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Multiplying and Dividing Mixed Numbers
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done, but four multiplications are required.
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done but four multiplications are required.
 This can be illustrated with an area model.
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done but four multiplications are required.
 This can be illustrated with an area model.
2
1
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done but four multiplications are required.
 This can be illustrated with an area model.
2
1 2
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done but four multiplications are required.
 This can be illustrated with an area model.
2
1 2
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done but four multiplications are required.
 This can be illustrated with an area model.
2
1 2
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done but four multiplications are required.
 This can be illustrated with an area model.
2
1 2
5
4
1
3
2
2 ×
Operations with Mixed Numbers
 Ex) Multiply in mixed number form.
 This can be done but four multiplications are required.
 This can be illustrated with an area model.
 It works, but usually converting to improper fractions is easier.
Operations with Mixed Numbers
 Ex 5) Multiply.
5
4
4
5
24
5
3
1
8
5
9
3
8
5
4
1
3
2
2
=
=
×=
×=
×
Operations with Mixed Numbers
 Ex 5) Multiply.
5
4
4
5
24
5
3
1
8
5
9
3
8
5
4
1
3
2
2
=
=
×=
×=
×
Reduce on the diagonal .
Divide by the common factor.
Operations with Mixed Numbers
 Ex 5) Multiply.
5
4
4
5
24
5
3
1
8
5
9
3
8
5
4
1
3
2
2
=
=
×=
×=
×
Reduce on the diagonal .
Divide by the common factor.
Operations with Mixed Numbers
 Ex 5) Multiply.
5
4
4
5
24
5
3
1
8
5
9
3
8
5
4
1
3
2
2
=
=
×=
×=
×
Reduce on the diagonal .
Divide by the common factor.
Operations with Mixed Numbers
 Ex 5) Multiply.
5
4
4
5
24
5
3
1
8
5
9
3
8
5
4
1
3
2
2
=
=
×=
×=
×
Reduce on the diagonal .
Divide by the common factor.
Operations with Mixed Numbers
 Ex 6) Divide.
5
4
1
1
5
4
4
1
5
16
1
4
5
16
4
5
1
3
=
×=
×=
÷=
÷
Operations with Mixed Numbers
 Ex 6) Divide.
5
4
1
1
5
4
4
1
5
16
1
4
5
16
4
5
1
3
=
×=
×=
÷=
÷
Operations with Mixed Numbers
 Ex 6) Divide.
Invert and Multiply
5
4
1
1
5
4
4
1
5
16
1
4
5
16
4
5
1
3
=
×=
×=
÷=
÷
Operations with Mixed Numbers
 Ex 6) Divide.
Invert and Multiply
5
4
1
1
5
4
4
1
5
16
1
4
5
16
4
5
1
3
=
×=
×=
÷=
÷
Reduce on the diagonal .
Divide by the common factor.
Operations with Mixed Numbers
 Ex 6) Divide.
Invert and Multiply
5
4
1
1
5
4
4
1
5
16
1
4
5
16
4
5
1
3
=
×=
×=
÷=
÷
Reduce on the diagonal .
Divide by the common factor.
Operations with Mixed Numbers
 Ex 7) Evaluate. 3
2
1
2 





Operations with Mixed Numbers
 Ex 7) Evaluate.
3
3
2
5
2
1
2






=






Operations with Mixed Numbers
 Ex 7) Evaluate.
2
5
2
5
2
5
2
5
2
1
2
3
3
××=






=






Operations with Mixed Numbers
 Ex 7) Evaluate.
8
125
2
5
2
5
2
5
2
5
2
1
2
3
3
=
××=






=






Operations with Mixed Numbers
 Ex 7) Evaluate.
8
5
15
8
125
2
5
2
5
2
5
2
5
2
1
2
3
3
=
=
××=






=






Operations with Mixed Numbers
 Ex 7) Evaluate.
8
5
15
8
125
2
5
2
5
2
5
2
5
2
1
2
3
3
=
=
××=






=






Notice how =
3
2
5






3
3
2
5
Operations with Mixed Numbers
Got it?

