Given:
#3/8+7/10#
In order to add fractions, they must have the same denominator. We can determine what the denominators should be, we find the least common denominator (LCD), also called the least common multiple (LCM)#.
List the multiples for #8# and #10#. The lowest multiple in common is the LCD.
#8:##8,16,24,32,color(red)40,48...#
#10:##10,20,30,color(red)40...#
The LCD is #40#.
#3/8# and #7/10# must each be multiplied by a multiplier equal to #1# to form an equivalent fraction that will give each of them the same denominator (40). The multipliers in this case are fractions equal to #1#, which means they have the same number in the numerator and denominator, and multiplying will therefore not change the value of the fraction. For example: #color(blue)(8)/color(blue)(8)=color(blue)(1#.
#(3/8xxcolor(magenta)(5/5))+(7/10xxcolor(teal)(4/4))#
Simplify.
#15/40+28/40#
#=43/40=1 3/40#
To show that the fractions are equivalent and have not changed in value, you can divide the original numerators by their original denominators; and divide the new numerators of the converted fractions by the new denominators.
#3/8=0.375##color(white)(...)#and#color(white)(...)# #15/40=0.375#
#7/10=0.7##color(white)(...)# and#color(white)(...)# #28/40=0.7#
#15/40+28/40=43/40# as an improper fraction.
To convert #43/40# to a mixed number, divide #43# by #40# to find a whole number, and then write the remainder as the numerator over the denominator #40#.
#43-:40=1 " Rem "3#
The mixed number is #1 3/40#.
