...FRACTIONS CONVERSIONS A. Changing a Mixed Number to an Improper Fraction Mixed number – 4 (contains a whole number and a fraction) Improper fraction - (numerator is larger than denominator) Step 1 – Multiply the denominator and the whole number Step 2 – Add this answer to the numerator; this becomes the new numerator Step 3 – Carry the original denominator over Example #1: 3 = 3 × 8 + 1 = 25 Example #2: 4 = 4 × 9 + 4 = 40 B. Changing an Improper Fraction to a Mixed Number Step 1 – Divide the numerator by the denominator Step 2 – The answer from step 1 becomes the whole number Step 3 – The remainder becomes the new numerator Step 4 – The original denominator carries over Example #1: = 47 ÷ 5 or 5 = 5 = 9 2 Example #2: = 2 = 2 = 4 C. Reducing Fractions into the Lowest Terms Step 1 – Find a number that will divide into both the numerator and the Denominator or the (GCF) Step 2 – Divide numerator and denominator by this number Example #1: = (because both 10 and 15 are divisible by 5) Example #2: = (because both 4 and 8 are divisible by 4) D. Raising Fractions to Higher Terms When a New Denominator is Known Step 1 – Divide the new denominator by the old denominator Step 2 – Multiply the numerator by the answer from step 1 to find the new numerator *Note: If the original...
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...Definition of a fraction – A fraction is a number that is an integer multiple of a unit fraction. Fractions are a part of our everyday lives and are used extensively in the business and finance related area. They may be represented as precents and rates – error rate, interest rate, employment rate, productivity levels, etc. Trades and manufacturing are also prolific users of fractions in the length of materials, how many lengths fit into a structure and working out quantities of material need to complete a batch or run of product, (Tucker, 2008). Fractions can be represented in many different ways, the mathematical notation for a fraction is represented as k(1/l) and for whole numbers k,l(l>0) or in the common form of ¼ or ½ . Commonly found representations of fraction for the purpose of teaching are equally divided circles or rectangle. The concept of fractions are a difficult to teach part of mathematics as the younger ages can struggle to comprehend the shift from whole numbers to units, fractions or parts of a number. This can be due to many factors including the inability to conceptualise the breaking up of a whole into parts or units, (Pengelly, 1991). A good start to allowing children to comprehend this is the use of base shapes such as triangles or squares and to break these up into parts and get the students to work out how many parts of the whole there are, therefore working out the fraction that is required. This can be progresses to more difficult learnings...
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...have when working with fractions. This essay will look at what some the misconceptions are and how we can try to help pupils overcome them. Common misconception associated with fractions. Fractions is a great area of mathematics to explore misconceptions as ‘Many errors occur when children work with fractions because of the lack of understanding of the concept of the unit involved.’ Frobisher et al (1999). Thus this assignment will only to look at a few misconceptions that occur at the beginning of studying fractions. We will look at what the common errors are when pupils are studying fractions and what the literature suggests to help pupils understand fractions and overcome these misconceptions. Understanding what a fraction represents Lamon (2005) explains how this is where a lot of misconceptions develop from early on where pupils don’t understand a fraction actually represents. A common error is that pupils look at fractions like they are ‘two unrelated whole numbers’ and would describe ‘2/3’ as ‘two and three’ (Mcleod & Newmarch, 2006). This is also an area which Hart (1981) highlights as when pupils are presented with a fraction ,for example, 2/5 many of the pupils will see this as 5/2 as they do not understand what the fraction represents and it is not interchangeable. Clausen-May (2005) discusses how the use of pictures can be useful to help pupils understand what a fraction means, however the use of pictures to analyse fractions needs to be used with...
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...{//*********************************multiplication************************************ class A { public int multiply(int a,int b) { return a * b; } public double multiply(int a, double b) { return a * b; } public double multiply(double a, double b) { //1 argument type different OVERLOADING can be performed return a * b; } }//*********************************fraction************************************ #region fraction class fraction { int numerator, denominator; //field public void display() { Console.WriteLine(numerator + "/" + denominator); } public fraction() { numerator = 0; denominator = 1; } public fraction( int n, int d) { numerator = n; denominator = d; } public fraction(int n) { numerator = n; denominator = 1; } } #endregion //*********************************length************************************ #region length class length { int feet, inches; public void display() { if (inches >= 12) { feet = feet + (inches / 12); inches = inches % 12; } Console.WriteLine(feet...
