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4.1 – Fractions and Mixed Numbers. Fractions. Defn : Numbers that show the number of parts existing compared to the number of parts in a whole. Numerator (a): the top number of a fraction that describes the number of parts existing. - PowerPoint PPT Presentation
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4.1 – Fractions and Mixed NumbersFractions
Defn: Numbers that show the number of parts existing compared to the number of parts in a whole.
Numerator (a): the top number of a fraction that describes the number of parts existing.
Denominator (b): the bottom number of the fraction that describes the number of parts that make a whole.
ba
4.1 – Fractions and Mixed NumbersWrite a fraction to represent the shaded portion of each figure.
52
85
127
4.1 – Fractions and Mixed NumbersWrite a fraction to represent the shaded portion of each figure.
107
53
65
4.1 – Fractions and Mixed NumbersDraw and shade each fraction.
73
4.1 – Fractions and Mixed NumbersProper Fractions
Defn: A fraction whose numerator is smaller than its denominator.
Defn: A fraction whose numerator is larger than its denominator.
Defn: A number which is made up of an integer and a fraction.
Improper Fractions
Mixed Numbers
4.1 – Fractions and Mixed NumbersClassify each of the following fractions:
2923
715
8562
3347
954
61277
proper
proper
improper
improper
mixed number
mixed number
4.1 – Fractions and Mixed NumbersConverting Mixed Numbers to Improper Fractions
1. Multiply the denominator by the integer.2. Add the numerator to the product of the denominator and the integer.3. Write the sum as the numerator over the original denominator.
7257
725
7235
737
3263
326
3218
320
4.1 – Fractions and Mixed NumbersConverting Mixed Numbers to Improper Fractions
1071010
10710
107100
10107
1211812
12118
121196
12107
4.1 – Fractions and Mixed NumbersConverting Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the integer of the mixed number.
3. The remainder is the numerator over the original denominator.
9559
54
1
54
1
4.1 – Fractions and Mixed NumbersConverting Improper Fractions to Mixed Numbers
239923
185
2
95
2
62131362
5210
4
1310
4
4.2 – Factors and Simplest FormDivisibility Tests
1. A whole number is divisible by 2 if the number is even.
2. A whole number is divisible by 3 if the sum of the digits is divisible by 3.
3. A whole number is divisible by 4 if the last 2 digits are divisible by 4.
236
354
9126
968 140
621 (is divisible by 3)
(36 is divisible by 4) 528,10 (28 is divisible by 4)
1824831 13842 (is divisible by 3)
4.2 – Factors and Simplest FormDivisibility Tests
4. A whole number is divisible by 5 if the number ends in a 0 or a 5.
5. A whole number is divisible by 6 if it is divisible by both 2 and 3.
6. A whole number is divisible by 9 if the sum of the digits is divisible by 9.
936
345
9126
1265 140
621 (is divisible by 2 and 3)
18 (is divisible by 9)
2124834 43842 (is divisible by 2 and 3)
639
4.2 – Factors and Simplest FormA Number as a Product of Prime Numbers
24
12
3
2
62
3222 323
2
Factor Trees24
8
2
3
42
3222 323
2
4.2 – Factors and Simplest FormA Number as a Product of Prime Numbers
72
36
9
2
182
33222 23 32
2
Factor Trees210
105
7
2
215
7532
3
3 3
4.2 – Factors and Simplest FormSimplest Form
30
152
53
4530
533532
Defn: A fraction is in simplest form when the numerator and denominator have no other common factors other than 1.
45
95
33
32
4.2 – Factors and Simplest FormSimplest Form
49
77
142
11249
7222277
Write in Simplest Form.
112
562
282
167
2 7
4.2 – Factors and Simplest FormSimplest Form
2064
16
2064
Write in Simplest Form.
5
16
5
common factor is 4
4.2 – Factors and Simplest FormSimplest Form
2
3
567aaa
2
3
567aa
Write in Simplest Form.
8a
8
common factor is 7a2
4.2 – Fractions and Simplest FormEquivalent Fractions – Two Methods
2721
97
7
997
97
?2721
97 equivalentandAre
1. Simplify each fraction. 2. Cross Multiply.
2721
97
189189
277219
Fractions are equivalent.
4.2 – Fractions and Simplest FormEquivalent Fractions – Two Methods
8534
156
52
52
175172
5332
?8534
156 equivalentandAre
1. Simplify each fraction. 2. Cross Multiply.
8534
156
510510
8563415
Fractions are equivalent.
4.2 – Fractions and Simplest FormEquivalent Fractions – Two Methods
185
3610
3912
134
332252
133322
?3610
3912 equivalentandAre
1. Simplify each fraction. 2. Cross Multiply.
3610
3912
390432
10393612
Fractions are not equivalent.
4.3 – Multiplying and Dividing FractionsMultiplying Fractions
1. Multiply the numerators.
2. Multiply the denominators.
3. The product of the numerators remains as the numerator as the product of the denominators remains as the denominator.
11753
115
73
7715
9311
91
31
271
4.3 – Multiplying and Dividing FractionsMultiplying Fractions
87776
87
776
3
41113
82734
83
274
2911
181
4
1
11443
1
2
1
9
4.3 – Multiplying and Dividing FractionsMultiplying Fractions
1611334
1633
114
1
4131
2332 y
23
32 y
1111 y y
4
3
143
1
1
1
1
4.3 – Multiplying and Dividing FractionsMultiplying Fractions
22
3
abba
22
3
ab
ba
a
11ba
43
43
43
3
43
3
3
43
6427
1
1
bba
4.3 – Multiplying and Dividing FractionsMultiplying Fractions
161062531
1625
103
61
1
1622511
2
5
2645
4.3 – Multiplying and Dividing FractionsDividing Fractions
1. Write the reciprocal of the second fraction (the divisor).
2. Change the division operator to multiplication.
3. Work the problem as a multiplication problem.
12
94
21
94
98
25
78
52
78
1754
4
1
720
4.3 – Multiplying and Dividing FractionsDividing Fractions
29
410
92
410
445
351
43
yy35
43 yy
254113y
1
2y
2203y
1495
5
1
4.3 – Multiplying and Dividing FractionsDividing Fractions
715
149
32
157
149
32
4945
92
43
29
43
3211
1
3
61
7711531
1
7
3
1
.29
43, yandxifyxexpressiontheEvaluate
1
2
4.3 – Multiplying and Dividing FractionsDividing Fractions
715
149
32
157
149
32
4945
49
89
12
49
892
4
94191
1
4
49
49
7711531
1
7
3
1
?492
89
xequationtheofsolutionaIs YES
4.3 – Multiplying and Dividing FractionsDividing Fractions
160
6160
61
11101
10
110
6061 of
Hershey Park is located in Pennsylvania. Of its sixty rides, one-sixth of them are roller coasters. How many roller coasters are in Hershey Park?
coastersroller
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