1. by Monica Yuskaitis, M.A.Ed.
6th Grade
Algebra 4
Solving Equations with
Multiplication & Division
5 · b = 25
by Monica Yuskaitis, M.A.Ed.
Copyright © 2013 by Monica Yuskaitis

2. Copyright © 2013 by Monica Yuskaitis
Essential Question
How can I solve equations using multiplication and division? 2
Copyright © 2013 by Monica Yuskaitis

3. Vocabulary 3

4. Copyright © 2013 by Monica Yuskaitis
Vocabulary
product – the answer to a multiplication problem.
factor – a number that is multiplied in a multiplication problem.
2 x 6 = 12
factor
factor
product
Copyright © 2013 by Monica Yuskaitis

5. Copyright © 2013 by Monica Yuskaitis
Vocabulary
divisor – a number that divides into another.
dividend – a number that the divisor is divided into.
quotient – the answer to a division problem. 3
quotient
2 ) 6
divisor
dividend
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6. Other Forms of Division
dividend
dividend
quotient 6
6 ÷ 2 = 3 3 =
quotient 2
divisor
divisor 3
quotient
divisor
2 ) 6
dividend
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7. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Equation – A mathematical sentence stating that 2 expressions are equal.
8 x 3 = 24
30 ÷ 3 = 10
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8. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Equation – A mathematical sentence with an equals sign.
16 ÷ 2 = 8
56 = 7 x 8
Copyright © 2013 by Monica Yuskaitis

9. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Equals Sign (=) means that the amount is the same on both sides.
4 x 2 = 8
25 ÷ 5 = 5
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10. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Inverse operation – An operation that undoes the results of another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.
5 + 2 = 7 inverse 7 – 5 = 2
4 x 3 = 12 inverse 12 ÷ 3 = 4
Copyright © 2013 by Monica Yuskaitis

11. Understanding
Equations 11

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An Equation is like a balance scale. Everything must be equal on both sides. =
3 x 4 12
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13. When an amount is unknown on one side of the equation you can find it out by using the inverse operation. =
n x 6 24

14. The inverse operation of multiplication is division
The inverse operation of multiplication is division. Divide both sides by 6 to find n. =
n x 6 24 6 6

15. 6 will go into 24 four times. 6 will go into 6 one time.=
n x 6 24 =4 =1 6 6

16. 1 times n equals n =
n x 1 4

17. Now we know n is equal to 4. Let’s substitute 4 in for n in the equation.= n 4

18. Does 4 times 6 equal 24? Yes! We solved the equation.=
nx6 24 4

19. Solving Multiplication
Equations 19

20. How to solve a multiplication equation
Use the inverse operation for multiplication which is division.
Divide each side by the number that is being multiplied by the variable.
m x 5 = 40 m x 5 ÷ 5 = 40 ÷ 5
m = x 5 = 40
Copyright © 2013 by Monica Yuskaitis

21. Now it’s your turn to solve the problems.
Copyright © 2013 by Monica Yuskaitis

22. Solve these equations using the inverse operations
4 x n = 36
n • 5 = 40
n x 6 = 36
4 x n ÷ 4 = 36 ÷ 4
n = 9
n • 5 ÷ 5 = 40 ÷ 5
n = 8
n x 6 ÷ 6 = 36 ÷ 6
n = 6
Copyright © 2013 by Monica Yuskaitis

23. Solve these equations using the inverse operations
8 • c = 48
s x 3 = 33
7f = 84
8 • c ÷ 8 = 48 ÷ 8
c = 8
s x 3 ÷ 3 = 33 ÷ 3
s = 11
7f ÷ 7 = 84 ÷ 7
f = 12
Copyright © 2013 by Monica Yuskaitis

24. Solving Division
Equations 24

25. How to solve a division equation
Use the inverse operation for division which is multiplication.
Multiply each side by the number that is dividing into the variable.
m ÷ 3 = 5 m ÷ 3 x 3 = 5 ÷ 3
m = ÷ 3 = 5
Copyright © 2013 by Monica Yuskaitis

26. Solve these equations using the inverse operations
n ÷ 9 x 9 = 6 x 9
n ÷ 9 = 6
n ÷ 3 = 8
n ÷ 8 = 3
n = 54
n ÷ 3 • 3 = 8 • 3
n = 24
n ÷ 8 x 8 = 3 x 8
n = 24
Copyright © 2013 by Monica Yuskaitis

27. Solve these equations using the inverse operations
d ÷ 5 x 5 = 5 x 5
d ÷ 5 = 5
r ÷ 6 = 7
y ÷ 7 = 4
d = 25
r ÷ 6 x 6 = 7 x 6
r = 42
y ÷ 7 • 7 = 4 • 7
y = 28
Copyright © 2013 by Monica Yuskaitis

28. Solve these equations using the inverse operations
w x 21 = 5 x 21 21
w = 5
k = 3
v = 4 21
w = 105
k • 30 = 3 • 30 30 30
k = 90
v x 24 = 4 x 24 24 24
v = 96
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29. Problem
Solving 29

30. The Science Museum Fieldtrip

31. Analysis Representation Resolution Problem Solving Steps
What information do you need?
What is the problem asking you to find out?
Is the answer going to be larger or smaller?
Analysis
Representation
What strategies will you use?
What operations will you use?
How many steps are there and in what order must you do them?
Resolution
How will you solve the problem?
Did you check your answer?
Does your answer make sense?

32. The sixth grades went to the Academy of Science Museum in San Francisco. There were 3 buses and each bus held 42 passengers. How many went on the field trip? n 3 = 42
3 ·
· 3
n = 126

33. This is for you for working so hard!
Copyright © 2013 by Monica Yuskaitis