[Music] for today's video we are going to talk about how to solve problems involving fractions and we are going to explain everything in details on the first example it took juliana six hours on the first day five hours the second day and three hours the third day to finish typing her term paper in business mathematics how long did julianna work express it as a fraction of 24 hours day to determine the number of hours she worked to finish her term paper in business mathematics let us simply add the number of hours she worked each day and let us express the number of hours as a fraction of 24 hours a day on the first day juliana took 6 hours and that is 6 over 24 on the second day that is 5 over 24 and on the third day that is 3 over 24 if we are going to add fraction with the same denominator let us simply copy the denominator and let us add the numerator that is 6 plus 5 plus 3 and that is 14 over 24. 14 over 24 can be written in simplest form because they are divisible by 2 so 14 becomes 7 and 24 becomes 12. so the number of hours she worked to finish certain paper in business mathematics that is 7 over 12 of a day and this will be our answer on example number 2 robert care is 5 and 1 4 kilograms of rice and 3 and 1 3 kilograms of fish how many kilograms of items does robert carries to determine the total kilograms of items he carries all we have to do is to add the kilograms of rice and kilograms of fish so let us have five and one-fourth plus three and one-third so to add this one let us have five plus three and then we have one-fourth plus one-third five plus three that is eight and then we have one-fourth plus one-third since we are adding fraction with different denominator all we have to do is to find the lcm the lcm of 4 and 3 that is 12 and then 12 divided by 4 that is 3 multiplied by 1 and then we have 12 divided by 3 that is 4 times 1. so let's simplify let's say right eight plus three times one that is three and four times one is four and then we have here eight plus three plus four that is seven over twelve and 8 plus 7 over 12 that is 8 and 7 over 12 kilograms of items so this will be our answer on example number three cathy bought a ribbon that is three and one fourth meters long she need to cut from it a piece measuring five over four meters how long is the remaining parts so let me show you two different solution and how we can determine the remaining parts of the ribbon the first one let us have 3 and 1 4 minus 5 over 4 so let us convert the mixed number into improper fraction let us have 4 times 3 that is 12 plus 1 that is 13 over 4 minus 5 over 4. since we have the same denominator let us simply copy the denominator and let's subtract the numerator that is 18 minus five 13 minus five that is eight and then we have four eight divided by four that is two so the remaining parts of the ribbon that is two meters and this will be our answer so the next solution that i'm going to show you since 5 over 4 is a improper fraction if you are going to convert this one into mixed number that is one and one for it so let us have three and one fourth minus one and one fourth so let us have three minus one and then let us have one fourth minus one fourth so we are going to cancel this one it will give us three minus one that is two meters so we come up with the same answer on example number four mrs de mesa bought six and one third kilograms of meat she used 2 and 1 4 kilograms for apritada 2 and 1 over 8 kilograms for minuto and the rest for adobo how many kilograms of meat did she use for adobo to determine the number of kilograms of meat she used for adobo let us add first the number of kilograms she used for apritada and menudo and subtract it from the total number of kilograms of meat she bought so let us have first two and one fourth plus two and one over eight so let us have two plus two that is four and then let us have one fourth plus one over eight so let us say right four and let us have one four plus one over eight since we are adding fraction with different denominator let us find the lcm of four and eight that is eight eight divided by four that is 2 times 1 and then 8 divided by 8 that is 1 times 1 so let us have 4 plus 2 multiplied by 1 that is 2 1 times 1 is 1 all over 8. so let us have two plus one that is three and then we have eight so we are going to have four and three over eight kilograms so this is the total number of kilograms she used for apretada and and then let's subtract this one let's have six and one third minus four and three over eight so let us convert six and one third and four and three over eight into improper fraction 3 multiplied by 6 that is 18 plus 1 that is 19 and let us write the denominator and then 8 multiplied by 4 that is 32 plus 3 that is 35 over eight since we are subtracting fraction with different denominator let us find the lcm of three and eight that is twenty-four twenty-four divided by three that is eight times nineteen and then 24 divided by 8 that is 3 times 35 8 multiplied by 19 that is 152 3 multiplied by 35 that is 105 and then let us write the denominator and then 152 minus 105 that is 47 over 24. 