Name: _________________________________
Date: ___________________
Day 3.30: Solving Equations with Cross Products
Entrance Task: Solve the following equation for p:
3
10
𝑝
=
16
Notes:
If you ever need to solve an equation that has two fractions equal to each other, you
can use Cross Products to help you.
If you ever have two equivalent fractions, the Cross Products are always equal.
𝑎
If
𝑐
= , then 𝑎𝑑 = 𝑐𝑏.
𝑏
𝑑
(This is sometimes called Cross Multiplication)
Example:
2
4
=
6
, so
12
Using cross products to solve equations:
3
10
=
𝑝
16
Notice you do not need a common denominator when using this method!
Use Cross Products to solve for the following variables:
1.
2.
3.
4.
5.
6.
15
33
27
20
𝑦
18
𝑐
28
3𝑘
4
19
𝑟
=
𝑚
22
=
36
=
21
=
49
=
=
𝑣
63
16
9
6
152
4
Name: _________________________________
Date: ___________________
Homework: Day 3.30 – Review for Quiz
Directions: Multiple Choice – Circle the best answer for each problem.
1. Which expression is equivalent to 7𝑥 + 4 − 𝑥 − 1?
A 6𝑥 + 3
B 8𝑥 + 3
C 6𝑥 + 5
D 8𝑥 + 5
2. Which expression represents the sum of (2𝑎 + 𝑏) and (𝑎 − 9𝑏)?
A 3𝑎 − 10𝑏
B 3𝑎 − 8𝑏
C 𝑎 − 10𝑏
D 𝑎 − 8𝑏
3. The expression below was simplified using two properties of operations.
3(4𝑘 + 7 + 2𝑘)
Step 1 3(4𝑘 + 2𝑘 + 7)
Step 2 3(6𝑘 + 7)
Step 3 18𝑘 + 21
Which properties were applied in Steps 1 and 3, respectively?
A commutative property, then identity property
B commutative property, then distributive property
C commutative property, then commutative property
D associative property, then distributive property
4. Which expression is equivalent to 3.5𝑔 + 4.5 − 1.2 + 5.6𝑔?
A 9.1𝑔 + 5.7
B 3.5𝑔 + 8.9
C 9.1𝑔 + 3.3
D 2.1𝑔 + 5.7
2
5. After using the distributive property, the expression (15𝑥 − 9𝑦) + 6𝑥 would
3
be equivalent to:
2
A (21𝑥 − 9𝑦)
3
B 10𝑥 − 6𝑦 + 6𝑥
C 10𝑥 − 9𝑦 + 6𝑥
D 3(5𝑥 − 3𝑦) + 6𝑥
For each polynomial, determine the number of terms and identify what type of
polynomial it is.
6. 𝑥 2 + 6𝑥 + 8 has _____ terms and is called a __________________.
7. 7𝑥 2 has _____ terms and is called a __________________.
8. 2𝑥 2 − 𝑦 3 has _____ terms and is called a __________________.
9. 𝑎𝑏 − 6𝑎3 𝑏 + 4𝑎𝑏 2 − 7 has _____ terms and is called a _________________.
10.
−9𝑥𝑦 3 𝑧 has _____ terms and is called a __________________.
Simplify completely each algebraic expression by using the distributive property
and/or combining like terms.
11.
12.
13.
14.
15.
16.
17.
12𝑥 + 2𝑥
𝑎 + 2𝑎 + 5𝑎
9𝑥 + 6𝑦 + 2𝑥 + 10𝑥
7(2𝑎 + 9)
(𝑛 − 5)4
8(2𝑛 − 6) + 7
1
(6𝑥 + 15) − 𝑥
3
________________
________________
________________
________________
________________
________________
________________
Subtract the following polynomials:
18.
(14 + 9𝑛) − (3𝑛 − 5)
________________
Solve the following equations algebraically, showing all steps:
19.
3(7𝑐 − 4) − 6𝑐 = 63
20.
21.
2𝑥
3
10
𝑧
+
10
=
15
9
12
=−
32
9