AlgOneLectOne

# When we carry out that division incompletely to form

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larger numerator by a smaller denominator. When we carry out that division incompletely to form a whole number quotient plus a remainder portion of the numerator (yet to be divided) we have produced the mixed number (whole number plus a proper fraction). Saxon Lesson Learning Concept Statement Number Concept Name Description (answers what is this concept?) Question (among many) Correct Answer 1 4 Mixed number notation m l/k means m + l/k What is a mixed number? A mixed number is a whole number plus a fraction with the plus sign "understood" Click me for video > QuickTimeª and a decompressor are needed to see this picture.

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9 Adding Mixed Numbers To add mixed numbers we keep in mind that each mixed number is itself two numbers: a whole number and a fraction to which it is added. Thus adding mixed numbers generally means we are adding four numbers: two are whole numbers and two are fractions. Since addition can proceed in any order we can separately add the fractions together and the whole numbers together to give us the procedure for adding mixed numbers. The result is then a mixed number. Sometimes the fraction is an improper fraction whose value exceeds one in which case further simplification is required. We cover that next. Saxon Lesson Learning Concept Statement Number Concept Name Description (answers what is this concept?) Question (among many) Correct Answer 1 5 Addition of mixed numbers Add fractions and add whole numbers. Then simplify fraction. m l/k + n i/j = ? (m + n) + (jl + ki)/kj _____________________________________________________________________________________________________ Saxon Lesson Learning Concept Statement Number Concept Name Description (answers what is this concept?) Question (among many) Correct Answer 1 6 Simplify fraction Convert to mixed number if fraction exceeds 1 m/n = ? If m > n Int + j/n where j < n A mixed number that has an improper fraction is not really following the rule for a mixed number in which the fractional part is preferred to be a proper fraction- less than one. When the mixed number resulting from the addition of mixed numbers produces an improper fraction, we convert the improper fraction to its own mixed notation. In that conversion a whole number and a proper fraction result. The whole number generated from the improper fraction is then added to the original whole number to produce the sought after mixed number result. Click me for video > QuickTimeª and a decompressor are needed to see this picture.
10 More on Mixed Numbers So for example, let’s consider the sum of: 2 7/8 + 3 5/9 =. After writing these with common denominators, we have instead 2 63/72 + 3 40/72 = Performing the indicated additions gives us: 5 103/72 = Then reducing the improper fraction to its own mixed form yields, 5 + 1 31/72 = 6 31/72, where we have shown the final mixed result containing the whole number 6 and the proper fraction 31/72. ___________________________________________________________________________________ Click me for video ^ QuickTimeª and a decompressor are needed to see this picture.

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11 Subtracting Mixed Numbers Subtracting mixed numbers is very similar to the addition of them. Here we subtract the fractional parts and the whole parts separately. If the two numbers each had proper fractional parts, the resulting fractional part will also be a proper fraction.
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