When dealing with fractions, we have to understand what the denominator and the numerator are, and what they’re telling us.
The denominator indicates the number of parts that a whole is divided into. The numerator is telling us how many of these parts there are, how many parts we’re dealing with.
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What are Fractions?
You may think of fractions as divisions that haven’t been done or finished yet. But why are we using fractions? Why not simply divide the 2 numbers in a fraction and put it in decimal form instead?
Well, that’s actually a good question. In these days of smartphones and calculators, we’re all used to see things demonstrated in decimals, right?
But the fact of the matter is that people were working with fractions long before we had decimal numbers. Today, we are used to seeing portions less than 1 shown as decimals, but we still are working with fractions.
Fractions are used in many ways. You’ll see them in construction, in sewing, when we’re cooking, and they’re also used across the globe in stock markets.
So you see, fractions are everywhere, and it is very important that you understand the terms and words in Math to be successful in tests.
Just as a short reminder, the numbers above the bar are called numerators, and the numbers below the bar are called denominators.
Types of Fractions
Proper Fractions: We use the term “proper fractions” when the numerators are less than the denominators. We call these expressions proper fractions.
Improper Fractions: Improper fractions occur when the numerators are greater than, or equal to, the denominators.
Mixed numbers: When expressions consist of whole numbers and proper fractions, we call these expressions mixed numbers.
Equivalent fractions: Fractions representing the exact same number are what we call equivalent fractions. Basically, these are the same things as equal ratios. To give you an example: the following fractions, ½, 2/4, and 4/8, are all equivalent fractions. If you want to see if fractions are equivalent, you can use your calculator and simply divide. If all the answers are the same, they are equivalent fractions.
Reciprocals: If the product of 2 fractions equals one (1), those fractions are reciprocals. All non-zero fractions have reciprocals. It’s quite simple to determine what the reciprocal of a fraction is. All you need to do is switch the fraction’s numerator and denominator. Just flip the fraction, turn it over. So the reciprocal of 3/4 is 4/3. If you want to find the reciprocals of whole numbers, simply put 1 over these whole numbers. For instance, the reciprocal of 3 is 1/3.
Reducing Fractions: Fractions are reduced to their lowest terms (or just simplified) when their numerators and denominators have no common factors. When fractions are simplified, it is much easier to add and subtract or multiply and divide these fractions. To simplify or reduce fractions, we need to find equivalent fractions where the numerators and denominators don’t have common factors.
Convert Mixed Numbers to Improper Fractions: To convert mixed numbers to improper fractions, first multiply the whole number of the mixed number by the fraction’s denominator. Then, add the fraction’s numerator to the product. Then, write our sum over the initial denominator.
Math Fraction Vocabulary
To be successful on Math exams, it is key to understand the Language of Math. And when dealing with Fractions, you need to understand a number of terms and expressions as well.
So check out the following list of words, terms, and definitions often used on Math tests. Here we go:
Whole: The term Whole represents a total, all of something.
Fractions: Fractions are numbers that indicate parts of a whole, parts of a collection, or parts of a set. So fractions are parts of a whole. Common fractions are made up of numerators and denominators. The numerator is the number that’s shown on top of a fraction’s line and indicates the number of parts (of the whole). The denominator is the number that’s shown below a fraction’s line and indicates the number of parts by which our whole was divided. For instance, in the fraction 2/3, the whole was divided into 3 parts, and in this fraction, we have 2 of the 3 parts.
Numerators: As said before, numerators are the numbers above the line in math fractions. They tell us how many parts of a whole are indicated. Numerators are the top parts of fractions. They indicate how many parts of the fraction’s denominator we deal with. In the fraction 2/3, for example, 2 is our numerator.
Denominators: Denominators are the numbers below the line in math fractions. They tell us how many parts are in the whole. Denominators are the bottom parts of fractions. They show us how many parts the whole was divided into. In the fraction 2/3, for example, 3 is our denominator.
Proper fractions: As said above, we speak of proper fractions if the numerators are less than the denominators, less than the whole. So proper fractions are fractions where the numerators (the top numbers) are less than the denominators (the bottom numbers). 2/3 and 5/6, for example, are proper fractions.
Improper fractions: Again, we speak of improper fractions if the numerators are greater than the denominators, so greater than the whole. The value of the fraction is greater than 1 (for example 4/3).
Equivalent fractions: These are fractions with equal values. They name equivalent amounts. These fractions may look different, but they have exactly the same values. To give you an example: 1/4 equals 2/8, which equals 25/100.
Complex fractions: Complex fractions are fractions where the numerators and/or denominators are fractions.
Higher term fractions: Higher term fractions refer to fractions where the numerators and denominators of those fractions have a common factor other than 1 (one). So these fractions can be reduced or simplified further. 2/8, for example, is a higher term fraction since 2 and 8 have a common factor, the factor 2, so 2/8 can be simplified (reduced) to 1/4.
Lowest term fraction: This expression refers to fractions that have been fully reduced. There’s only one common factor between the fractions’ numerators and denominators, and that’s 1 (one). 3/4, for example, is a so-called lowest term fraction since it is not possible to reduce it any further.
Mixed numbers: We speak of Mixed Numbers when we deal with numbers that are made up of whole numbers plus fractions. Mixed Numbers have whole number parts and fraction parts, for example, 4 1/5
Simplest terms: This refers to fractions of which the numerators and denominators have only the number one (1) as the common factor.
Decimals: Decimals are numbers based on the number ten (10). You can think of decimals as special types of fractions where the fraction’s denominator is a power of ten (10).
Decimal points: These are periods or dots that are parts of decimal numbers. They indicate where whole numbers stop and the fraction portions begin.
Percents: -Percents are special types of fractions where the denominators are 100 (one hundred). We can write them using the % (percent) sign. For example, we can write 50%, which is the same as 50/100 or 1/2.
Proportions: Proportions are equations that state that two ratios are equivalent. For example, 1/2 = 2/4 and 1/4 = 2/8 are proportions.
Ratios: We speak of ratios when we compare two numbers. We can write ratios in a number of ways. The following, for example, are all different ways for writing the same one ratio: 1:2, 1/2, 1 of 2.
Reciprocals: We speak of reciprocals of fractions when we switch (or flip) the fractions’ numerators and denominators. When we multiply these reciprocals with the original numbers, we always get the number one (1). For example, the reciprocal of 3/6 is 6/3, and the reciprocal of 6 is 1/6. All numbers, except for 0, have reciprocals.
If you get used to these terms, words, and expressions, you’ll be better prepared to complete Math exams successfully.