Mixed numerals and comparing fractions

Converting between mixed numerals and improper fractions, and comparing and ordering fractions, including negative fractions, using common denominators.

Mixed numerals and improper fractions

An improper fraction has a numerator bigger than its denominator, like $\dfrac{11}{4}$. A mixed numeral has a whole part and a fraction, like $2\tfrac{3}{4}$.

Comparing fractions

Rewrite the fractions with the same denominator (use the LCM), then compare the numerators.

Example 1●●

Which is larger, $\dfrac{5}{6}$ or $\dfrac{7}{9}$?

LCM of $6$ and $9$ is $18$.

$\dfrac{5}{6} = \dfrac{15}{18}$ and $\dfrac{7}{9} = \dfrac{14}{18}$.

$\dfrac{5}{6}$ is larger.

Example 2: negative fractions●●

Order $-\tfrac{1}{2}, \tfrac{1}{3}, -\tfrac{3}{4}$ from smallest to largest.

Negatives are smaller than positives. Between the negatives, $-\tfrac{3}{4}$ is further left.

$-\tfrac{3}{4}, -\tfrac{1}{2}, \tfrac{1}{3}$

Flashcards

$3 frac{2}{5}$ as an improper fraction

$\dfrac{17}{5}$

$dfrac{13}{4}$ as a mixed numeral

$3\tfrac{1}{4}$

To compare fractions

Use a common denominator, then compare numerators.

Practice

Write $2\tfrac{3}{4}$ as an improper fraction.
Write $\dfrac{13}{4}$ as a mixed numeral.
Which is larger?
Which is smallest?
Write $3\tfrac{2}{5}$ as an improper fraction.
Which is bigger, $\dfrac{1}{5}$ or $\dfrac{1}{3}$?
Which fraction lies between $\tfrac{1}{2}$ and $\tfrac{3}{4}$?
How many whole numbers are there in $\dfrac{37}{7}$? (The whole part of the mixed numeral.)