Number - Fractions of Amounts

Solutions

Question 1

a) To find $\frac12$ of $6$, need to divide $6$ by the denominator.

$6\div2=3$

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b) To find $\frac12$ of $10$, need to divide $10$ by the denominator.

$10\div2=5$

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c) To find $\frac13$ of $6$, need to divide $6$ by the denominator.

$6\div3=2$

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d) To find $\frac13$ of $12$, need to divide $12$ by the denominator.

$12\div3=4$

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e) To find $\frac14$ of $12$, need to divide $12$ by the denominator.

$12\div4=3$

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Question 2

a) To find $\frac12\times8$, need to divide $8$ by the denominator.

$8\div2=4$

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b) To find $\frac13\times15$, need to divide $15$ by the denominator.

$15\div3=5$

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c) To find $\frac14\times16$, need to divide $16$ by the denominator.

$16\div4=4$

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Question 3

a) To find $\frac23$ of $6$, need to divide $6$ by the denominator and multiply this answer by the numerator.

$\begin{align}6\div3&=2\\2\times2&=4\end{align}$

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b) To find $\frac23$ of $12$, need to divide $12$ by the denominator and multiply this answer by the numerator.

$\begin{align}12\div3&=4\\4\times2&=8\end{align}$

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c) To find $\frac25$ of $10$, need to divide $10$ by the denominator and multiply this answer by the numerator.

$\begin{align}10\div5&=2\\2\times2&=4\end{align}$

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e) To find $\frac34$ of $16$, need to divide $16$ by the denominator and multiply this answer by the numerator.

$\begin{align}16\div4&=4\\4\times3&=12\end{align}$

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Question 4

a) To find $\frac35\times20$, need to divide $20$ by the denominator and multiply this answer by the numerator.

$\begin{align}20\div5&=4\\4\times3&=12\end{align}$

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b) To find $\frac56\times18$, need to divide $18$ by the denominator and multiply this answer by the numerator.

$\begin{align}18\div6&=3\\3\times5&=15\end{align}$

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Question 5

a) To find $\frac32\times6$, need to divide $6$ by the denominator and multiply this answer by the numerator.

$\begin{align}6\div2&=3\\3\times3&=9\end{align}$

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b) To find $\frac32$ of $10$, need to divide $10$ by the denominator and multiply this answer by the numerator.

$\begin{align}10\div2&=5\\5\times3&=15\end{align}$

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c) To find $\frac52\times10$, need to divide $10$ by the denominator and multiply this answer by the numerator.

$\begin{align}10\div2&=5\\5\times5&=25\end{align}$

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d) To find $\frac43$ of $18$, need to divide $18$ by the denominator and multiply this answer by the numerator.

$\begin{align}18\div3&=6\\6\times4&=24\end{align}$

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Question 6

a) To find $1\frac12\times10$ it is a sensible idea to change the fraction to a top heavy/improper fraction. Then divide the number by the denominator and multiply this answer by the numerator.

$1\frac12=\frac32$

$\begin{align}10\div2&=5\\5\times3&=15\end{align}$

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b) To find $2\frac12$ of $8$ it is a sensible idea to change the fraction to a top heavy/improper fraction. Then divide the number by the denominator and multiply this answer by the numerator.

$2\frac12=\frac52$

$\begin{align}8\div2&=4\\4\times5&=20\end{align}$

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c) To find $1\frac13\times15$ it is a sensible idea to change the fraction to a top heavy/improper fraction. Then divide the number by the denominator and multiply this answer by the numerator.

$1\frac13=\frac43$

$\begin{align}15\div3&=5\\5\times4&=20\end{align}$

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d) To find $1\frac15$ of $20$ it is a sensible idea to change the fraction to a top heavy/improper fraction. Then divide the number by the denominator and multiply this answer by the numerator.

$1\frac15=\frac65$

$\begin{align}20\div5&=4\\4\times6&=24\end{align}$

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n) To find $5\frac{8}{17}$ of $51$ it is a sensible idea to change the fraction to a top heavy/improper fraction. Then divide the number by the denominator and multiply this answer by the numerator.

