INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### Multiplication and Division Techniques

• For more complex equations, isolate the variable and solve the equation by using the multiplication property of equality. If you multiply each side of an equation by the same quantity, the resulting equation has the same solutions as the original one.
• You can also isolate the variable and solve the equation by using the division property of equality. If you divide each side of an equation by the same nonzero quantity, the resulting equation has the same solutions as the original one.
• Use these properties to convert an equation in which the variable has a coefficient different from 1 into an equation in which the coefficient is 1.

### Multiplication and Division Techniques

[y/12] = 3
• 12 ×( [y/12] ) = 3 ×12
y = 36
[g/9] = 17
• 9 ×( [g/9] ) = 17 ×9
g = 153
22i = 132
• [22i/22] = [132/22]
• i = [132/22]
i = 6
( 3[1/3] )s = [2/4]
• [10/3]s = [2/4]
• ( [3/10] ) ×[10/3]s = [2/4] ×( [3/10] )
• s = [6/40] = [3/20]
s =[(3)/(20)]
( 4[2/7] )l = [3/5]
• [30/7]l = [3/5]
• ( [7/30] ) ×[30/7]l = [3/5] ×( [7/30] )
• l = [21/150] = [7/50]
l =[(7)/(50)]
− 12j = 480
• [( − 12j)/( − 12)] = [480/12]
j = 40
Four and one fifths times a number is equal to two and three eighths. What is the number?
• 4[1/5]x = 2[3/8]
• [21/5]x = [19/8]
• ( [5/21] ) ×[21/5]x = [19/8]v ×( [5/21] )
x =[(95)/(168)]
Three tenths of a number is equal to three and seven eighths. What is that number?
• [3/10]d = 3[7/8]
• [3/10]d = [31/8]
• ( [10/3] ) ×[3/10]d = [31/8] ×( [10/3] )
• d = [310/24] = [155/12]
d =[(155)/(12)]
Fifty - two divided by a number is four.
• [52/h] = 4
• h ×[52/h] = 4 ×h
• 52 = 4h
13 = h
( 12[4/9] )w = [11/13]
• [112/9]w = [11/13]
• ( [9/112] ) ×[112/9]w = [11/13] ×( [9/112] )
w =[(99)/(1456)]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Multiplication and Division Techniques

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Isolating the Variable
• Techniques 0:34
• Multiplication Principle
• Example
• Division Principle
• Example
• Strategy 3:12
• Example
• Opposite Operation
• Example 1: Solve Equation 5:07
• Example 2: Solve Equation 6:50
• Example 3: Solve Equation 10:05
• Example 4: Word Problem 12:07