Math homework help 
converting between
percentages, decimals
and fractions
Math homework help home
Students send me scans (or cell phone pictures) of their math
homework with their own answers written down. I review and rectify
mistakes, if any so that they have all correct answers by the time they
turn them in to their school teachers. I also make efforts to explain
the concepts/steps briefly.
Note
that this is a paid service but
costs significantly less than live tutoring sessions. Here are a few
examples from pre algebra to show what I receive and what I send back.
You can use these solutions as solved examples to learn on your own.
Don't miss out on the tips and tricks, if any.
Percentage to decimal and decimal to percentage
Convert between fractions, decimals and percentages
Percentage to decimal and decimal to percentage
What I received

What I sent back

click on pictures to enlarge

Convert between fractions, decimals and percentages
What I received

What I sent back

click on pictures to enlarge

More sample maths homework help by email
Tip:

To convert a decimal to its equivalent percentage: Multiply the decimal number by 100. For example,
0.28 = 0.28 × 100 = 28%

To convert a percentage to its equivalent decimal: Divide the given percentage by 100. For example,
86% = 86 ÷ 100 = 0.86

To convert a fraction to its equivalent decimal: Divide the numerator with the denominator (remember, the fraction bar is just another way of writing the division symbol). For example,
^{3}⁄_{4} = 3 ÷ 4 = 0.75

To convert a decimal to its equivalent fraction: Rewrite the decimal as a fraction with 1 as the denominator. Since the fraction bar is equivalent to division and dividing a number with 1 gives the same number, you can do that.
Thus, 3 = ^{3}⁄_{1}, 10 = ^{10}⁄_{1} and so on.
The given fraction, let's say 0.35 = ^{0.35}⁄_{1}
Your next job is to multiply the numerator and denominator with a number to find one of its equivalent forms, so that the decimal numerator changes to an integer.
In our example, ^{0.35}⁄_{1} = ^{0.35× 100}⁄_{1× 100}
= ^{35}⁄_{100}
Now simplify.
^{35}⁄_{100} = ^{35÷ 5}⁄_{100÷ 5}
= ^{7}⁄_{20}

To convert a fraction to its equivalent percentage: Rewrite its equivalent form with 100 in the denominator. The numerator is the equivalent percentage. For example,
^{2}⁄_{5} = ^{?}⁄_{100}
Since 5 × 20 = 100, ? = 2 ×20 = 40
Therefore, ^{2}⁄_{5} = ^{40}⁄_{100} = 40%
If you can't change the denominator to 100, you can change the fraction to its decimal form and then change that decimal to its equivalent percentage. For example,
^{3}⁄_{8} = ^{?}⁄_{100}
But 8 × nothing (I mean no integer) = 100. So,
^{3}⁄_{8} = 3 ÷ 8 = 0.375 = 37.5%

To convert a percentage to its equivalent fraction: Rewrite the percentage as over 100 and simplify. Remember, 'per cent' means per 100 or over 100. For example,
52% = ^{52}⁄_{100} = ^{52÷ 4}⁄_{100÷ 4} = ^{13}⁄_{25}