The word common brings disparate images to the imagination. Once upon a time, it was used as a derogatory term for someone not of the upper, privileged classes. Generally, however, it is known as something that all of us share. Our common humanity, for example, is what gave rise to the United Nations and the Human Rights charters. A common theme repeats in a variety of settings, either in literature or music. A common denominator is what brings seemingly random fractions together. Math tutors spend time with students delineating denominators.
Why do students struggle with fractions?
Students begin learning fractions in primary school. Most do not have a problem with learning parts related to the whole. Common fractions, 1/4, 1/2, 2/3, are all recognized, even by computer programs. It is easy to learn fractions with food. Pizza is an excellent learning tool, as are oranges, apples and any other fruit or vegetable that a group can share. Being creative with it and dividing something into parts becomes colorful and fun. Fractions and division go hand in hand. Once something is divided into parts, you have the option of a whole or a fraction. A whole is all the parts together in one place: 1=2/2, 3/3, 5/5, 11/11. Compound fractions involve both whole numbers and parts, and confusion can occur at this point. A student who cannot discern the whole or the parts will benefit after an assessment at one of our local and affordable maths tutoring centres.
Using fractions requires competence in multiplication and division and flexibility between the two speeds recognition and prepares students to determine equivalence and common denominators. However, a foundational step is recognizing what a denominator is. The representation of one half is 1/2; 1 is the numerator (number of parts present), and 2 is the denominator (number of parts possible). So far, so good. If you add quarters, it is simple – 1/4 + 3/4 = 4/4 = 1; the denominator stays the same, so you add the numerators to arrive at the correct answer. If this has confused you, or your student is struggling here, please call for an assessment, and one of our friendly math’s tutors will sort it out for you.
However, a deeper understanding is required to add, subtract, or multiply fractions that do not have the same denominator. What do you do when confronted by 1/5 + 3/4? The common denominator is the solution. A common denominator is one where both numbers are factors of it. In this equation, it is 20. Once you find the denominator, the numerators also change by the factor used to change the other fraction. For example – 1/5 = 4/20, and 3/4 = 15/20; now, you can add them together to form 19/20. Our experienced, expert math’s Private tutors delight in ensuring that students know how to do this and then simplify back, if possible.
Another aspect of fractions that some students find difficult is simplifying. Once you have completed the equation, you may find a large, ungainly, awkward-looking fraction. Again, you need to look for commonality, this time in the numerator and denominator. Can you find a number to divide both by to achieve a smaller number? For example, 25/20 becomes 1 5/20 => 1 1/4, or 15/20 becomes 3/4. The possibilities for practicing common denominators and simplifying are endless. All you need are your times’ tables and an active, alert imagination. If those times’ tables are not automatic, and they usually are by the end of grade 5, we suggest an assessment at one of our local, affordable, and friendly Epping tutors.