Fractions

Ontario 09 Academic (MPM1D)

Adding and subtracting fractions

Lesson

As we have already seen in More or Less of Similar Fractions and Adding Parts, we can add and subtract fractions with 'easily relatable denominators' (which means part of our benchmark families), and also with unlike denominators (by finding common denominators).

You may be pleased to know we don't have to learn any new ways of adding and subtracting fractions now, but we will be facing some tougher questions.

This is the process we already have:

**Evaluate**: $\frac{3}{4}+\frac{2}{5}$34+25

**Think**: Find the LCM between $4$4 and $5$5 and find equivalent fractions. Then we will be able to add them.

**Do**: The LCM between $4$4 and $5$5 is $20$20.

$\frac{3}{4}+\frac{2}{5}$34+25 | $=$= | $\frac{15}{20}+\frac{8}{20}$1520+820 |

$=$= | $\frac{23}{20}$2320 |

But now we need to work with more difficult fractions like the following example - remember though the ideas and process are still the same.

**Evaluate**: $\frac{7}{19}+\frac{12}{95}$719+1295

**Think**: Before we can add fractions I have to have a common denominator, so I need the lowest common multiple between $19$19and $95$95. After some investigation I can see that $19\times5=95$19×5=95, so $95$95is the lowest common multiple. I will need to make both fractions with denominators of $95$95.

**Do**:

$\frac{7}{19}+\frac{12}{95}$719+1295 | $=$= | $\frac{7\times5}{19\times5}+\frac{12}{95}$7×519×5+1295 | |

$=$= | $\frac{35}{95}+\frac{12}{95}$3595+1295 | ||

$=$= | $\frac{47}{95}$4795 |

Evaluate $\frac{5}{6}+\frac{1}{36}$56+136.

Evaluate $\frac{3}{4}-\frac{1}{8}$34−18.

Evaluate $\frac{63}{56}+\frac{18}{48}$6356+1848.

Work out $7\frac{1}{5}-4\frac{1}{9}$715−419, giving your answer as a mixed number in its simplest form.

Simplify numerical expressions involving integers and rational numbers, with and without the use of technology