47 divided by 24 that is one and we have a remainder of 23 and then 24. so this is the total number of kilograms she used for adobo and this will be our answer on example number five a cookie sheet is 12 and 3 4 inches long and 8 and 1 4 inches wide what is the area of the cookie sheet to determine the area of the cookie sheet let us illustrate first our problem so let us have a rectangle so this will be the length which is 12 and 3 4 inches and this will be our weed that is 8 and 1 4 inches and to find the area let us use the formula area equals length times width so let us have the length that is 12 and 3 4 multiply by width that is eight and one fourth so let us convert this one into improper fraction so let us have 12 multiplied by 4 that is 48 plus 3 that is 51 over 4 and then 4 multiplied by 8 that is 32 plus 1 that is 33 over 4 so to simplify this one let us simply multiply numerator or to numerator and denominator to denominator so let us have 51 multiplied by 33 3 times 1 that is 3 and 3 times 5 is 15 and the left side 3 times 1 is 3 and 3 times 5 is 15 so let us add that sub 3 5 plus 3 that is 8 and then 1 plus 5 that is 16 and l sub 1. so 51 times 33 that is 1683 and 4 times 4 that is 16 so if you are going to divide this one let us have 1683 divided by 16 16 divided by 16 is 1 1 times 16 is 16 and 16 minus 16 f is zero so we are going to cancel this one let's bring down eight eight divided by sixteen that is zero zero times sixteen is zero eight minus zero is eight let us bring down three eighty three divided by sixteen is 5 and 5 times 16 that is 80 and we have a remainder of 3. so therefore 1 683 divided by 16 that is 105 and 3 over 16 square inches so this will be the area of our cookie sheet and this will be our answer on example number six joel earns 100 000 pesos a year if he spend one over five for food one over eight for lent one over ten for clothing and one over twenty for recreation on letter a how much does he spend for each letter b how much is his total expenses let us see how much does he save and letter d what rational part of his earning in his savings so let us find first the amount he spend for food rent clothing and recreation so let us have letter a so let us have one hundred thousand multiply by one over five that is the amount he spent for food so one hundred thousand multiplied by one is one hundred thousand divided by five then that is twenty thousand pesos for food and then let's have one hundred thousand multiply by one over eight that is the amount he spent for rent so one hundred thousand times one is one hundred thousand divided by eight that is twelve thousand five hundred and this is four rent and then one hundred thousand multiplied by one over ten and that is ten thousand so this is the amount he spent for clothing and then let us have 100 000 times 1 over 20 and that is 5 000 pesos and this is the amount he spent for recreation and then on letter b how much is his total expenses so for food that is twenty thousand and then for rent that is twelve thousand five hundred and then for floating that is ten thousand and for recreation that is 5000 so if we are going to add this one we are going to have 0 0 and then 5 and then we are going to have 7 and then four so the total amount he spends for food rent clothing and recreation that is forty seven thousand five hundred now on letter c how much does he save so let's subtract 100 000 minus 47 500 and that is 52 500. so this is the amount he saved and this is the amount he spent and on letter d what fractional part of his earning in his savings since he saves 52 500 over the total amount he earned for a year let us cancel 0 and that is 525 over 1 525 and 1 000 are divisible by 25 525 divided by 25 that is 21 1000 divided by 25 that is 40 and this will be our answer on letter d on example number 7 if ken bought 3 and 3 4 meters of cable of wire and divided equal meters for the extension of his tbk ball for each of the three rooms of his house how long was each piece so to determine how long each piece let us simply divide three and three four meters by three so let me show you two different solution and how we can divide this one first let us have 3 and 3 4 divide by 3. so let us convert this one into improper fraction 4 multiplied by 3 that is 12 plus 3 that is 15 over 4 divided by 3. if you are going to divide 15 over 4 by 3 you are going to multiply 4 by 3 or if you want you can get the reciprocal of 3 and proceed to multiplication that is 15 over four multiplied by one third so if you are going to divide let us have 15 and then four times three 15 divided by 3 is 5 so 15 becomes 5 and 3 becomes 1 so let us have 5 and then over 4 5 over 4 that is 1 and 1 4 meters and this will be our answer but if you are going to multiply 15 over 4 times one third you simply multiply numerator to numerator and denominator to denominator 15 times 1 that is 15 and then 4 times 3 i'm going to the right in this one because we can cancel 15 and three 15 divided by three that is five and three becomes one so this is five over four that is same as one and one fourth meters and this will be our answer on our last example enriquez spends stupif of his monthly salary saves one-third of the remainder and shared the rest equally to his two sisters and a brother if his monthly salary is 60 000 pesos how much does he give to his brother every month to determine how much he give to his brother every month let us determine first how much enriquez spends every month since the monthly salary of enrique that is 60 000 pesos so let us have 60 000 pesos multiplied by 2 feet and that is 120 000 pesos divided by 5 it will give us 24 000 pesos so this is the amount he spends every month and then let us find the remaining amount that is 60 000 pesos minus 24 000 pesos and that is 36 000 pesos so this is the remaining amount and then let us find one third of the remaining amount so this is 36 000 pesos multiplied by one third and that is twelve thousand pesos so this is the amount he saves every month and then let us find 36 000 pesos minus 12 000 pesos and that is 24 000 pesos so this is the amount he shares to his two sisters and a brother so to determine how much he give to his brother every month let us divide twenty four thousand by three this is twenty four thousand divide by three and that is eight thousand pesos so this is the amount he give he gives to his brother every month so i hope you've learned from this video thank you so much for watching and god bless us all