 Hello and welcome to this session. In this session, we will learn how to use units of measure to guide the solution of multi-step problems and interpret units consistently in formulae. Now in our earlier session, we have learned how to convert units of measure from one unit to another. In continuation with that, in this session, we will discuss how to convert rates and units of areas and volumes. Now let us discuss how to convert rates. Now we know when a rate is simplified, it has denominator as one that is unit rate. For example, Sam gives two cards per week to his grandmother. Now a derived unit is a unit that is derived from a measurement system-based unit such as length, mass or time like square feet minus square r, cubic meter, etc. Now let us discuss unit ratio. Now a unit ratio is a ratio in which denominator is one unit. For example, we have one yard is equal to three feet. Now we can write it as unit ratio three feet upon one yard. Similarly, one kilometer is equal to one thousand meters and we can write it as unit ratio one thousand meters upon one kilometer. So here we can see unit ratio is the ratio in which denominator is one unit. Now you must know that to convert from larger unit to smaller unit, multiply by appropriate unit ratio and to convert from smaller unit to larger unit, multiply by the reciprocal of the unit ratio. Now let us discuss our example values. Now here we want to convert one to three miles. Now first see here we have two units miles and r. Now here unit of length that is miles will be converted to other unit of length that is feet and unit of time that is r will be converted to other unit of time that is second. Now here let us denote r by h and second by s and minutes by simply writing and now one fifty three miles per hour can be written as unit rate one fifty three miles upon one hour. Now first of all we will convert one fifty three miles into feet and then we convert one hour to seconds. Now we know that one mile is equal to an eighty feet this can be written as unit ratio five thousand two hundred and eighty feet upon one mile to convert larger unit miles to smaller unit, multiply it by this unit ratio. So one fifty three miles is equal to one fifty three miles into five thousand two hundred and eighty feet upon one mile. Now let us convert one hour into seconds. Now we know that one hour is equal to sixty minutes and one minute is equal to sixty seconds. So one hour is equal to sixty into sixty seconds which is equal to three thousand six hundred seconds. So we have one hour is equal to three thousand six hundred seconds and it can be written as unit ratio three thousand six hundred seconds upon one hour and now to convert larger unit hour to smaller unit second we multiply one hour by this unit ratio. So one hour is equal to one hour into three thousand six hundred seconds upon one hour. Now dividing out the common units this implies one hour is equal to three thousand and six hundred seconds. Now one fifty three miles upon one hour will be equal to now here one fifty three miles is equal to now again dividing out the common units it will be one fifty three into five thousand two hundred and eighty feet and one hour is equal to three thousand six hundred seconds. So this is equal to one fifty three into five thousand two hundred and eighty feet upon three thousand six hundred seconds. Now two forty into fifteen is three thousand six hundred and two forty into twenty two is five thousand two hundred and eighty now fifteen into one is fifteen and fifteen into ten point two is one fifty three. So this is equal to two twenty four point four feet upon one second. Thus one fifty three miles per hour is equal to two twenty four point four feet per second and now let us discuss a multi step problem and here we have to find area of a rectangle that is thirty eight inches by ten yards. Now here you can see that both the dimensions of this rectangle have different units one is in inches and other is in yards. Now in the first step we will convert both the dimensions into same unit here let us convert both the dimensions into inches now one dimension is already in inches so let us convert ten yards into inches. Now we know that one yard is equal to three feet and one foot is equal to twelve inches. So one yard is equal to three into twelve inches which is equal to thirty six inches. So ten yards will be equal to ten into one yard which is equal to ten into now one yard is thirty six inches so on multiplying this is equal to three sixty inches. Now in step two let us find area of rectangle now we know that area of rectangle is length into breadth. Now length is forty eight inches and breadth is three sixty inches so this is equal to forty eight inches into three sixty inches and on multiplying this is equal to seventeen thousand two hundred and eighty square inches. Now to find area volume parameter etc. the dimensions that is length breadth height radius of the geometrical figure should have same units of measure. Now let us see how to convert units of area. Now units of area are of the form square foot square inch square centimeter etc. Now as we used unit ratios to convert units of length similarly we will use unit ratios to convert units of area. Now let us discuss an example for this. Here we have to convert three square feet into square inches. Now we know that one square foot is equal to one foot into one foot so three square feet will be equal to three into one square foot which is equal to three into one foot into one foot. Now one foot is equal to twelve inches which can be written as unit ratio twelve inches upon one foot. Now to convert larger unit feet into smaller unit inches we must get feet by this unit ratio. Now three square feet which is equal to three into one foot into one foot will be equal to three into one foot into twelve inches upon one foot into one foot into twelve inches upon one foot. Now deriving out the common units which is equal to three into twelve inches into twelve inches which is equal to four thirty-two square inches. So we get three square feet is equal to four thirty-two square inches. So in this session we have learnt how to use units of measure to guide the solution of multi-step problems and this complete session hope you all have enjoyed the session.