Fractions, Decimals, Percent, and Ratios

Question 1

In what ways you can express a part-to-whole relationship?

Answer 1

Fraction = 1 / 4
Decimal = 0.25
Percent = 25%
Ratio = 1 : 4 (note that the ratio in that case is in a part-to-whole relationship, and not in a part-to-part relationship as usual)

Question 2

For each way of expressing a part-to-whole relationship, what is the whole that you are dividing by?

Answer 2

Fraction = out of the denominator = 1 / 4 = 1 out of 4)
Decimals = out of 1 (the whole) = 0.25 = 0.25 of the whole
Percent = out of 100 = 25% = 25 out of 100 pieces of the whole
Ratios = out of the second term in the ratio = 1 : 4 = 1 out of 4 pieces of the whole

Question 3

How to convert from a decimal to percent?

Answer 3

Move the decimal point to the right two places (add zeros if necessary).
0.25 = 25%
0.4 = 0.40 = 40%
0.03 = 3%
1.7 = 1.70 = 170%

Question 4

How to convert from a percent to a decimal?

Answer 4

Move the decimal point two places to the left. If the decimal point isn’t visible, it’s actually just before the percent sign.
39% = 0.39
8% = 0.08

Question 5

How to convert from decimal or percent to fraction?

Answer 5

You just need to put the number over whole and simplify the new formed fraction.
0.25 = 0.25 / 1 = 0.5 / 2 = 1 / 4
45% = 45 / 100 = 9 / 20

Question 6

How to convert from a fraction to decimal or percent?

Answer 6

A fraction represents division. The decimal equivalent is the result of that division.
You can either:
a) memorize the relation between fractions and its respective decimal or percent (1 / 4 = 0.25 = 25%)
b) you can do the long division to find the number
c) if the denominator has only 2 and 5 as factors, you can multiply the denominator and the numerator by the same number to turn the denominator into a power of 10
1 / 4 = 1 x 25 / 4 x 25 = 25 / 100 = 0.25
If the denominator contains other factors than 2 or 5, you’ll need to use a long division

To convert to a percent, first convert to a decimal and then convert to a percent

Question 7

How to multiply and divide a decimal by a power of 10?

Answer 7

Multiplication: If the power of 10 is positive, move the decimal point right a number of places corresponding to the exponent of 10
Division: If the power of 10 is positive, move the decimal point left a number of places corresponding to the exponent of 10

If the power of 10 is negative, you only need to apply the inverse (go left if multiplying and right if dividing)

Question 8

How to add or subtract two decimals?

Answer 8

Line up the points (add zeros to the right to help you to line up)

0.3 + 0.65 =
0.30
+ 0.65
= 0.95

Question 9

How to multiply two decimals?

Answer 9

Ignore the point first and do the normal multiplication as if they were integers. Then count the number of digits to the right of the decimal points, so move the decimal point of the answer up to the number of digits found.
0.25 x 0.5 =
25 x 5 = 125
[we have three digits after the decimal]
= 0.125

Question 10

How to multiply a decimal and a big number?

Answer 10

Trade decimal places from the big number to the small one
50,000 x 0.007 =
50 x 7 = 350

Question 11

How to divide two decimals?

Answer 11

Move the decimal points in the same direction to eliminate decimals as far as you can
3.39 / 0.003 =
3390 / 3 =
1130

Question 12

What the word “of” means in math?

Answer 12

The word “of” means “times” in math terms. In other word, “of” indicates multiplication
30% of $60 = 30% x 60 = 0.30 x 60 = 3 x 6 = 18

Question 13

How to calculate percentage of a real value?

Answer 13

a) convert the percentage into a decimal or fraction and then multiply to the real value, or
b) use benchmarks: e.g., to find 30%, find 10% and multiply by 3 to reach 30%

Question 14

How to find a percentage from the real values?

Answer 14

Use a variable to represent the searched percentage.
What percent of 125 is 25?
Y / 100 * 125 = 25
Y / 4 * 5 = 25
Y / 4 = 25 / 5
Y = 5 * 4
Y = 20

Question 15

What to do when faced with percent change problems?

Answer 15

Calculate: original + change = new
The original value will be always 100%.
The change will be a percentage in comparison to the original.
The new will be the sum of both

E.g., you have $200 in a bank account. You deposit an additional $30 in that account. By what percent did the value of the bank account increase?
100 + 30 = 230

30 = 15% of 100
So, 100% + 15% = 115%
The value of the bank account increased by 15%

Short cut:
Change / original = 30 / 200 = 15%

Question 16

What does it mean the wording “percent more than” and “percent less than”?

Answer 16

It has the same meaning as percent increase and percent decrease, respectively

30 is what percent more than 20? = is 50% more than 20

Please note that this is different from “percent of”. E.g., 30 is what percent of 20? = is 150% of 20

Question 17

How to turn ratios in percentage?

Answer 17

You will need to compare the terms of the ratio with the whole.
E.g., 5 white roses to 3 red roses. What percent of all the roses are red?
W = 5
R = 3
Total = 8
Red = 3 / 8 = 37.5%

Question 18

If the ratio of a to b is 4 t 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?

Answer 18

When you are given two ratios, their product or quotient will always produce a third ratio.
a / c = (a / b) * (b / c) = (4 / 3) * (1 / 5) = 4 / 15

Alternatively, it is possible to pick numbers.
If a = 4 and b = 3, c needs to be equal to 15 (to attend the ratio of 1:5). Therefore, the ratio between a and c is 4:15.