Dividing fractions
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This document discusses three methods for dividing fractions: 1) Using the "keep-change-flip" rule where the first fraction is kept, the division symbol is changed to multiplication, and the second fraction is flipped. 2) Modeling the division problem by determining how many parts of the divisor fit into the dividend. 3) Converting both fractions to decimals and performing decimal division.
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Division of decimals
Dividing decimals involves the following steps:
1. When dividing a decimal by a whole number, place the decimal point in the quotient above the decimal point in the dividend. Divide as usual.
2. When dividing one decimal by another, move the decimal point in the divisor right until the end of its digits and move the decimal point in the dividend the same number of places.
3. Terminating decimals stop at a certain digit. Repeating decimals have a repeating digit or group of digits that is usually denoted with a bar.
Dividing decimals part 1
This document provides instructions and examples for dividing decimals. It explains that when dividing a decimal by a whole number, the decimal point is placed in the quotient directly above the decimal point in the dividend. It also explains that when dividing decimals, the decimal point in the divisor is moved to the right until the end of its digits, and the decimal point in the dividend is moved the same number of places. This is demonstrated through examples of dividing decimals by whole numbers and decimals.
Dividing Fractions
This document provides instructions for dividing fractions. It begins by giving examples of dividing whole numbers and fractions. It explains that when dividing fractions between 0 and 1, the quotient will be larger than at least one of the fractions. The steps for dividing fractions are then outlined: 1) convert fractions to improper form, 2) keep the first fraction, 3) change the operation to multiplication, 4) take the reciprocal of the second fraction, 5) multiply the numerators and denominators, and 6) simplify if possible. Several examples are worked through to demonstrate the process.
Decimals Problem Solving
Rashid has Dh 45 and spends some of it buying coffee and hot dogs. The document also includes word problems about purchasing items with certain amounts of money and prices of drinks at a coffee shop. It provides exercises for students to practice solving word problems involving decimals when making purchases and converting numbers to words.
Multiplication of decimals
This document provides examples and instructions for multiplying mixed decimals. It explains that when multiplying a mixed decimal by a whole number or another mixed decimal, you multiply as usual but pay attention to the number of decimal places in the factors and product. The product should have the same number of decimal places as the total number of decimal places in the factors. Several word problems involving rates and distances are solved as examples using multiplication of mixed decimals.
Adding and subtracting fractions
Adding and subtracting fractions involves making the bottom numbers the same by finding the lowest common multiple and multiplying the top numbers of each fraction by the same amount. Then the top numbers are either added or subtracted, while keeping the bottom number the same, to obtain the final fraction answer. The document provides steps for adding the fractions 3/4 and 1/3 as an example.
Adding Fractions With Unlike Denominators
To add or subtract fractions with unlike denominators:
1. Find the least common multiple (LCM) of the denominators.
2. Write the fractions with this LCM as the new denominator by multiplying the numerators and denominators.
3. Add or subtract the new numerators and put over the common denominator.
4. Simplify the final fraction if possible by dividing the numerator and denominator by common factors.
Proper; Improper & Mixed Number Fractions
This document discusses different types of fractions:
- Proper fractions have a numerator less than the denominator (e.g. 1/4).
- Improper fractions have a numerator greater than or equal to the denominator (e.g. 5/3).
- Mixed numbers are a combination of a whole number and a proper fraction (e.g. 2 1/4).
The document provides examples of converting between improper fractions and mixed numbers by dividing the numerator by the denominator to get the whole number part and remainder.
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Division of decimals
Dividing decimals involves the following steps:
1. When dividing a decimal by a whole number, place the decimal point in the quotient above the decimal point in the dividend. Divide as usual.
2. When dividing one decimal by another, move the decimal point in the divisor right until the end of its digits and move the decimal point in the dividend the same number of places.
3. Terminating decimals stop at a certain digit. Repeating decimals have a repeating digit or group of digits that is usually denoted with a bar.
