Download Mastery Quiz Fraction-Decimal-Percent Objectives – with the Ways

Mastery Quiz Fraction-Decimal-Percent Objectives – with the Ways to Do Each
Combining Basic Arithmetic, Number Sense, and Mental Math
The student should be able to (by hand, without using a calculator):
1. Put a fraction into lowest terms.
2. Put a fraction into higher terms.
3. Rewrite an improper fraction as a mixed number.
4. Rewrite a mixed number as an improper fraction.
5. Add and subtract fractions (and mixed numbers).
a. For mixed numbers you can leave them as mixed numbers (and perhaps regroup).
b. For mixed numbers you may switch to improper fractions, then add or subtract, then switch
back to mixed.
6. Add and subtract decimals
7. Read a decimal number properly. (2.03 is “two and three hundredths”)
8. Convert fractions (and mixed numbers) to decimals and to percents.
a. For fraction to percent, one method is to divide to get the decimal and then move the decimal
point two places to get the percent. Note: When doing the long division there are two options
(assuming it does not come out even):
i. Stop after two decimal places and bring up the remainder over the divisor. For
3
6
6
example, 7 = .42 7 = 42 7 %.
ii. Keep dividing and either round off or write it as a repeating decimal. For example,
3
̅̅̅̅̅̅̅̅̅̅%.
= .4285714285… ≈ 42.86% or = 42.857142
7
b. For fraction to percent, the other way to get the percent is to use a proportion. Set the fraction
𝑝
equal to 100, and then solve the proportion to find p.
9. Convert decimals to fractions (or mixed numbers) and to percents.
10. Convert percents to decimals and to fractions (or mixed numbers).
11. Multiply fractions (and mixed numbers).
a. To multiply mixed numbers the “preferred” method is to switch to improper fractions,
multiply, and then switch back to mixed.
b. To multiply mixed numbers you can also use “FOIL.” For example,
1 1
1
1 1 1
2 ∙4 = 2∙4+2∙ +4∙ + ∙
3 2
2
3 3 2
4 1
= 8+1+ +
3 6
1
= 10
2
12. Multiply decimals.
13. Divide fractions (and mixed numbers).
14. Divide decimals.
15. Solve percent problems of the form ___% of ___ is ___, where two of the three blanks are known and
one of the blanks is unknown.
a. Change to an equation: known numbers go in as numbers; change the percent to a decimal;
“of” becomes multiplication; “is” becomes “=”; the “what” (the unknown, the blank) becomes
x. Then solve using basic algebra.
b. Another way is to use a proportion. Use “percent”% of “whole” is “part.” Set up the
percent
part
proportion as 100 = whole. Then solve the proportion for the unknown. Students are
sometimes taught
percent
100
"is"
= "of".
part
c. A third way is a bit of a hybrid. Use percent = whole. In the “percent” position, put the
percent as a decimal. Then solve the equation for the unknown.
16. In a percent change situation, find the percent change, the amount of change, or the original amount.
amount of change
a. Use percent change = original amount . Plug in the known’s and unknown (use x). Then use
algebra to solve. Very efficient if finding percent change. Somewhat difficult if finding
original amount (because the variable is in the denominator).
b. change% of original amount is amount of change. These problem can be done like the ___%
of ___ is ___. That is, using algebra (with x in for the blank) or with a proportion. Has the
advantage of using (leveraging) known ___% of ___ is ___ strategies. An additional
advantage is that the formula does not involve a fraction. Therefore, if algebra is used, steps
are a little easier.
i. Use the algebra method (above).
percent
"is"
ii. Use proportion method (above) 100 = "of".
c. Think about the resulting percent. That is, the percent you get after the percent change. If a
percent decrease, your resulting percent will be less than 100%. For example, a 20% discount
results in 80%. If a percent increase, your resulting percent will be more than 100%. For
example, a 35% increase results in 135%.
Then use resulting% of original amount is new amount. Then, as above, use any of the ___%
of ___ is ___ strategies.