$5\frac{8}{17}=\frac{93}{17}$

$\begin{align}51\div17&=3\\3\times93&=279\end{align}$

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Question 7

a) To increase $10$ by $\frac12$ first find $\frac12$ of $10$ and then add this to $10$.

$\begin{align}\frac12\text{ of }10&=5\\5+10&=15\end{align}$

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b) To increase $6$ by $\frac13$ first find $\frac13$ of $6$ and then add this to $6$.

$\begin{align}\frac13\text{ of }6&=2\\2+6&=8\end{align}$

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c) To increase $20$ by $\frac14$ first find $\frac14$ of $20$ and then add this to $20$.

$\begin{align}\frac14\text{ of }20&=5\\5+20&=25\end{align}$

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j) This is still the same as previous questions. To increase $10$ by $\frac32$ first find $\frac32$ of $10$ and then add this to $10$.

$\begin{align}\frac32\text{ of }10&=15\\15+10&=25\end{align}$

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m) This is still the same as previous questions. To increase $18$ by $1\frac13$ first find $1\frac13$ of $18$ and then add this to $18$.

$\begin{align}1\frac13\text{ of }18&=24\\24+18&=42\end{align}$

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Question 8

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Question 9

a) If you decrease a number by $\frac12$ this number must represent $1-\frac12=\frac12$ of the original number.

If the original number multiplied by $\frac12$ is $4$ then if we divide $4$ by $\frac12$ we will get the original number.

(in algebra if $x$ is the original number:
$\begin{align}x\times\frac12&=4\\x&=4\div\frac12\\x&=4\times\frac21\\x&=4\times2\\x&=8\end{align}$

So the original number is $8$

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b) If you decrease a number by $\frac13$ this number must represent $1-\frac13=\frac23$ of the original number.

If the original number multiplied by $\frac23$ is $4$ then if we divide $4$ by $\frac23$ we will get the original number.

(in algebra if $x$ is the original number:
$\begin{align}x\times\frac23&=4\\x&=4\div\frac23\\x&=4\times\frac32\\x&=\frac{12}{2}\\x&=6\end{align}$

So the original number is $6$

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e) If you decrease a number by $\frac14$ this number must represent $1-\frac14=\frac34$ of the original number.

If the original number multiplied by $\frac34$ is $6$ then if we divide $6$ by $\frac34$ we will get the original number.

(in algebra if $x$ is the original number:
$\begin{align}x\times\frac34&=6\\x&=6\div\frac34\\x&=6\times\frac43\\x&=\frac{24}{3}\\x&=8\end{align}$

So the original number is $8$

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g) If you decrease a number by $\frac23$ this number must represent $1-\frac23=\frac13$ of the original number.

If the original number multiplied by $\frac13$ is $5$ then if we divide $5$ by $\frac13$ we will get the original number.

(in algebra if $x$ is the original number:
$\begin{align}x\times\frac13&=5\\x&=5\div\frac13\\x&=5\times\frac31\\x&=5\times3\\x&=15\end{align}$

So the original number is $15$

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Question 10

a) If you increase a number by $\frac12$ this number must represent $1+\frac12=\frac32$ of the original number.

If the original number multiplied by $\frac32$ is $6$ then if we divide $6$ by $\frac32$ we will get the original number.

(in algebra if $x$ is the original number:
$\begin{align}x\times\frac32&=6\\x&=6\div\frac32\\x&=6\times\frac23\\x&=\frac{12}{3}\\x&=4\end{align}$

So the original number is $4$

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g) If you increase a number by $\frac25$ this number must represent $1+\frac25=\frac75$ of the original number.

If the original number multiplied by $\frac75$ is $21$ then if we divide $21$ by $\frac75$ we will get the original number.

(in algebra if $x$ is the original number:
$\begin{align}x\times\frac75&=21\\x&=21\div\frac75\\x&=21\times\frac57\\x&=\frac{105}{7}\\x&=15\end{align}$

So the original number is $15$

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Question 11

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