This document contains a pre-algebra review created by Anna Wells for students at Mendez Fundamental Intermediate School. It includes over 60 mental math problems covering topics like properties of operations, solving equations, finding slopes of lines, calculating areas and perimeters of shapes, and more. The problems are followed by their answers to allow students to self-check their work.
2. Created By: Anna Wells
Anna.wells@sausd.us
Mendez Fundamental Intermediate School
Santa Ana Unified School District
Santa Ana, California
Licensed under Creative Commons
1/30/2015 2
127. How do you get the slope?
What is the slope of the given line?
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128. How do you get the slope? Look at the
points. Write a fraction that shows:
The change in Y over the change in X.
What is the slope
of the given line?
3 over 4, 3/4
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129. How do you get the slope?
What is the slope of the given line?
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130. 1/30/2015
How do you get the slope? Look at the
points. Write a fraction that shows:
The change in Y over the change in X.
What is the slope of
the given line?
1 over 2, 1/2
130
131. How do you get the slope?
What is the slope of the given line?
Does it matter
which points
you use?
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132. 1/30/2015
How do you get the slope? Look at the
points. Write a fraction that shows:
The change in Y over the change in X.
What is the slope of
the given line?
*DOWN* 3 over 3, 3/3 = -1
Does it matter which points
you use? NO, you get the same slope (after
you simplify the fraction) no matter which
points you use!
132
133. How do you find the slope of
the line that passes through
any two points?
For example, how do you find
the slope of a line that passes
through (3,5) and (-1,-2)?
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134. 1/30/2015
You plot the two points on a graph, and
write a fraction that shows:
The change in Y over the change in X
134
135. How do you find the slope of
the line that passes through
any two points?
For example, how do you find
the slope of a line that passes
through (-3, 16) and (-4,-2)?
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136. 1/30/2015
You plot the two points on a graph, and
write a fraction that shows:
The change in Y over the change in X
136
137. A square has an area of 49
feet2. How long is each side?
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153. What is the slope?
0
y = 5
y = 0x + 5
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154. How do you find the length of x?
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155. How do you find the length of x?
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a2 + b2 = c2
156. How do you find the length of x?
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157. How do you find the length of x?
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c2 - a2 = b2
158. 1. A right triangle has legs that are 6 cm and
8 cm long. How do you find the length of
the hypotenuse?
2. In the problem above, if you found
the length of the hypotenuse but it
was way too big (it doesn’t make
sense) you probably forgot to do the
last calculation. What is the last
calculation in an a2 + b2 = c2 problem?
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159. 1. A right triangle has legs that are 6 cm and 8 cm
long. How do you find the length of the
hypotenuse?
2. In the problem above, if you found the length of
the hypotenuse but it was way too big (it doesn’t
make sense) you probably forgot to do the last
calculation. What is the last calculation in an a2 +
b2 = c2 problem?
Take the square root of
both sides!
1/30/2015 159
a2 + b2 = c2
2
225 c
c15
160. 6 m
5 m
How do you
find the length
of x?
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161. 6 m
5 m
How do you
find the length
of x?
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3
c2 - a2 = b2
52 - 32 = b2
Notice 3 not 6
183. What is wrong with this
sentence: Slope is the
ratio (fraction) of the
change in x to the change
in y.
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184. 1/30/2015
What is wrong with this sentence: Slope is
the ratio (fraction) of the change in x to the
change in y.
It is backwards, slope is the ratio
of the change in Y to X,
not X to Y.
21
21
xx
yy
Notice
y’s in the numerator,
x’s in the denominator!
184
185. How do you calculate the
SLOPE of the hypotenuse?
How do you
calculate the LENGTH
of the hypotenuse?
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186. How do you calculate the SLOPE of
the hypotenuse?
You write a FRACTION that shows:
the CHANGE IN Y over the
CHANGE IN X.
How do you
calculate the LENGTH
of the hypotenuse?
Use a2 + b2 = c2 (because
it is a right triangle).
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187. How do you calculate the
SLOPE of the hypotenuse?
How do you
calculate the LENGTH
of the hypotenuse?
1/30/2015 187
188. 1/30/2015 188
How do you calculate the SLOPE of
the hypotenuse?
You write a FRACTION that shows:
the CHANGE IN Y over the
CHANGE IN X.
How do you
calculate the LENGTH
of the hypotenuse?
Use a2 + b2 = c2 (because
it is a right triangle).
189. What is the unit rate shown in this chart?
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190. What is the unit rate shown in this chart?
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15
Find the rate for
ONE (1) hour!
= 15 miles per hour
30
2 Or find the slope,
change in Y over
change in X (30/2) and
simplify it (15/1),
= 15 miles per hour
190
191. What is the slope shown in this chart?
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192. What is the unit rate shown in this chart?
1/30/2015
15
Find the rate for
ONE (1) hour!
Slope = 15/1 = 15
30
2 Or find the slope,
change in Y over
change in X (30/2) and
simplify it (15/1),
Slope = 15
192
195. What step(s) would you take to solve
this problem?
If Mary types 240 words in 6
minutes, how long will it take
her to type 440 words?
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196. What step(s) would you take to solve
this problem?
If Mary types 240 words in 6 minutes, how
long will it take her to type 440 words?
Set up a proportion,
then cross multiply (butterfly)
240 words 440 words
---------- = -------------
6 minutes x minutes
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197. Convert 6/7 into a
decimal or percent.
What is the first step?
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198. Convert 6/7 into a
decimal or percent.
Long Division!!!
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199. Convert 152/7 into a
decimal or percent.
What is the first step?
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200. Convert 152/7 into a
decimal or percent.
What is the first step?
Long division, 2 divided
by 7.
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201. Convert 43/8 into a
decimal or percent.
What is the first step?
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202. Convert 43/8 into a
decimal or percent.
What is the first step?
Long division, 3 divided
by 8.
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203. Convert 62/9 into a
decimal or percent.
What is the first step?
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204. Convert 62/9 into a
decimal or percent.
What is the first step?
Long Division, 2 divided
by 9.
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210. 1/30/2015
0.375 Three hundred seventy-
Five thousandths.
Convert 0.375 into a fraction.
What are the two steps?
Write 375 over 1000 (375/1000),
then simplify.
210
212. 1/30/2015
Convert 3.4 into a mixed
number.
What are the two steps?
212
Write 4 over 10 (4/10),
then simplify (2/5), then write the
3 alongside the fraction:
5
2
3
214. 1/30/2015
How do you solve this
problem?
“What is 7/8 of 3/4?”
Multiply them together!
When used with fractions
or percents, “of” means
multiply!
214
215. 1/30/2015
How do you solve
this problem?
“What is two-thirds
of five eighths?”
215
216. 1/30/2015
How do you solve this
problem?
“What is two-thirds of
five eighths?” Multiply
them together! When
used with fractions or
percents, “of” means
multiply!
216
217. 1/30/2015
How do you solve
this problem?
“What is six-fifths of
nine-tenths?”
217
218. 1/30/2015
How do you solve this
problem?
“What is six-fifths of
nine-tenths?” Multiply
them together! When
used with fractions or
percents, “of” means
multiply!
218
235. 1/30/2015
It took the contractor 33
person-hours to paint the
house. There were 3 workers
on the job. How long did the
job take? Include units with
your answer.
235