Dividing decimals part 1
This document provides instructions and examples for dividing decimals. It explains that when dividing a decimal by a whole number, the decimal point is placed in the quotient directly above the decimal point in the dividend. It also explains that when dividing decimals, the decimal point in the divisor is moved to the right until the end of its digits, and the decimal point in the dividend is moved the same number of places. This is demonstrated through examples of dividing decimals by whole numbers and decimals.
Dividing Fractions
This document provides instructions for dividing fractions. It begins by giving examples of dividing whole numbers and fractions. It explains that when dividing fractions between 0 and 1, the quotient will be larger than at least one of the fractions. The steps for dividing fractions are then outlined: 1) convert fractions to improper form, 2) keep the first fraction, 3) change the operation to multiplication, 4) take the reciprocal of the second fraction, 5) multiply the numerators and denominators, and 6) simplify if possible. Several examples are worked through to demonstrate the process.
Decimals Problem Solving
Rashid has Dh 45 and spends some of it buying coffee and hot dogs. The document also includes word problems about purchasing items with certain amounts of money and prices of drinks at a coffee shop. It provides exercises for students to practice solving word problems involving decimals when making purchases and converting numbers to words.
Multiplication of decimals
This document provides examples and instructions for multiplying mixed decimals. It explains that when multiplying a mixed decimal by a whole number or another mixed decimal, you multiply as usual but pay attention to the number of decimal places in the factors and product. The product should have the same number of decimal places as the total number of decimal places in the factors. Several word problems involving rates and distances are solved as examples using multiplication of mixed decimals.
Adding and subtracting fractions
Adding and subtracting fractions involves making the bottom numbers the same by finding the lowest common multiple and multiplying the top numbers of each fraction by the same amount. Then the top numbers are either added or subtracted, while keeping the bottom number the same, to obtain the final fraction answer. The document provides steps for adding the fractions 3/4 and 1/3 as an example.
Adding Fractions With Unlike Denominators
To add or subtract fractions with unlike denominators:
1. Find the least common multiple (LCM) of the denominators.
2. Write the fractions with this LCM as the new denominator by multiplying the numerators and denominators.
3. Add or subtract the new numerators and put over the common denominator.
4. Simplify the final fraction if possible by dividing the numerator and denominator by common factors.
Proper; Improper & Mixed Number Fractions
This document discusses different types of fractions:
- Proper fractions have a numerator less than the denominator (e.g. 1/4).
- Improper fractions have a numerator greater than or equal to the denominator (e.g. 5/3).
- Mixed numbers are a combination of a whole number and a proper fraction (e.g. 2 1/4).
The document provides examples of converting between improper fractions and mixed numbers by dividing the numerator by the denominator to get the whole number part and remainder.
Changing improper fractions to mixed forms and vice
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2) There are several methods to find the GCF and LCM, including listing factors, using a factor tree, and continuous division. These methods involve breaking numbers down into their prime factors to identify common factors or multiples.
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The daily lesson plan outlines a mathematics lesson for year 6 pupils on dividing fractions, with the learning objective being that pupils will learn to divide fractions with a whole number and a fraction. The lesson includes a paper-folding activity, interactive questions to check understanding, and a plenary game where pupils will roll dice to generate division problems and find quotients in groups. The vocabulary, previous knowledge, problem, and learning outcome are also defined.
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The document provides instructions and materials for a 6th grade math project on fractions. It includes objectives, materials needed, how to make the project, rubric for grading, and content about fraction meanings, equivalent fractions, comparisons, operations, and exercises. The content is organized into sections covering key fraction concepts.
Fractions & decimals
This document provides instructions for converting decimals to fractions and fractions to decimals. It explains that for decimals to fractions, the whole number is the numerator, the place value of the decimal determines the denominator, and the number to the right of the decimal is the numerator. For fractions to decimals, the fraction is set up as a division problem, with the numerator as the dividend and denominator as the divisor, zeros are added as placeholders, and the decimal is pulled up into the quotient. Examples are provided and the document emphasizes keeping track of place value in the conversions.
