Simplifying Fractions

Simplifying Fractions exercise

• How do we simplify a fraction?

  Hints

  When simplifying a fraction we can only divide the numerator and denominator by the same number, or it will not have the same value. For example:

  When the fraction is simplified we should check if there are no more common factors.

  If there are not then the fraction is fully simplified.

  Solution

  1. Find the highest common factor of the numerator and denominator.
  2. Divide both the numerator and the denominator by the HCF.
  3. Write the new values as the simplified fraction.
  4. If there are no more common factors, the fraction is finally in its simplest form.

• Simplify the fractions.

  Hints

  Find the HCF of the numerator and the denominator.

  Divide them by the HCF.

  Check there are no more factors which are common.

  When simplifying $\frac{3}{9}$ we would find the factors of $3$ and $9$.

  Factors of $3$ are $1$ and $3$.

  Factors of $9$ are $1$, $3$, $9$.

  HCF is $3$ so we divide numerator and denominator by $3$.

  Solution

  • $\mathbf{\dfrac{3}{9}}$ = $\mathbf{\dfrac{1}{3}}$

  ${}$

  • $\mathbf{\dfrac{4}{16}}$ = $\mathbf{\dfrac{1}{4}}$

  ${}$

  • $\mathbf{\dfrac{6}{9}}$ = $\mathbf{\dfrac{2}{3}}$

  ${}$

  • $\mathbf{\dfrac{13}{26}}$ = $\mathbf{\dfrac{1}{2}}$

  ${}$ ${}$

  The method for each fraction:

  1. Find the factors of the numerator and the denominator.
  2. Choose the HCF (the highest common factor).
  3. Divide them by the HCF.
  4. Check there are no more factors that are common.

• Find the percentage of watermelon in a fruit salad.

  Hints

  The fraction of melon is $\frac{150}{300}$.

  How can we simplify this?

  Find all the factors of $150$ and all the factors of $300$.

  Find the HCF and divide by this.

  The HCF of $150$ and $300$ is $150$.

  Divide the numerator and the denominator by $150$.

  Solution

  $\mathbf{\frac{1}{2}}$

  Here are some of the factors of $150$

  $1$, $5$, $25$, $150$,.......

  Here are some of the factors of $300$.

  $1$, $2$, $3$, $5$, $25$, $100$, $150$,.....

  We can see that $150$ is the HCF.

  Divide the numerator and denominator by $150$.

• Fraction Match!

  Hints

  We do these the same way although the numbers are bigger.

  The factors of $12$ are $1$, $2$, $3$, $4$, $6$ and $12$

  Some of the factors of $72$ are $1$, $2$, $6$ and $12$ .....

  The HCF is $12$.

  Divide by this.

  The HCF is $24$.

  We divide the numerator and denominator by this.

  Solution

  $\mathbf{\frac{22}{44}}$ = $\mathbf{\frac{1}{2}}$ (divided by $22$)

  $\mathbf{\frac{15}{45}}$ = $\mathbf{\frac{1}{3}}$ (divided by $15$)

  $\mathbf{\frac{24}{96}}$ = $\mathbf{\frac{1}{4}}$ (divided by $24$)

  $\mathbf{\frac{12}{72}}$ = $\mathbf{\frac{1}{6}}$ (divided by $12$)

  We find the HCF of each and divide the numerator and denominator by this.

• Simplify the fraction.

  Hints

  List the factors of the numerator and the denominator. This will make spotting the HCF easier.

  For example, factors of $12$ are $1$, $2$, $3$, $4$, $6$, $12$.

  Find the HCF of the numerator and the denominator and divide by this number. For example:

  Solution

  $\mathbf{\frac{4}{5}}$

  List the factors of $12$ ($1$, $2$, $3$, $4$, $6$, $12$)

  List the factors of $15$ ($1$, $3$, $5$, $15$)

  HCF is $3$

  Divide the numerator and denominator by $3$.

• Simplify a fraction to solve the problem.

  Hints

  We are looking for the amount of money Luke has left!

  We must subtract first.

  $56$ - $14$ spent = $42$.

  Once we have subtracted the money spent at the cinema, it leaves the fraction $\frac{42}{56}$.

  We can now find the HCF and divide the numerator and denominator by it to simplify the fraction.

  Solution

  The correct answer is $\mathbf{\frac{3}{4}}$

  $56$ - $14$ = $42$

  Fraction is $\frac{42}{56}$

  Factors of $42$ are $1$, $2$, $3$, $7$, $14$.

  Factors of $56$ are $1$, $2$, $4$, $7$, $8$, $14$, $28$, $56$.

  HCF = $14$

  We divide the numerator and the denominator by $14$.