Definition Of A Common Denominator

Common Denominator

A mutual denominator is helpful to perform numerous mathematical operations on numbers. An of import concept in Mathematics is the addition and subtraction of fractions. Fractions include a numerator (the number on acme) and a denominator (the number below). The fractions which take the same denominators, such denominators are called common denominators. Consider the post-obit examples: 1/2 + 1/2 = i and 3/iv + 1/iv = 1 In both cases, the denominators in the fractions are common, hence, it is easy to calculate the answer.

Withal, if yous are given a problem with unlike denominators, how would you solve it. A adding of 2/v + 3/4 is difficult to perform because of different denominators. Since the denominators in the fractions are not the same, nosotros have to solve them using a different method. Allow the states explore this topic to learn more most the common denominators.

1.	What is a Common Denominator?
2.	How to find a Common Denominator?
iii.	Common Denominator Examples
4.	Common Denominator Methods
five.	FAQs on Common Denominator

What is a Mutual Denominator?

Two or more fractions having the same denominator are referred to every bit a mutual denominator. The common denominator helps to easily perform numeric calculations. The number shown in the lower role of a fraction is called the denominator. The denominator shows you lot how many equal parts an item is divided into.

Common Denominator

In the above figure, there are four slices in the offset pizza. Thus, it is represented as 1, that is, a whole. When we take away one slice, nosotros accept 3 out of 4 slices, remaining. Thus, the fraction of the remaining slices is given every bit 3/4. This also means that i/4 slice has been taken away. If we are to add these 2, nosotros get: 1/iv + 3/4 = 4/4 = 1. Further, depending on the size of the pizza, you can split it into as many parts every bit y'all desire.

How to find a Common Denominator?

While the example of the pizza shows you how simple information technology is to discover the common denominator, you may not always exist presented with such a situation. There may be times where you are asked to add fractions with unlike denominators like 3/7 + 12/xiii. In such cases, we need to find the common denominator and then solve the fractions. Permit's expect at a simpler example 1/three + 1/6. Given below are the two mutual denominator methods to detect the reply:

By finding the least common multiple
By cross multiplication

When you solve for the mutual denominator using the LCM method, you observe the to the lowest degree mutual multiple of the given numbers. In this equation, the least mutual multiple is 6. Hence, the equation becomes 1/iii + 1/6 = (1 x 2 + 1)/six = (2 + i)/half dozen = 3/half dozen = ane/two. If you cross multiply, you will find the solution every bit: one/3 + 1/6 = 2/6 + 1/6 = (2 + one)/half-dozen = 3/vi = one/two

Common Denominator Examples

Examples of common denominators in our everyday lives include pizza slices, money, cooking and baking, then on. The pizza every bit an example can be sliced into iv slices and the possible parts of the pizza can be 1/four. 2/4, three/4 respectively. Further, nosotros tin can detect the common denominators in instances we are sharing equal amounts of a quantity. In such a situation, the common denominators would be equal to i/2 and 1/2 or 1/four and 1/iv respectively.

Example of Common Denominator

Practically much of the daily life examples where quantities have been divided tin can be expressed every bit a common denominator. Another practiced example of a common denominator can exist found in cooking and baking - yous need fractions and denominators to measure the ingredients to make a cake.

Mutual Denominator Method

The common denominator methods, as explained above, include calculating the to the lowest degree common multiple or cross-multiplying. Mutual denominators are the products of the denominators of the given fractions. However, you demand to remember that also this, common denominators are also the factors that the fractions have in mutual and the factors that brand each fraction different. A common denominator includes all factors from each fraction.

Examples on Common Denominator

Example 1: Stephen is a silversmith who is soldering two silverish coins together. The first coin has a diameter of 3/iv inch and the second coin has a bore of 7/8 inch. What is the sum of the diameters of the coins?

Solution:

Here, nosotros need to add the diameters of the two coins. The bore of the first money is 3/4 inch and that of the second coin is 7/eight. The sum of the diameters is 3/4 + 7/8 = (3 ten 2)/(4 10 2) + 7/8 = half-dozen/8 + 7/8 = (7 + 6)/viii = xiii/viii = \(ane\frac{v}{8}\). Thereforethe sum of the diameters of the 2 coins is \(1\frac{five}{8}\).
Example 2: Violet's stopwatch is malfunctioning and now, it just shows time in fractions. She is running effectually a track and recording the time it takes to complete each of the ii laps. Her start lap time was 54/five minutes and her second lap time was 85/4 minutes. Find the total time.

Solution:

The sum of the times of each of the laps is 54/5 + 85/4 = 216/20 + 425/20 = (216 + 425)/twenty = 641/xx. Thus, the sum of the time of the two laps is 641/20 minutes.

\(\therefore\) the full time for the two laps is 641/xx minutes.
Example 3: Can you help Terry find the common denominator for 2/3 and iv/5?

Solution:

The denominators of both the fractions are 3 and v respectively. The lcm of iii and 5 is 15 and 15 is the common denominator of the two given fractions.

\(\therefore\) the mutual denominator for 2/3 and iv/5 is 15.
Instance 4: Are the rational numbers -9/12 and 21/-28 equal?

Solution:

The two given fractions can be simplified -nine/12 = -3/4 and 21/-28 = iii/-iv = -iii/4. Since the simplified value of the two fractions is the same the two rational numbers are also equal.

\(\therefore\) the two rational numbers -nine/12 and 21/-28 are equal.

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FAQs on Mutual Denominator

What Is a Common Denominator?

A mutual denominator is that in which the denominator i.e. the number below the fraction is the aforementioned throughout, thereby making your adding process simpler. In case the two fractions do not have a common denominator, and so yous demand to calculate the common denominator to become your answer.

How to Find the Common Denominator?

For a sum like 3/4 + 1/4 = 1, the common denominator is 4. Withal, when you are given a adding such as 3/4 + 1/2, then you volition demand to find the common denominator for both three/four + 1/two. You can practice this past either finding the least common multiple or cross-multiplying the in a higher place equation.

What is the Common Denominator of 3 and 4?

Unlike the previous instance, in this case, neither iii nor four are factors of each other. In this instance, you can calculate the value of the common denominator past multiplying both numbers to get 12.

What is the Another Name for Common Denominator?

Another possible name for common denominator is the mutual divisor. Further, based on the denominators, the common denominator tin can be the lcm of the two denominators. Also, if i denominator is the factor of another denominator, then we tin take the larger number as the to the lowest degree common denominator.

How to Find the Least Common Denominator?

The least mutual denominator depends on the kind of denominator. For denominators with co-prime number numbers, the least common denominator is the product of the two denominators. Also, the least mutual denominator is the lcm of the two given denominators. Allow us consider two denominator values: 4, half-dozen. The to the lowest degree common denominator is the lcm of 4, six, which is the number 12.

What is the Greatest Common Denominator?

The Greatest Mutual Denominator of ii or more fractions, which are not goose egg, is the largest positive integer that divides each of the given denominators.

Can a Common Denominator exist Equal to Zero or 1?

For a fraction with the mutual denominator of zero, it becomes undefined. And for fractions with just whole numbers equally numerators and i equally a denominator, the mutual denominator is i. In the case of whole numbers being considered every bit fractions, the mutual denominator is i.