

$$\frac{11}{5}$$  to a mixed number

• $$2\ \frac{1}{5}$$  

• $$1\ \frac{2}{5}$$  

• $$5\ \frac{1}{2}$$  

How to Convert a Mixed Number to an Improper Fraction.

Multiple Choice

The first step when converting a mixed number to an improper fraction is to multiply the denominator times the whole number.

• True

• False

Multiple Choice

Convert the mixed number

$$2\ \frac{2}{3}$$  to an improper fraction

• $$\frac{7}{3}$$  

• $$\frac{12}{3}$$  

• $$\frac{8}{3}$$  

To Compare Improper Fractions to Mixed Numbers, you have to make both fractions the same format

either both as improper fractions or both as mixed numbers.

Compare

 $\frac{12}{5}$  and  $2\ \frac{3}{5}$  

• Convert  $2\ \frac{3}{5}$  to an improper fraction

• Multiply 5 x 2 + 3 =  $\frac{13}{5}$  

• Why doesn't the denominator change?

• Now compare  $\frac{12}{5}$  to  $\frac{13}{5}$  

•  $\frac{12}{5}$  <  $\frac{13}{5}$  so  $\frac{12}{5}$  <  $2\ \frac{3}{5}$  

Multiple Choice

Compare

$$2\ \frac{2}{5}$$             $$\frac{12}{5}$$  

• >

• <

• =

Multiple Choice

Ms. Gallindo needs  $$\frac{15}{4}$$  yards of red bulletin paper and  $$4\ \frac{1}{4}$$  yards of blue bulletin paper. Which comparison is true?

• $$\frac{15}{4}$$  <  $$4\ \frac{1}{4}$$  

• $$\frac{15}{4}$$  >  $$4\ \frac{1}{4}$$  

• $$\frac{15}{4}$$  =  $$4\ \frac{1}{4}$$  

Multiple Choice

Compare

$$\frac{56}{6}$$           $$5\ \frac{2}{6}$$  

• >

• <

• =