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...The worksheet consists of a chart with a given decimals, fractions, and/or percent. The student must evaluate and convert the given information to solve for the remaining equivalent percent, decimal, and/or percent. “In converting a decimal to a fraction, we take advantage of the fact that we use the base ten system to write each decimal number. For example, the number 0.3 is called three-tenths and so is equivalent to 3/10. The number 0.35 is read as 35 hundredths and so is the same as 35/100.” “Some fractions can be converted to an equivalent fraction with a denominator that is a power of 10, such as 10, 100, or 1000. In this case, the new equivalent fraction can be written as a decimal quite easily. For example, 3/25 is equivalent to 3x4/25x4=12/100=0.12. We used the factor 4 because 4 times 25 gives us the product 100.” “It is useful to convert some fractions into decimal form by finding the equivalent fraction with the denominator of 100. In converting decimals to percent’s, you can multiply the decimal by 100 to get the percent. For instance (0.75)(100) =75%. We will illustrate this using the “Conversion Chart” worksheet. Test your skills by completing...
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...7 7.1 Introduction to Rational Expressions 7.2 Multiplication and Division of Rational Expressions 7.3 Addition and Subtraction with Like Denominators 7.4 Addition and Subtraction with Unlike Denominators 7.5 Complex Fractions 7.6 Rational Equations and Formulas 7.7 Proportions and Variation Rational Expressions There is nothing wrong with making mistakes. Just don't respond with encores. —ANONYMOUS ne of the most significant problems facing the U.S. transportation system is chronic highway congestion. According to a newly released “Highway Statistics,” Americans drove about 3 trillion miles in 2009. Our ability to keep traffic moving smoothly and safely is key to keeping our economy strong, and traffic congestion costs motorists more than $87 billion annually in wasted time and fuel. A 2007 study found that, collectively, Americans spend as many as 4.2 billion hours stuck in traffic each year. If the amount of traffic doubles on a highway, the time spent waiting in traffic may more than double. At times, only a slight increase in the traffic rate can result in a dramatic increase in the time spent waiting. (See Example 6 in Section 7.1.) Mathematics can describe this effect by using rational expressions. In this chapter we introduce rational expressions and some of their applications. O ISBN 1-256-49082-2 Source: Randy James, “America: Still Stuck in Traffic.” Time.com, July 9, 2009; U.S. Department of Transportation, 2011. 419 Beginning and Intermediate...
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... |余数 | |prime number |质数，素数 | |prime factor |质因子，质因数 | |composite number |合数 | 2.分数 |common factor |公因子 | |reciprocal/inverse |倒数 | |mixed number |带分数 | |improper fraction |假分数 | |proper fraction...
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... THREADED DISCUSSION PROBLEMS – Fractions, Decimals & Percents – WEEK # 1 1) Convert percentage 4.0005 % to decimal. = .040005 (1) Solution: Move the decimal 2 places to the left and drop the percent sign. Since there is only one number to the left you need to add a “0”. 2) Convert percentage 400.05 % to an improper and a mixed fraction. = 8,001/2,000 and 4 1/ 2,000 ((1 pt each) Solution: Move the decimal 2 places to the left and drop the percent sign (4.0005). Place this number over 4 zeros (the number of places to the right of the decimal in the numerator). Precede it with a “1” (.0005/10,000) NOTE: The “4” is not included here but brought back when the final answer is stated. Drop the decimal in the numerator and you have 0005/10,000. Since the zeros no longer have relevance, eliminate them and you now have 5/10,000 that reduces to 1/2,000. Now bring back the whole number 4 and you have 4 1/2,000…your mixed number answer. To get an improper fraction where your numerator is greater than your denominator just take your mixed fraction and multiply the whole number (4) times the denominator of the fraction portion of the mixed number (2,000) to get 8,000...then add the numerator of (1) to the 8,000 and place it all over the denominator of the fraction (2,000) to get 8,001/2,000,your improper fraction answer. 1 pt each) 3) Convert decimal 4.0555 to an improper and a mixed fraction. = 8,111/2,000 and 4 111/2,000 (1...
