Question

Sarah cut off one eighth of a 48 inch piece of ribbon Jane cutoff one nineth of a 36 peace ribbon they compared their cut pieces whose piece is longer how much longer

Answer 1

Sarah: 48 * 1/8
Jane: 36 * 1/9
you could do 2 things here
a. solve the problem by multiplying the two "fractions" together for each person to get a number, and the larger number means the larger piece
or
b. take a step back and look at it piece by piece
first lets compare
Sarah has a piece of Ribbon equal to 48 inches while
 Jane's ribbon is only 36 inches in length
so Sarah has the most ribbon to start out with
now lets compare the two fractions
1/8 and 1/9
the smaller the denominator the bigger the number actually is
because the denominator just means "divided by" this number, so the smaller the number, the less "groups" the numerator is being split up into.
now in that case, 1/8 is the bigger fraction, and this fraction belongs to Sarah
now if Sarah has the larger Ribbon and the larger fraction, then she automatically has the larger ribbon.

however, in this problem it asks for "how much longer"
so we have to treat each of the numbers for each person as if it was a fraction
48 inches for Sarah and 36 inches for Jane will be over 1, showing that it is 48 and 36 "wholes" or whole numbers
48/1 and 36/1
now we multiply 48/1 by 1/8 because that i how much ribbon sarah needs
multiply the numerator by the numerator and the denominator by the denominator
48/1* 1/8 = 48/8 or simplified to 6/1 or 6 inches of ribbon for Sarah
do the same for Jane
36/1 * 1/9 = 36/9 or simplified to 4/1 or 4 inches of Ribbon for Jane
therefore we can conclude
Sarah has 2 more inches of Ribbon than Jane