This document provides information about fractions, decimals, and percentages including: - Examples of how fractions, decimals, and percentages relate and can be converted between each other. - Steps for converting a fraction to a decimal by dividing the numerator by the denominator. - How to convert a decimal to a percentage by moving the decimal point two places to the right and adding the percent sign. - How to convert a percentage to a decimal by moving the decimal point two places to the left and dividing by 100. - Examples of percentage word problems and how to set them up proportionally to solve. - Additional tips for working with fractions, decimals, and percentages like when a percentage can be greater than 100%.

1. Parts of the whole

9. All represent part of a whole

10. Reference Numbers
Fraction Decimal Percent
51/100 0.51 51%
¼ 0.25 25%

11. A fraction is based on
the number into
which the whole is
divided (the
denominator).
The numerator (the
top) is the PART, the
denominator (the
bottom) is the whole.
½; ¼; ⅝…
A decimal is based on the
number in terms of
tenth, hundredths,
thousandths, etc…
0.5; 0.05; 0.005

12. Divide the denominator
(the bottom of the
fraction) into the
numerator (the top of
the fraction). Place a
decimal after the
number inside the
division “box” and
attach as many zeros as
necessary to complete
the division. If the
quotient does not come
out evenly, follow the
rules for “rounding off”
numbers.
numerator
denominator

13. .50 = 50%
(0.50 x 100 = 50.0)
Attach the % sign
Move the decimal point
two (2) places to the
right (this multiplies
the number by 100)

14. 50% = .50
50 ÷ 100 = .50
Move the decimal point
two (2) places to the
left (this divides the
number by 100)

15. Place the number over
100 and reduce.

16. Multiply the number by
100, reduce and attach
a percent (%) sign.

17. You will be using place value to do this! Count the
decimal places of the decimal starting from the
decimal point. If there is one decimal point, place
the number over 10 and reduce. If there are two
decimal places, place the number over 100, and
reduce. If there are three decimal places, place the
number over 1000, and reduce…Etc.
(This is really just using your knowledge of place value to name
the denominator.)
1 decimal place = tenths,
2 decimal places = hundredths,
3 decimal places = thousandths

20. When solving a problem with a percent
greater than 100%, the part will be greater
than the whole.

21. 1) what is 60% of 30?
2) what number is 25% of 160?
3) 45 is what percent of 90?

22. Sloths may seen lazy, but
their extremely slow
movement helps make them
almost invisible to predators.
Sloths sleep an average of
16.5 hours per day. What
percent of the day do they
sleep?
Solution

23. Proportional method
Part Part
Whole Whole
24
5.16
100
n

24. 1) 27 is what percent of 30?
2) 45 is 20% of what number?
3) What percent of 80 is 10?
4) 12 is what percent of 19?
5) 18 is 15% of what number?
6) 27 is what percent of 30?
7) 20% of 40 is what number?
8) 4 is what percent of 5?