Fractions
Fractions represent quantities that cannot be represented by whole numbers. A fraction consists of a numerator and denominator, where the denominator tells how many equal parts the whole is divided into and the numerator tells how many of those parts are being considered. Fractions can have equivalent forms when the whole is divided into a different number of parts. To compare fractions, they must first be converted to equivalent fractions with a common denominator. The fraction with the larger numerator is the greater fraction.
M & d fractions
This document provides instructions and examples for multiplying and dividing fractions. It explains that when multiplying fractions, you change any mixed numbers to improper fractions, cross cancel where possible, and multiply horizontally. When dividing fractions, you keep the first fraction, switch the division sign to multiplication, flip the second fraction, cross cancel where possible, and multiply horizontally. It then gives examples of multiplying fractions like 1/2 x 1/4 = 1/8 and dividing fractions like 3 1/2 / 1 3/4 = 2 1/2 using these methods. The document concludes with a quiz and answers to check understanding of dividing fractions.
Fractions division
The document discusses dividing fractions. It explains that dividing by a fraction is the same as multiplying by its reciprocal. Specifically, it states that to divide fractions, you turn the second fraction upside down and change the division sign to a multiplication sign. This works for dividing any fractions. Two examples are provided to demonstrate dividing fractions using this method.
Adding and subtracting fractions
1) You cannot add fractions with different denominators without first finding a common denominator. This involves finding the lowest common multiple (LCM) of the denominators and converting the fractions to equivalent fractions with this common denominator.
2) To find the LCM, find the lowest number that both denominators will divide into.
3) Once fractions have a common denominator, you can simply add the numerators and keep the same denominator to add the fractions.
Day 2 multiplying and dividing
This document provides instructions and examples for multiplying and dividing fractions and mixed numbers. It begins with a "Do Now" activity involving subtracting fractions. It then lists homework assignments and provides instructions on dividing fractions by multiplying by the reciprocal of the divisor. The remainder of the document gives examples of multiplying and dividing fractions and mixed numbers, asking for the answers to be written in simplest form.
Ch 2 fractions and decimals
1. The document discusses fractions and decimals, including multiplication of fractions.
2. It introduces multiplying a whole number by a fraction by multiplying the whole number by the numerator and keeping the denominator the same.
3. To multiply two fractions, we multiply the numerators and multiply the denominators of the fractions being multiplied.
CoNverTinG FraCtioNs tO DeCiMaLs
This document discusses converting fractions to decimals. It begins by asking students to explain fractions and decimals. Then it provides two methods for converting fractions to decimals: using proportions or dividing. Examples are shown for converting 1/4, 3/4, and 4/5 to decimals. The document suggests an activity of sorting Skittles by color into fractions and decimals. It concludes by directing students to an online game to practice converting fractions and decimals.
Level 2 prompt
The document provides information on various math topics including counting, ordering numbers, number sequences, times tables, addition, subtraction, multiplication, division, shapes, position and measurement. It includes examples and explanations of concepts like ascending and descending number sequences, number bonds, mental calculation strategies, recording number sentences, properties of 2D and 3D shapes, using measures and sorting/organizing data.
Dividing Decimals By Decimals
This document provides a lesson on dividing decimals. It includes examples of dividing decimals by decimals through multiplying the divisor and dividend by powers of ten to move the decimals. It also includes word problems involving dividing decimals to find averages and unit rates. The lesson concludes with a quiz to assess understanding of dividing decimals.
Four rules of fractions
The document discusses rules for adding, subtracting, multiplying, and dividing fractions. It explains that when adding or subtracting fractions, they must have a common denominator. It demonstrates converting fractions to equivalent fractions with a common denominator to allow for addition or subtraction. The document also covers multiplying and dividing fractions, showing examples like half of 3/4 and 3 1/3 divided by 4 2/3. It encourages practicing fraction operations with number cards and checking the work with a calculator.
