Multiplying Mixed Numbers

Related calculator: Fractions Calculator

Note! Rules for determining sign of the result are same as when multiplying integers.

Example 1. Find $$${2}\frac{{4}}{{5}}\cdot\frac{{7}}{{8}}$$$.

First number is mixed: convert it into improper fraction: $$${2}\frac{{4}}{{5}}=\frac{{14}}{{5}}$$$.

$$$\frac{{14}}{{5}}\cdot\frac{{7}}{{8}}=\frac{{{14}\cdot{7}}}{{{5}\cdot{8}}}=\frac{{98}}{{40}}$$$.

Now, reduce fraction: $$$\frac{{98}}{{40}}=\frac{{49}}{{20}}$$$.

Convert to mixed number: $$$\frac{{49}}{{20}}={2}\frac{{9}}{{20}}$$$.

Answer: $$$\frac{{49}}{{20}}={2}\frac{{9}}{{20}}$$$.

Next example.

Example 2. Find $$${3}\frac{{8}}{{9}}\cdot{2}\frac{{1}}{{5}}$$$.

Convert both numbers into improper fractions: $$${3}\frac{{8}}{{9}}=\frac{{35}}{{9}}$$$ and $$${2}\frac{{1}}{{5}}=\frac{{11}}{{5}}$$$.

Now, multiply fractions: $$$\frac{{35}}{{9}}\cdot\frac{{11}}{{5}}=\frac{{{35}\cdot{11}}}{{{9}\cdot{5}}}=\frac{{385}}{{45}}$$$

Reduce fraction: $$$\frac{{385}}{{45}}=\frac{{77}}{{9}}$$$.

Convert to mixed number: $$$\frac{{77}}{{9}}={8}\frac{{5}}{{9}}$$$.

Answer: $$$\frac{{77}}{{9}}={8}\frac{{5}}{{9}}$$$.

Next example.

Example 3. Find $$${2}\frac{{1}}{{3}}\cdot{\left(-{3}\frac{{1}}{{4}}\right)}$$$.

Convert both numbers into fractions: $$${2}\frac{{1}}{{3}}=\frac{{7}}{{3}}$$$ and $$$-{3}\frac{{1}}{{4}}=-\frac{{13}}{{4}}$$$.

Multiply fractions: $$$\frac{{7}}{{3}}\cdot{\left(-\frac{{13}}{{4}}\right)}=\frac{{{7}\cdot{\left(-{13}\right)}}}{{{3}\cdot{4}}}=-\frac{{91}}{{12}}$$$.

Fraction is irreducible.

Convert to mixed number: $$$-\frac{{91}}{{12}}=-{7}\frac{{7}}{{12}}$$$.

Answer: $$$-\frac{{91}}{{12}}=-{7}\frac{{7}}{{12}}$$$.

Now, it is time to practice.

Exercise 1. Find $$${2}\frac{{2}}{{5}}\cdot{2}\frac{{1}}{{3}}$$$.

Answer: $$$\frac{{28}}{{5}}={5}\frac{{3}}{{5}}$$$.

Next exercise.

Exercise 2. Find $$$-{1}\frac{{4}}{{7}}\cdot{1}\frac{{4}}{{5}}$$$.

Answer: $$$-\frac{{99}}{{35}}=-{2}\frac{{29}}{{35}}$$$.

Next example.

Exercise 3. Find $$$-{9}\frac{{1}}{{2}}\cdot{\left(-{3}\frac{{3}}{{5}}\right)}$$$.

Answer: $$$\frac{{171}}{{5}}={34}\frac{{1}}{{5}}$$$.