8:00 GED Math Wednesday Fractions
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This document provides instructions and examples for adding, subtracting, multiplying, and dividing fractions and mixed numbers. It discusses representing whole numbers as fractions, raising fractions to higher terms, reducing fractions to lowest terms, finding common denominators, multiplying fractions as finding a fraction of a fraction, dividing fractions by inverting the divisor, and solving word problems involving fractions.
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Fractions for year 3
1. Fractions represent parts of a whole that is divided into equal parts. A fraction has a numerator above a denominator, where the numerator tells how many parts are being considered and the denominator tells how many parts make the whole.
2. Fractions can be represented on a number line, where each increment represents another equal part of the whole. Common fractions include halves, thirds, and quarters.
3. Fractions are used in everyday situations like baking, where recipes call for measurements like 1/4 cup of an ingredient. They help describe portions or percentages of a whole object or quantity.
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The document discusses key concepts for fractions including changing improper fractions to mixed numbers and vice versa, equivalent fractions through reducing and raising to higher terms, and comparing fractions by finding a common denominator. It provides examples for how to change fractions between improper and mixed number form, reduce fractions, raise fractions to higher terms, and compare fractions.
Year 4 equivalent fractions
This document provides a lesson on equivalent fractions. It explains that two fractions are equivalent if they represent the same amount or portion. For fractions to be equivalent, the same operation must be applied to both the numerator and denominator. Some examples are provided of determining if fractions are equivalent by dividing or multiplying both terms by the same number. Strategies for identifying equivalent fractions involve looking at relationships between the numerator and denominator and applying the same operations to both terms.
Fractions slideshare
This document provides an overview of fractions. It defines a fraction as a number that is not a whole number but part of a whole. Fractions have a numerator and denominator, with the numerator on top and denominator on bottom. The document describes different types of fractions such as proper, improper, and mixed numbers. It provides examples of how fractions are used in everyday situations like measuring ingredients. The objectives are to understand fractions, their components, types, and how to write them in word form.
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This document is a PowerPoint presentation about fractions that contains definitions of key fraction terms and concepts. It discusses what fractions are, the meaning of the numerator and denominator, equivalent fractions using multiplication and division, improper fractions and mixed numbers, adding fractions with common denominators, and finding equivalent fractions using scale factors or cross-multiplication. The overall goal is to help students understand fractions including representing them, comparing them, and performing operations with them.
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This document discusses mixed numbers and improper fractions. It defines proper, improper, and mixed fractions. It provides examples of converting between improper and mixed fractions by multiplying or dividing the whole number by the denominator and writing any remainder over the denominator. Steps are given for converting mixed fractions to improper fractions by multiplying the whole number by the denominator and adding to the numerator, and for converting improper fractions to mixed fractions by dividing the numerator by the denominator.
Multiplying fractions
Multiplying fractions involves multiplying the numerators and denominators, then simplifying the resulting fraction. When multiplying a fraction by a whole number, change the whole number to an equivalent fraction. It is often easier to simplify fractions before multiplying them. To multiply mixed numbers, first convert them to improper fractions, then multiply the numerators and denominators and simplify. Practice problems are provided for the learner to try.
Dividing fractions and Mixed numbers!
Fraction division is the opposite of fraction multiplication. To divide fractions, invert the second fraction and multiply. The steps are to change any whole numbers or mixed numbers to improper fractions, invert the divisor fraction, and multiply the numerators and denominators. Division is not commutative like multiplication, so the order of the fractions matters in word problems involving splitting, sharing, or grouping items.
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Fractions for year 3
1. Fractions represent parts of a whole that is divided into equal parts. A fraction has a numerator above a denominator, where the numerator tells how many parts are being considered and the denominator tells how many parts make the whole.
2. Fractions can be represented on a number line, where each increment represents another equal part of the whole. Common fractions include halves, thirds, and quarters.
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The document discusses key concepts for fractions including changing improper fractions to mixed numbers and vice versa, equivalent fractions through reducing and raising to higher terms, and comparing fractions by finding a common denominator. It provides examples for how to change fractions between improper and mixed number form, reduce fractions, raise fractions to higher terms, and compare fractions.
