AlgMap-3.3 Express the following, as a single fraction: \[{@a/b@}+{@c/d@}.\]
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Leave your answer in it's lowest terms in the form \(\frac{a}{b}\). [[validation:ans]]

]]> The first task in adding fractions is to rewrite each as an equivalent fraction with the same denominators. You can guarantee this by multiplying the two denominators together or find the Lowest Common Multiple (LCM).

In this example, \({@a/b@}+{@c/d@}\), the we need the lowest common multiple of {@b@} and {@d@} which is \({@lcm@}\).

Next re-write the expression in the form: \[\frac{a}{@lcm@}+\frac{b}{@lcm@}.\] To convert a fraction to an equivalent form we must multiply the denominator and numerator by the same number. In this case, multiply the numerator of the first fraction by \({@ev(lcm/b,simp)@}\) and the numerator of the second by \({@ev(lcm/d,simp)@}\). So we obtain: \[{@a/b@}+{@c/d@} = \frac{@a*ev((lcm/b),simp)@}{@b*ev((lcm/b),simp)@}+\frac{@c*ev((lcm/d),simp)@}{@d*ev((lcm/d),simp)@} = \frac{@ev(a*(lcm/b),simp)@}{@lcm@}+\frac{@ev(c*(lcm/d),simp)@}{@lcm@} = \frac{@ev(a*(lcm/b)+c*(lcm/d),simp)@}{@lcm@}.\] We may need to cancel any common factors in the numerator and denominator to obtain the answer in lowest terms \({@ta@}\).

]]> 1 0.1 0 simp:true; b:rand([3,5,7,9]); a:b-rand(b-2)-1; d:b+1+2*rand(3); c:d+rand(3)+1; ta:(a/b)+(c/d); lcm:lcm(b,d); simp:false; [[feedback:prt1]]

]]> \[{@a/b@}+{@c/d@} = {@ta@}.\] 0 0 0 *10 dot 1 i cos-1 lang [ 0 {"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}} ans algebraic ta 15 1 0 0 1 0 1 1 1 prt1 1.0000000 0 1 0 EqualComAss ans ta 0 = 1.0000000 -1 1-0-T = 0.0000000 2 1-0-F 1 AlgEquiv ans (a+c)/(b+d) 0 = 0.0000000 -1 1-1-T Remember that the first step in adding fractions is to make both denominators equal. It is not simply adding the numerators and the denominators.

]]> = 0.0000000 -1 1-1-F 2 AlgEquiv ans ta 0 = 0.0000000 -1 1-2-T Please perform all arithmatic to write the fraction fully into the form \(\frac{a}{b}\) and leave in it's lowest terms.

]]> = 0.0000000 1 1-2-F 73699510 251827869 1630492411 123979407 1188141115 1815072118 1293584268 1 ans ta prt1 1.0000000 0.0000000 1-0-T 2 ans (a+c)/(b+d) prt1 0.0000000 0.1000000 1-1-T 3 ans ta+1 prt1 0.0000000 0.1000000 1-1-F 4 ans a/b+c/d prt1 0.0000000 0.1000000 1-2-T