# Math homework help -converting betweenpercentages, decimalsand fractions

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 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
Tip:
1. To convert a decimal to its equivalent percentage: Multiply the decimal number by 100. For example,
0.28 = 0.28 × 100 = 28%
2. To convert a percentage to its equivalent decimal: Divide the given percentage by 100. For example,
86% = 86 ÷ 100 = 0.86
3. 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,
34 = 3 ÷ 4 = 0.75
4. 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 = 31, 10 = 101 and so on.
The given fraction, let's say 0.35 = 0.351
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, 0.351 = 0.35× 1001× 100
= 35100
Now simplify.
35100 = 35÷ 5100÷ 5
= 720
5. 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,
25 = ?100
Since 5 × 20 = 100, ? = 2 ×20 = 40
Therefore, 25 = 40100 = 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,
38 = ?100
But 8 × nothing (I mean no integer) = 100. So,
38 = 3 ÷ 8 = 0.375 = 37.5%
6. 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% = 52100 = 52÷ 4100÷ 4 = 1325