HESI_A2_Math_Study_Guidebook

  HESI A2 Math Study Guide Introduction to Fractions A fraction is a mathematical tool which helps us to count in terms of equal parts of a whole. For example, a recipe requires 2 3 cups of milk, Mike ate 2 of a cake, Sarah run 3 of a mile, John repaid 4 6 4 4 of a loan. 5 A fraction is any number of equal parts. For example, if we cut a small size sausage pizza into 4 equal slices, then 3 such slices of the pizza are the same as: 3 out of the 4 equal slices of the pizza, or three fourth of the pizza, or 3 of the pizza. 4 As we can see from the above example, a fraction has two components, which are called numerator and denominator. For example, if we consider 1 of a cake, then 1 is the numerator and 4 is the denominator. 4 A denominator tells us a number of equal parts that make up a whole while a numerator tells us how many of them we are considering. For example, when we say 7, we are talking about 7 equal parts such that 4 of them make up a whole; 4 in other words, we divided a whole into 4 equal parts and now considering 7 such parts. Both numerator and denominator of a fraction are integers; however, denominator cannot be zero (we cannot divide a whole into zero parts). Exercise 1. The cost of the vacation trip is $4,500 and we are required to pay 2 of that amount when 5 we reserve the trip. How much we need to pay during the reservation? Solution. All we need to do is to calculate 2 of the cost of the trip. 5 Since the denominator of the fraction 2 is 5, we understand that the cost is divided into 5 equal amounts: 5 $4,500 = $900 + $900 + $900 + $900 + $900 The numerator of the fraction 2 (which is two) tells us how many of those equal amounts we have to 5 pay to reserve the trip: $900 + $900 = $1,800 Answer. So, we need to pay $1,800. Exercise 2. There are 24 students in a class. If 2 of the students are girls, then how many boys are 3 there in the class? Solution. Let’s calculate the number of girls. Then if we subtract the number of girls from the total number of students, we will get the number of boys. The denominator of the fraction 2 (which is three) tells us that the class is divided into three groups of 3 equal numbers of students: 24 = 8 + 8 + 8 The numerator of the fraction 2 (which is two) tells us that two of these groups are girls: 3 8 + 8 = 16 Answer. So, the number of boys is 24 − 16 = 8. Finally, we would like to give a different interpretation of a fraction. We said that a fraction is any number of equal parts; equivalently, a fraction can be thought of as a division of two integers. For example, 2 (two fifth) is the same as 2 divided by 5, 5 1 (one third) is the same as 1 divided by 3, 3 5 (five seventh) is the same as 5 divided by 7, 7 6 (six fourth) is the same as 6 divided by 4. 4 Summary A fraction is any number of equal parts