Back

Ratio, Rate and Proportion | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

Views 0

Lesson Objectives

Ratio

  • Simplest way to say is one quantity divided by another quantity presented in a:b form
    • For example 4/5 can also be presented as 4:5
    • Another way to say this aspect is that if you are given a:b you can also write it as a/b
  • Ratio of more than 2 numbers
    • If you are given a:b:c:d for example or any number of components greater than 2
    • Then, you can convert each of these components in fraction using the following formula
    • frac{textup{a or b or c or d}}{a+b+c+d}
    • In other words
      • Add all the numbers given to find the denominator
    • For example
      • 1:5:8:10
      • Then, individual fractions will be
        • 1/24
        • 5/24
        • 8/24
        • 10/24
      • Because
        • 1+5+8+10 = 24
  • When you are talking about ratio, you must also know that equal ratios can be used to solve equations
  • For example
    • If the examiner tell you that the two ratios a:b and c:d are equal, then
    • frac{a}{b} = frac{c}{d}
    • This way, you can find any missing values using simple algebra.

Proportion

  • Proportionate changes are those that occur when change in one value causes a proportionate amount of change in another value.
    • Direct proportion
      • Increase in one variable increases the other variable
      • For example, if 2 kilo of wheat produced 10 breads, then 4 kilo of wheat will produce MORE breads than 2 kilos.
      • In this case, its direct proportion
      • For direct proportion questions following the following steps
      • Step 1
        • The equation we will use is
        • frac{a}{b} = frac{c}{d}
        • a is the given variable, b is the increased or decreased value of variable a, c is the output of variable a, d is the output of variable b
      • Step 2
        • Insert the values
        • Our variable was 2 kilo of wheat, our different value for the same variable was 4 kilo, our output for 2 kilo of wheat was 10 breads, our output for 4 kilo is unknown
        • So
        • frac{2}{4} = frac{10}{d}
        • Now use algebra to simply solve it.
    • Inverse Proportion
      • Inverse proportion is where the change in one variable causes an OPPOSITE change in the other variable
        • Variable a increase, the output of a decreases
        • Variable a decreases, the output of a increases
      • For example, it took 3 workers to build a fence in 10 days. How many days would it take for 6 workers to build the same fence/
      • In this case
      • Step 1
        • The equation we will use is
        • frac{a}{b} = frac{c}{d}
        • BUT a is the given variable, b is the different value for variable a, c is the output of the variable a, d is the output for variable a (REMEMBER, the C and D here are different than C and D in direct proportion)
        • frac{3}{6} = frac{c}{10}
        • Now use simple algebra to solve it.

Rate

  • The same concepts apply to other calculations in mathematics as well
  • The rate based calculations may require you to find a ratio for two given amounts
  • Divide the amount 1000 USD between 3 partners in the following ratio: 10:20:30
  • Step 1
    • Find denominator and individual fractions
    • 10+20+30 = 60
    • 10/60
    • 20/60
    • 30/60
  • Step 2
    • Multiply each with the given value to find the shares
    • 1000 *10/60 = 166.67 USD
    • 1000 * 20/60 =333.33 USD
    • 1000 * 30/60 =500 USD
Hunain Zia

Hunain Zia has previously achieved considerable success in the high-school educational stream, gaining a massive 154 Total A Grades and 7 Major Distinctions, a process in which he broke/ set 11 different world records, including the most A grades ever achieved, most subjects ever appeared in, most distinctions, gaining distinctions across two separate boards (Pearson Edexcel and CAIE) within the same year/ ever, and even 19 hours of constant examination. All records stand intact today. Hunain pursued his Honors Accounting Degree from the prestigious Bentley University, and then completed an LLB (in Honors) from University of London. Currently, he manages multiple social and commercial projects, has founded digital streams and works tirelessly in the education sector.

Educate A Change focuses on truly bringing change in the educational sector worldwide. All our courses are designed to ensure success, and provide complete preparation without requiring any other external material. Therefore, it takes away the expense of academies, books, past paper compilations and other miscellaneous items. Instead, by just the courses we offer, the student can prepare fully for the best grades in their CAIEs, Edexcel and other high-school exams. The earnings from our course-sales are invested in social projects and growing the free educational activities of Educate A Change.