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2.2 multply and divide mixed numbers 3

  • 1. Multiplying and Dividing Mixed Numbers
  • 2. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.
  • 3. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done, but four multiplications are required.
  • 4. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done but four multiplications are required.  This can be illustrated with an area model.
  • 5. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done but four multiplications are required.  This can be illustrated with an area model. 2 1
  • 6. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done but four multiplications are required.  This can be illustrated with an area model. 2 1 2
  • 7. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done but four multiplications are required.  This can be illustrated with an area model. 2 1 2
  • 8. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done but four multiplications are required.  This can be illustrated with an area model. 2 1 2
  • 9. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done but four multiplications are required.  This can be illustrated with an area model. 2 1 2
  • 10. 5 4 1 3 2 2 × Operations with Mixed Numbers  Ex) Multiply in mixed number form.  This can be done but four multiplications are required.  This can be illustrated with an area model.  It works, but usually converting to improper fractions is easier.
  • 11. Operations with Mixed Numbers  Ex 5) Multiply. 5 4 4 5 24 5 3 1 8 5 9 3 8 5 4 1 3 2 2 = = ×= ×= ×
  • 12. Operations with Mixed Numbers  Ex 5) Multiply. 5 4 4 5 24 5 3 1 8 5 9 3 8 5 4 1 3 2 2 = = ×= ×= × Reduce on the diagonal . Divide by the common factor.
  • 13. Operations with Mixed Numbers  Ex 5) Multiply. 5 4 4 5 24 5 3 1 8 5 9 3 8 5 4 1 3 2 2 = = ×= ×= × Reduce on the diagonal . Divide by the common factor.
  • 14. Operations with Mixed Numbers  Ex 5) Multiply. 5 4 4 5 24 5 3 1 8 5 9 3 8 5 4 1 3 2 2 = = ×= ×= × Reduce on the diagonal . Divide by the common factor.
  • 15. Operations with Mixed Numbers  Ex 5) Multiply. 5 4 4 5 24 5 3 1 8 5 9 3 8 5 4 1 3 2 2 = = ×= ×= × Reduce on the diagonal . Divide by the common factor.
  • 16. Operations with Mixed Numbers  Ex 6) Divide. 5 4 1 1 5 4 4 1 5 16 1 4 5 16 4 5 1 3 = ×= ×= ÷= ÷
  • 17. Operations with Mixed Numbers  Ex 6) Divide. 5 4 1 1 5 4 4 1 5 16 1 4 5 16 4 5 1 3 = ×= ×= ÷= ÷
  • 18. Operations with Mixed Numbers  Ex 6) Divide. Invert and Multiply 5 4 1 1 5 4 4 1 5 16 1 4 5 16 4 5 1 3 = ×= ×= ÷= ÷
  • 19. Operations with Mixed Numbers  Ex 6) Divide. Invert and Multiply 5 4 1 1 5 4 4 1 5 16 1 4 5 16 4 5 1 3 = ×= ×= ÷= ÷ Reduce on the diagonal . Divide by the common factor.
  • 20. Operations with Mixed Numbers  Ex 6) Divide. Invert and Multiply 5 4 1 1 5 4 4 1 5 16 1 4 5 16 4 5 1 3 = ×= ×= ÷= ÷ Reduce on the diagonal . Divide by the common factor.
  • 21. Operations with Mixed Numbers  Ex 7) Evaluate. 3 2 1 2      
  • 22. Operations with Mixed Numbers  Ex 7) Evaluate. 3 3 2 5 2 1 2       =      
  • 23. Operations with Mixed Numbers  Ex 7) Evaluate. 2 5 2 5 2 5 2 5 2 1 2 3 3 ××=       =      
  • 24. Operations with Mixed Numbers  Ex 7) Evaluate. 8 125 2 5 2 5 2 5 2 5 2 1 2 3 3 = ××=       =      
  • 25. Operations with Mixed Numbers  Ex 7) Evaluate. 8 5 15 8 125 2 5 2 5 2 5 2 5 2 1 2 3 3 = = ××=       =      
  • 26. Operations with Mixed Numbers  Ex 7) Evaluate. 8 5 15 8 125 2 5 2 5 2 5 2 5 2 1 2 3 3 = = ××=       =       Notice how = 3 2 5       3 3 2 5
  • 27. Operations with Mixed Numbers Got it?