Fraction-PPT.pptx
To divide fractions by whole numbers or whole numbers by fractions:
1) Write the division as a fraction divided by a whole number or vice versa.
2) Change the division sign to a multiplication sign and multiply by the reciprocal of the divisor.
3) Simplify the resulting fraction by multiplying the numerators and denominators.
For example, to divide 11/8 by 2: 11/8 ÷ 2 becomes 11/8 × 1/2 = 11/16.
Level 4 prompt
1. This document provides information on mathematical concepts including number patterns, fractions, decimals, percentages, ratios, coordinates, properties of shapes, and probability.
2. Methods for operations with whole numbers, decimals, and fractions are described, including written algorithms for addition, subtraction, multiplication, and division.
3. Information is also provided on topics like factors and multiples, square numbers, angles, perimeter, area, graphs, frequency tables, and Venn and Carroll diagrams.
Level 3 prompt
The document provides examples and explanations of various math concepts including place value, multiples, fractions, decimals, addition, subtraction, multiplication, division, measuring units, classifying shapes, and representing data visually using charts, diagrams and tables. It covers essential math topics for levels 3-4 such as number sequences, operations, geometry, measurement, and data handling.
Understanding fractions
This document is a PowerPoint presentation about fractions for 8th grade students. It contains definitions of key fraction terms like numerator, denominator, improper fractions, and mixed numbers. It explains how to add, subtract, multiply, and divide fractions, including using common denominators for addition and subtraction of unlike fractions. It also discusses equivalent fractions and how to determine if two fractions are equivalent using scale factors or cross-multiplication. The learning objectives are for students to understand fraction operations and how to find equivalent fractions.
DIVISION OF POLYNOMIALS.pptx
The document discusses the steps to perform long division of polynomials. It explains that polynomials are divided by arranging terms in descending order and then repeatedly dividing and subtracting terms until the remainder is zero or has a lower degree than the divisor. The key steps are to divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, multiply the divisor by the quotient term, and subtract it from the dividend. This process is repeated until the division is complete.
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Dividing fractions
- 2. SIMPLE DIVISION 10 2=5 How else can we divide 10 by 2?
- 3. 10 ÷ 2 = 5 How else can we divide 10 by 2? 10 x 1 10 1 10 10 x 2 = 1 x 2 =2= 5 You can multiply by the reciprocal of 2 and you will get the same result. 1 2 and are called multiplicative 2 inverses, or reciprocals.
- 4. METHOD #1: USING THE RULES FOR DIVIDING FRACTIONS: “K. C. F.” 1) Keepthe first fraction. 2) Change the to x. 3) Flip the second fraction. 1 3 1 Ex: a) 5 4 b) 2 4 3 2 6 1 K C FK C Fx= = 1 4 1 2 4 5 x 4 = 20
- 5. METHOD #2: MODELING How can the quotient be larger than the dividend and/or divisor? 1 5 4 This actually means how many ¼-sized pieces can fit into 5 wholes?
- 6. MORE MODELING… 3 1 4 2 How many ½-sized pieces fit in ¾? 3 4 1 1 2 2 1 whole and 1 half of the ½-sized pieces fit in the ¾ space, so = 3 1 1 1 4 2 2
- 7. EVEN MORE MODELING… 1 3 2 ÷ 4 What part of the ¾-sized piece fits in ½? 1 2 3 4 2 of the ¾-sized 3 piece fits in ½
- 8. METHOD #3: DIVIDING DECIMALS INSTEAD Students can turn both fractions into decimals and can divide those instead: 1 = 0.5 3 = 0.75 2 4 3 1 1 3 ÷ = 0.75 ÷ 0.5 ÷ = 0.5 ÷ 0.75 4 2 2 4