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...fuelgaugereport.com/ 2. Using the internet, find a website that will show you houses for sale. http://www.trulia.com/ 3. Find a website that shows one how to do fraction to decimal conversions. http://www.webmath.com/fract2dec.html 4. Using the internet, find a website that one can use to find the national average cost of food for an individual, as well as for a family of 4 for a given month. http://www.cnpp.usda.gov/sites/default/files/usda_food_plans_cost_of_food/CostofFoodJan2012.pdf 5. Find a website for your local city government. http://www.usa.gov/Agencies/Local.shtml 6. Find the website for your favorite sports team (state what that team is as well by the link). http://blackhawks.nhl.com/ (Chicago Blackhawks) 7. Many of us do not realize how often we use math in our daily lives. Many of us believe that math is learned in classes, and often forgotten, as we do not practice it in the real world. Truth is, we actually use math every day, all of the time. Math is used everywhere, in each of our lives. Math does not always need to be thought of as rocket science. Math is such a large part of our lives, we do not even notice we are computing problems in our lives! For example, if one were interested in baking, one must understand that math is involved. One may ask, “How is math involved with cooking?” Fractions are needed to bake an item. A real world problem for baking could be as such: Heena is baking a cake that requires two and one-half cups of flour. Heena poured...
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...digit. 8) Perform the calculation mentally. 25 ? 25 ? 8 9) Find all the factors of the number. 56 10) If a natural number is divisible by 7, then it must also be divisible by 21. 11) The city bridge has 9 lanes, all carrying equal numbers of cars. If 414 cars drive across the bridge, how many cars cross in each lane? 12) Use each number 5, 6, 7, 8, 9, 10, 11, 12, and 13 once. 13) Find the mixed number or rational fraction in lowest terms represented by the repeating decimal. 0.6969696 . . . 14) Find the amount of money in an account after 7 years if $3600 is deposited at 8% annual interest compounded annually. 15) A man earned $3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15th year? 16) Write or illustrate the number in the indicated form. 7 5 8 9, using expanded notation with exponents 17) Evaluate on a calculator. ( 475 + 7377) - ( 14 + 6) 18) Determine whether the number is abundant or deficient. 150 19) Perform the computation. -3 + ( -20) 20) Write the decimal as a fraction in lowest terms. 4.07 21) Solve the problem. The trim for a costume costs $38.25 for 4.5 yd. Find the unit price in dollars per yard. 22) A rose garden has 16 bushes in one row, 13 bushes in the next row, then 10, and so on. If there are 51 bushes in the garden, in how many rows are they planted? 23) Identify the following. 24) An electrician needs 766 feet of 12-gauge wire to do a wiring job. He has 140 feet o...
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...the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? Let “x” be the number we will find for the bear population. x = 100 I will cross multiply this equation. 50 2 2x = 50 * 100 After cross multiplying. 2x = 5,000 Multiplied the number of released bears to the Sample bears X = 2,500 Divided 2 on each side and this is the final answer Of how many bears is the estimated population. The second problem is #10 from page 444. For the second equation, I need to solve for y. This is a single fraction ratio on both sides of the equal sign. This would be considered a proportion which I can solve by cross multiplying the extreme means of the equation. y-1 = -3 Equation x+3 4 y-1 * (x+3) = -3 * (x+3) Multiply x+3 to both sides. x+3 4 y-1 = -3x+3 Add 1 to 3. This appears to be a solution but causes 4. 0 in a denominator is called an extraneous Solution. Y = -3x +4 Answer. 4 The type of equation that was the answer in problem 10 is called a linear equation. The coefficient of x is different than the original problem. It was x+3 and in this case, it was...
