Problem Solving

 
2.4  Problem Solving
 

EXAMPLE 1:

Ali spends RM 230. His sister spends 250% of Ali's expenses. Count his sister's expenses.

SOLUTION:

Ali's spendings: RM 230
Sister's spendings: RM 230 \(\times\) 250%

\(=\frac{25\cancel0}{1\cancel0\cancel0}\times\text{ RM }23\cancel0\)

\(=25 \times\text{RM }23\)

\(=\text{RM }575\)

So, Ali's sister's spending is RM 575.

 

EXAMPLE 2:

Convert percentage to mixed numbers.
a) 130%
b) 370%
c) 412%
d) 505%

SOLUTION:

\(\text{a) }130\%\to\frac{130}{100}\\ \,\,\,\,\,\,\frac{13\cancel0}{10\cancel0}\to\frac{13}{10}\to1\frac{3}{10}\)

In decimals,

\(1\frac{3}{10}\to1.3\)

 

\(\text{b) }370\%\to\frac{370}{100}\\ \,\,\,\,\,\,\frac{37\cancel0}{10\cancel0}\to\frac{37}{10}\to3\frac{7}{10} \)

In decimals,

\(3\frac{7}{10}\to3.7\)

 

\(\text{c) }412\%\to\frac{412}{100}\to4\frac{12}{100}\\ \,\,\,\,\,\,4\frac{12\,\div\,4}{100\,\div\,4}=4\frac{3}{25}\\ \)
In decimals,

\(4\frac{12}{100}\to4.12\)

 

\(\text{d) }505\%\to\frac{505}{100}\to5\frac{5}{100}\\ \,\,\,\,\,\,\,5\frac{5\,\div\,5}{100\,\div\,5}=5\frac{1}{20}\)

In decimals,

\(5\frac{5}{100}\to5.05\)

 

 

Problem Solving

 
2.4  Problem Solving
 

EXAMPLE 1:

Ali spends RM 230. His sister spends 250% of Ali's expenses. Count his sister's expenses.

SOLUTION:

Ali's spendings: RM 230
Sister's spendings: RM 230 \(\times\) 250%

\(=\frac{25\cancel0}{1\cancel0\cancel0}\times\text{ RM }23\cancel0\)

\(=25 \times\text{RM }23\)

\(=\text{RM }575\)

So, Ali's sister's spending is RM 575.

 

EXAMPLE 2:

Convert percentage to mixed numbers.
a) 130%
b) 370%
c) 412%
d) 505%

SOLUTION:

\(\text{a) }130\%\to\frac{130}{100}\\ \,\,\,\,\,\,\frac{13\cancel0}{10\cancel0}\to\frac{13}{10}\to1\frac{3}{10}\)

In decimals,

\(1\frac{3}{10}\to1.3\)

 

\(\text{b) }370\%\to\frac{370}{100}\\ \,\,\,\,\,\,\frac{37\cancel0}{10\cancel0}\to\frac{37}{10}\to3\frac{7}{10} \)

In decimals,

\(3\frac{7}{10}\to3.7\)

 

\(\text{c) }412\%\to\frac{412}{100}\to4\frac{12}{100}\\ \,\,\,\,\,\,4\frac{12\,\div\,4}{100\,\div\,4}=4\frac{3}{25}\\ \)
In decimals,

\(4\frac{12}{100}\to4.12\)

 

\(\text{d) }505\%\to\frac{505}{100}\to5\frac{5}{100}\\ \,\,\,\,\,\,\,5\frac{5\,\div\,5}{100\,\div\,5}=5\frac{1}{20}\)

In decimals,

\(5\frac{5}{100}\to5.05\)