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This document provides a lesson on equivalent fractions. It explains that two fractions are equivalent if they represent the same amount or portion. For fractions to be equivalent, the same operation must be applied to both the numerator and denominator. Some examples are provided of determining if fractions are equivalent by dividing or multiplying both terms by the same number. Strategies for identifying equivalent fractions involve looking at relationships between the numerator and denominator and applying the same operations to both terms.
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This document provides an overview of fractions. It defines a fraction as a number that is not a whole number but part of a whole. Fractions have a numerator and denominator, with the numerator on top and denominator on bottom. The document describes different types of fractions such as proper, improper, and mixed numbers. It provides examples of how fractions are used in everyday situations like measuring ingredients. The objectives are to understand fractions, their components, types, and how to write them in word form.
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This document is a PowerPoint presentation about fractions that contains definitions of key fraction terms and concepts. It discusses what fractions are, the meaning of the numerator and denominator, equivalent fractions using multiplication and division, improper fractions and mixed numbers, adding fractions with common denominators, and finding equivalent fractions using scale factors or cross-multiplication. The overall goal is to help students understand fractions including representing them, comparing them, and performing operations with them.
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Multiplying fractions
Multiplying fractions involves multiplying the numerators and denominators, then simplifying the resulting fraction. When multiplying a fraction by a whole number, change the whole number to an equivalent fraction. It is often easier to simplify fractions before multiplying them. To multiply mixed numbers, first convert them to improper fractions, then multiply the numerators and denominators and simplify. Practice problems are provided for the learner to try.
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Fraction division is the opposite of fraction multiplication. To divide fractions, invert the second fraction and multiply. The steps are to change any whole numbers or mixed numbers to improper fractions, invert the divisor fraction, and multiply the numerators and denominators. Division is not commutative like multiplication, so the order of the fractions matters in word problems involving splitting, sharing, or grouping items.
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The document provides information about fractions including:
1) Definitions of the different types of fractions such as proper, improper, and mixed fractions.
2) Methods for converting between improper and mixed fractions.
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5) Procedures for performing operations like addition, subtraction, multiplication, and division on fractions.
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Fractions can represent parts of a whole that is divided into equal sections. A fraction has a numerator above the line and a denominator below. Equivalent fractions have the same value even if they look different. Mixed numbers contain a whole number and fraction, while improper fractions are larger than 1. To add or subtract fractions, their denominators must be the same, so they may need to be converted to an equivalent form by multiplying the numerator and denominator by the same number.
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Fractions can represent parts of a whole that is divided into equal sections. A fraction has a numerator above the line and a denominator below. Equivalent fractions have the same value even if they look different. Mixed numbers contain a whole number and fraction, while improper fractions are larger than 1. To add or subtract fractions, their denominators must be the same, so they may need to be converted to an equivalent form by multiplying the numerator and denominator by the same number.
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This document provides instructions for adding and subtracting fractions. It begins by defining key fraction terms like numerator, denominator, and different fraction types. It then explains how to add and subtract similar fractions by keeping the same denominator and combining numerators. The document also demonstrates how to change dissimilar fractions into similar fractions by finding a common denominator. Finally, it shows how to add and subtract mixed numbers and dissimilar fractions by first changing them into similar fractions if needed. Exercises with worked out solutions are provided for students to practice adding, subtracting, and simplifying fractions.
Adding Fractions with Unlike Denominators
Adding fractions with unlike denominators requires finding the least common denominator (LCD) so the fractions have the same denominator. You find the LCD by finding the least common multiple of the denominators. Then you create equivalent fractions with the LCD as the new denominator by multiplying the original numerators and denominators by the same number. Finally, you add the new numerators and keep the LCD as the denominator.
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This document outlines topics to be covered in an upcoming math class, including reducing fractions, comparing fractions, finding common denominators, and setting up and reducing fractions in word problems. It also notes that there will be no class the following Monday as the teacher will be attending a conference. Examples are provided for reducing fractions, comparing fractions, and setting up fractions in word problems.