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...Why can’t I divide by zero? The explanation of why we cannot divide any number by zero is really easy. The three links contain different explanations, but eventually, they all come down to one. To begin, it is said that we students are told that a division by zero is undefined. And this, supposedly is not entirely true, but somewhat true, they tell us this because they, and we eventually cannot define an answer that would work. But in the other hand, if we are told that a division by zero equals to infinity, then that is entirely NOT true. Why? Because as the contents say, infinity is not a number, it is simply like a concept let’s say, because if it would be a number, there would be many contradictions, like the “collision” of our whole number system. So, as mathematician Mahavira (9th century A.D.) said “A number remains unchanged when divided by zero.”, we can get to the simple and easy conclusion that a number cannot be divided by zero simply because, if you multiply that number by zero, the answer will ALWAYS be zero. Now, in the case of 0/0=0, we may say that that is true because 0x0=0, and that may lead to us thinking or realizing that dividing by zero can give you a real number, but this is wrong. We must not confuse, as I said above, any number times zero will equal zero, so therefore the answer to 0/0 can be any number. And also, we must not forget that any number divided by that same number, will equal to one (1/1=1, 2/2=1,3/3=1..), so in that case of zero...
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...Convert Decimals to Fractions (Multiply top and bottom by 10 until you get a whole number, then simplify) To convert a Decimal to a Fraction follow these steps: Step 1: Write down the decimal divided by 1, like this: decimal/1 Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Step 3: Simplify (or reduce) the fraction Example: Express 0.75 as a fraction Step 1: Write down 0.75 divided by 1: 0.75 1 Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100): × 100 0.75 = 75 1 100 × 100 (Do you see how it turns the top number into a whole number?) Step 3: Simplify the fraction (this took me two steps): ÷5 ÷ 5 75 = 15 = 3 100 20 4 ÷5 ÷ 5 Answer = 3/4 Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction ! Example: Express 0.625 as a fraction Step 1: write down: 0.625 1 Step 2: multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000) 625 1,000 Step 3: Simplify the fraction (it took me two steps here): ÷ 25 ÷ 5 625 = 25 = 5 1,000 40 8 ÷ 25 ÷ 5 Answer = 5/8 Example: Express 0.333 as a fraction Step 1: Write down: 0.333 1 Step 2: Multiply both top and bottom by...
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...A Detailed Lesson Plan in Mathematics VI I. OBJECTIVES * Name the fractions and described by a shaded region. Value: Work Cooperatively II. SUBJECT MATTER “Writing Fractions Described” REFERENCE: PELC IV G-I MATERIALS: Flashcards, Visual aids, basket, ball. III. PROCEDURE TEACHER’S ACTIVITY | PUPIL’S ACTIVITY | 1. PRAYER Class, stand up and let us pray.(The teacher will call a student to lead the prayer.) 2. GREETING “Good morning Class”You may now take your seat. 3. CHECKING OF ATTENDANCE Alright, before we start let us check first your attendance. 4. CHECKING OF ASSIGNMENTClass do we have an assignment? Pass your notebook in front and we will check it later. 5. ENERGIZERClass, do you like to sing and dance? Let us sing your mathematics song. | (The assign student will come in front and pray.) Good morning Ma’am. Good morning classmates it’s nice to see you. (The assign student will stand and tell who is absent in the class.) Yes Ma’am. (The student will pass their assignment.) Yes Ma’am. (The student will sing together with the teacher.) | 6. DRILL Class I have here a flashcards that contains of number that you need to answer orally. 5x4 =6x6 =7x8 =1x5 =9x6 = 7. REVIEW Class, before we start our new lesson...
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...Rational Expressions A rational expression is a quotient of two polynomials P and Q, with . A rational expression is a ratio of two polynomials in which the denominator is not the zero polynomial. The denominator must also have a variable in it to be considered a rational expression. The domain of a rational expression includes any number that DOES NOT make the denominator zero. (Remember: you cannot divide by zero.) Example: Objectives: -Find the domain of a rational expression -Putting an expression in lowest terms -Multiplying and dividing rational expressions -Adding and subtracting rational expressions -Simplifying complex fractions The domain of a rational expression can be found by setting the factored denominator equal to zero and solving the resulting equation. For the example above, you would set x + 2 = 0 and get x = 2. Therefore, the domain is every number except x = 2. You can write the domain in two ways… Set notation: This reads…x such that x cannot equal 2. Interval notation: Example 1: Find the domain of each rational expression. (a) Since the denominator is already factored, we can set each part equal to zero and find our exclusions for the domain. This expression can actually be simplified as well, but you ALWAYS find the domain before you simplify the expression. and Domain: or (b) First, factor the denominator. factors into Now set both parts equal to zero and Domain: ***Most of the time, set notation is used...
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