FRACTIONS AND MIXED NUMBERS Machinery's Handbook, 31st Edition
7
Example, Addition of Common Fractions
Example, Subtraction of Common Fractions
1 4
1 4
4 4 × = × = 1 1
4 16
15 16 7 12
15 16 7 12
3 3 4 4
45 48 28 48 17 48
=
×
LCD = 16
LCD = 48
3 16
3 16
3 16
=−
−
− ×
7 8
7 8
14 16 21 16
2 2
+ × = +
+
To Add Mixed Numbers: Two methods for adding mixed numbers are shown below the explanations. First method: 1) Raise fraction parts to the higher terms of the LCD; 2) add whole num- ber parts and fraction parts separately; 3) if result has an improper fraction, convert it to a mixed number and add the whole number parts. Second method: 1) Convert mixed numbers to improper fractions; 2) raise resulting fractions to the higher terms of the LCD; 3) add fractions as usual and convert back to a mixed number; reduce, if needed. Examples, Addition of Mixed Numbers Method 1 2 2 2 4 4 4 1 1 1 7 1 2 1 2 1 4 16 16 16 32 8 32 1 4 8 8 15 32 15 32 1 1 = = + + + 7 32 7 32 7 1 8 = + = = → × × × Method 2 2 4 1 + + 1 2 5 2 5 2 16 16 80 32 1 4 17 4 47 32 17 4 47 32 8 8 1 1 136 32 15 32 = = = + = 47 32 263 32 7 32 8 → = = = × × × To Subtract Mixed Numbers: The methods are similar to those for adding, except the fraction part may need to “borrow” from the whole number. The examples show the details. 1) Convert fraction parts to equivalent fractions with LCD; 2) subtract whole number and fraction parts separately, unless the first fraction’s numerator is smaller than the sec- ond. In that case, proceed as shown in the second and third examples below, borrowing 1 in the form of a fraction and then subtracting. Examples, Subtraction of Mixed Numbers Example 1 Example 2 Example 3 Example 4 12 43 43 20 19 1 19 19 19 15 32 39 3 2 4 5 14 15 14 15 2 2 2 9 11 9 9 8 7 1 7 = = + = = = + = − 7 7 7 1 − = − = − 1 1 − − = = − − −
2 9 4 9
3 5
1 2
1 2
4 1 5
1 2
4 9
4 9
1
5
5 15 24 24 =
6
3 5
7 9
1 3
1 2
8
12
Multiplying Fractions and Mixed Numbers To Multiply Common Fractions: 1) Multiply numerators; 2) multiply denominators; and 3) convert improper fractions to mixed numbers, if necessary. To Multiply Mixed Numbers: 1) Convert mixed numbers to improper fractions; 2) mul- tiply numerators; 3) multiply denominators; and 4) convert improper frac tions to mixed numbers, if necessary. Examples, Multiplication of Fractions
22 5 22 4 5 3 × = = = 4 3 × 1 × 1 3 × 22 4 5 3 × × × × 2 5 22 5 4 3 1 3
8 15 × = = 2 3 8 15 2 8 3 15 × ×
2 8 3 15 × × × = =
16 45
88 15
16 45
88 15
2 3
2 5
4
4
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