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The document discusses how to reduce fractions to their simplest form by finding common factors between the numerator and denominator. It explains that to simplify a fraction, you divide both the numerator and denominator by any number that divides into both. Examples show reducing 3/6 to 1/2 and 6/10 to 3/5. It emphasizes the importance of reducing fractions all the way to their lowest form by finding the highest common factor.
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The document introduces fractions using examples like sharing a pizza and cutting pattern blocks and candy bars into equal parts. It explains that a fraction represents a part of a whole and how to write fractions by naming the numerator and denominator. Examples are given for halves, thirds, and fourths. Students are directed to online and book resources to practice visualizing, naming, and exploring fractions using different representations.
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This document provides an overview of fractions including:
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- Explaining equivalent fractions and how to simplify fractions by dividing the numerator and denominator by their greatest common factor
- Describing the different types of fractions such as proper, improper, and mixed fractions
- Covering the key operations of adding, subtracting, multiplying, and dividing fractions including converting fractions to have a common denominator when needed
- Providing examples for simplifying, converting between fraction types, and performing the different fraction operations
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Okay, let's break this down step-by-step:
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* So the increase is $26.70
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Improper fractions have a numerator that is greater than or equal to the denominator and can be converted to mixed numbers. To do so, divide the numerator by the denominator and write the whole number result with the remainder over the denominator. For example, an improper fraction of 15/4 would convert to a mixed number of 3 7/4 by dividing 15 by 4 to get 3 with a remainder of 3, written with the 3 and remainder over the original denominator.
Addition and Subtraction of Similar and Dissimilar Fraction.pptx
The document provides instructions for adding and subtracting fractions with similar and dissimilar denominators. It explains the steps for each process and provides multiple examples. For similar fractions, it describes adding the numerators and copying the denominator before reducing the answer. For dissimilar fractions, it outlines multiplying the denominators, cross multiplying the numerators and denominators, adding or subtracting the products, and reducing the final answer. Several word problems demonstrate applying the steps to real-world scenarios involving fractions.
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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8:00 GED Math Wednesday Fractions
- 1. • 1. GED Practice (Fractions) • 2. Review: Improper/Mixed Numbers • 3. Adding/Subtracting Fractions/Mixed Numbers • 4. Multiplying/Dividing Fractions
- 2. • Change to a mixed number. • Change to an improper fraction. • Raise to higher terms. • Reduce to lowest terms.
- 3. • Find a common denominator. • Write three equivalent fractions for the above with a common denominator of 20.
- 4. +
- 5. • 1. How can one whole be represented as a fraction? • 2. How do you raise a fraction to higher terms? • 3. How do you reduce a fraction to lowest terms? • 4. Why would you raise a fraction to higher terms?
- 7. • When you multiply, you are finding a fraction of a fraction. • The product is smaller than the fractions you multiply. • The phrase “a fraction of” means to multiply. • Multiplying fractions means finding a “part of a part”.
- 8. • Step 1: Multiply the numerators together • Step 2: Multiply the denominators together. • Step 3: Reduce the answer if possible. 21 80
- 9. • To cancel, find a number that divides evenly into the numerator of one fraction and the denominator of the other. 1 2 •Step 1: Divide 3 and 15 by 3 2 •Step 2: Divide 4 and 8 by 4 •Step 3: Multiply the new 1 5 5 numerators and denominators.
- 10. • A whole number can be written as a fraction with a denominator of 1. • Remember: a fraction of means to multiply. Find ¾ of 24. •Step 1: Write 24 as a fraction. •Step 2: Divide 4 and 24 by 4. •Step 3: Multiply across. •Step 4: Change the improper fraction to a whole number.
- 11. • Step 1: Change to an improper fraction. • Step 2: Divide 4 and 6 by 2. • Step 3: Multiply across. • Step 4: Change the improper fraction to a mixed number.
- 12. • In division problems with fractions or mixed numbers, you must invert (flip) the divisor. invert inverse flip
- 13. • Step 1: Write each number in fraction form. (K) • Step 2: Invert the divisor and change the ÷ to a × sign. (SF!) • Step 3: Follow the rules for multiplying fractions. ×
- 14. 1. Can you cross cancel? 2. Multiply Tops and Bottoms straight across! 3. Are you done? 2 × 1
- 15. • Change to an improper fraction and then proceed as usual.