Fraction Equivalent 3 4

[Telly Piatt]

Equivalentfractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the . A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole.

Equivalent fractions state that two or more than two fractions are said to be equal if both results the same fraction after simplification. Let us say, a/b and c/d are two fractions, after the simplification of these fractions, both result in equivalent fractions, say e/f, then they are equal to each other.

Equivalent fractions are evaluated by multiplying or dividing both the numerator and the denominator by the same number. Therefore, equivalent fractions, when reduced to their simplified value, will all be the same.

Note: We can only multiply or divide by the same numbers to get an equivalent fraction and not addition or subtraction. Simplification to get equivalent numbers can be done to a point where both the numerator and denominator should still be whole numbers.

Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both are equal to 3/4 when simplified.

All equivalent fractions get reduced to the same fraction in their simplest form as seen in the example given above. Explore the given lesson to get a better idea of how to find equivalent fractions and how to check if the given fractions are equivalent.

Equivalent fractions are defined as those fractions which are equal to the same value irrespective of their numerators and denominators. For example, both 6/12 and 4/8 are equal to 1/2, when simplified, which means they are equivalent in nature.

Example: 1/2, 2/4, 3/6, and 4/8 are equivalent fractions. Let us see how their values are equal. We will represent each of these fractions as circles with shaded parts. It can be seen that the shaded parts in all the figures represent the same portion if seen as a whole.

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified. Let us understand the two ways in which we can make equivalent fractions:

To find the equivalent fractions for any given fraction, multiply the numerator and the denominator by the same number. For example, to find an equivalent fraction of 3/4, multiply the numerator 3 and the denominator 4 by the same number, say, 2. Thus, 6/8 is an equivalent fraction of 3/4. We can find some other equivalent fractions by multiplying the numerator and the denominator of the given fraction by the same number.

To find the equivalent fractions for any given fraction, divide the numerator and the denominator by the same number. For example, to find an equivalent fraction of 72/108, we will first find their common factors. We know that 2 is a common factor of both 72 and 108. Hence, an equivalent fraction of 72/108 can be found by dividing its numerator and denominator by 2. Thus, 36/54 is an equivalent fraction of 72/108. Let us see how the fraction is further simplified:

We need to simplify the given fractions to find whether they are equivalent or not. Simplification to get equivalent numbers can be done to a point where both the numerator and denominator should still be whole numbers. There are various methods to identify if the given fractions are equivalent. Some of them are as follows:

The denominators of the fractions, 2/6 and 3/9 are 6 and 9. The Least Common Multiple (LCM) of the denominators 6 and 9 is 18. Let us make the denominators of both fractions 18, by multiplying them with suitable numbers.

Note: If the fractions are NOT equivalent, we can check the greater or smaller fraction by looking at the numerator of both the resultant fractions. Hence, this method can also be used for comparing fractions.

We can see that the shaded portions of both the circles depict the same value. In other words, it can be seen that the shaded parts in both the figures represent the same portion if seen as a whole. Hence, the given fractions are equivalent.

Charts and tables are often used to represent concepts in a better way since they serve as a handy reference for calculations and are easier to understand. Anchor charts and tables, like the one given below, make it easier for the students to understand equivalent fractions. Let us use the following chart to find the equivalent fractions of 1/4.

Two or more fractions are said to be equivalent fractions if they are equal to the same value irrespective of their numerators and denominators. For example, 2/4 and 8/16 are equivalent fractions because they get reduced to 1/2 when simplified.

If the given fractions are simplified and they get reduced to a common fraction, then they can be termed as equivalent fractions. Apart from this, there are various other methods to identify whether the given fractions are equivalent or not. Some of them are as follows:

When two fractions are equivalent, it means they are equal to the same value irrespective of their different numerators and denominators. In other words, when they are simplified they get reduced to the same fraction.

An equivalent improper fraction means an equivalent fraction in an improper form. A fraction is said to be improper when its numerator is greater than its denominator. For example, 3/2 is an improper fraction that is equivalent to 9/6.

Any two fractions can be considered to be equivalent if they are equal to the same value. There are various methods to find out if the fractions are equivalent. The basic method is by reducing them. If they get reduced to the same fraction they are considered to be equivalent.

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified. For example, let us write an equivalent fraction for 2/3. We will multiply the numerator and denominator by 4 and we will get (2 4)/(3 4) = 8/12. Therefore, 8/12 and 2/3 are equivalent fractions.

Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.

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Purpose: Overprediction of the potency and toxicity of high-dose ablative radiotherapy such as stereotactic body radiotherapy (SBRT) by the linear quadratic (LQ) model led to many clinicians' hesitating to adopt this efficacious and well-tolerated therapeutic option. The aim of this study was to offer an alternative method of analyzing the effect of SBRT by constructing a universal survival curve (USC) that provides superior approximation of the experimentally measured survival curves in the ablative, high-dose range without losing the strengths of the LQ model around the shoulder.

Methods and materials: The USC was constructed by hybridizing two classic radiobiologic models: the LQ model and the multitarget model. We have assumed that the LQ model gives a good description for conventionally fractionated radiotherapy (CFRT) for the dose to the shoulder. For ablative doses beyond the shoulder, the survival curve is better described as a straight line as predicted by the multitarget model. The USC smoothly interpolates from a parabola predicted by the LQ model to the terminal asymptote of the multitarget model in the high-dose region. From the USC, we derived two equivalence functions, the biologically effective dose and the single fraction equivalent dose for both CFRT and SBRT.

Results: The validity of the USC was tested by using previously published parameters of the LQ and multitarget models for non-small-cell lung cancer cell lines. A comparison of the goodness-of-fit of the LQ and USC models was made to a high-dose survival curve of the H460 non-small-cell lung cancer cell line.

Conclusion: The USC can be used to compare the dose fractionation schemes of both CFRT and SBRT. The USC provides an empirically and a clinically well-justified rationale for SBRT while preserving the strengths of the LQ model for CFRT.

Equivalent fractions come up a lot in elementary school and some children can be a little unsure as to what they are. This article is aimed at teachers to help make things a little clearer.

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