3.4 Adding and Subtracting Fractioins

how do we add or subtract fractions that have different denominators, such as 5/6 + 3/4. Interpret the sum 5/6 + 3/4 using the example total distance walked

(120)

(adding fractions with like denominators) 4/15 + 7/15 =

(pg 120)

Interpret the sum 4/15 + 7/15 as total fraction of a fence painted

(pg 120)

add 5/6 and 3/4 with the common denominator 12 using fraction strips

(pg 121)

give 5/6 and 3/4 a common denominator show at least two ways to add 5/6 and 3/4 using different common denominators

(pg 121)

give examples of mixed numbers

2(3/4) and 5 (7/8)

use the way we add fractions to show that every mixed number can be written as an improper fraction

A B/C = A x c + B/C

since a whole number A can also be written as fraction, named, A/1, we can write the mixed number A (B/C) as

A(B/c) = A + B/C = A/1 + B/C

in general, suppose A/B and C/D are two fractions (where B is not equal to 0 and D is not equal to zero). then...

A/B = Ax D/B x D and C/D = C x B/D x B, and the latter two fractions Ax D/Bx D and CxB/D X B both have denominators equal to B x D

every finite decimal stands for

a finite sum of fractions

As in comparing fractions, explain the process of breaking 5/6 and 3/4 into like parts

achieved numerically by giving the fractions 5/6 and 3/4 a common denominator

Ax D/Bx D and CxB/D X B both have denominators equal to B x D, What can you do from here

add or subtract these fractions by adding or subtracting the number of parts (numerator)

why is combining not adding

because fractions of quantities that are to be combined refer to different wholes

why can we read the decimal 0.491 as four hundred ninty-one thourandths

because we can write the decimal as a fraction

whenever we add two numbers, such as 3 + 4 or 2/3 + 3/4 whenever we subtract two numbers such as 4 -3 or 3/4 - 2/3

both summands and the sum refer to the same whole the minuend, the subtrahend, and the difference all refer to the same whole.

every finite decimal stands for a finite sum of fractions. How can you see this representation

by writing the decimal in its expanded form

the method for writing decimals as fractions applies only to

finitie decimals. It does not apply to a decimal such as 0.4444444444, where the 4s repeat forever.

what is a mixed number or mixed fraction

number that is written in the form A(B/C) where a, b , and c are whole numbers, and B/C is a proper fraction (the numerator is less that then denominator)

by giving these fractions a common denominator, we can write the decimal as a fraction: For example, 2.7 = 0.491 =

pg 123

write the mixed number 2(3/4) as an improper fraction

pg 123

interpret the sum 3 + 4 using apples' interpret the sum 3 + 4 by combining 3 bananas and 4 blocks interpret the sum 1/3 + 1/4 using the same pie interpret the sum 1/3 + 1/4 using a small pie and a large pie. Does the combined amount represent the sum 1/3 = 1/4

pg 124

when working with fraction addition or subtraction words problems, what should we careful of

the fractions in question refer to the same underlying wholes. in some cases, fractional amounts that are to be combined or taken away refer to different wholes, thus the problem is not a fraction addition or subtraction problem

the mixed number A (B/c) stands for

the sum of its whole number part and its fractional part: A + B/C

by giving these fractions a common denominator, we can

write the decimal as a fraction

If two fractions have the same denominator,

you can add/subtract these fractions by adding or subtracting the numerators and leaving the denominator unchaged