Fractions and Geometry with Ms. Strickert
Models of rational numbers Fraction equivalence, ordering, and simplifying Adding fractions subtracting fractions multiplying fractions Dividing fractions Denseness of fractions
Table of Contents
- Models of Rational Numbers
- Comparing Fractions using Models
- Visualizing Equivalent Fractions Using Models
- Copy of Fraction Models
- Fraction Equivalence, Ordering, and Simplifying
- Equivalent Fractions Number Line
- Simplifying Fractions
- Ordering Fractions
- Adding Fractions
- Fraction Addition/Subtraction - Common Denominators
- Grade 3 Adding Fractions
- Adding fractions on a number line
- Subtracting Fractions
- Subtracting Proper Fractions
- Fraction Addition and Subtraction
- Subtracting fractions
- Multiplying Fractions
- Multiplying Fractions: Array model activity
- Fraction Multiplier
- Multiplying fractions with area model
- Dividing Fractions
- Dividing Fractions
- Dividing Fractions based on patterns
- Denseness of Fractions
- Fraction Between Two Fractions
Comparing Fractions using Models
Compare these fractions.
[size=200]I[/size][size=150][size=200]s the fraction on the left greater than >, less than <, or equal to = the one on the right? [br][br]How do you know? (hint - use the sliders on the right to slide the parts of the circle on top of the other circle). [br][/size][br][size=200]Compare the fractions using the correct symbol (>, < or =).[/size][/size]
What do you notice about the denominators of these fractions?
[size=150][size=200]When fractions have the same denominator, does a larger numerator make the fraction greater than > or less than < the other one?[br][br]Is the fraction on the left greater than > or less than < the one on the right?[br][br]Compare the fractions using the correct symbol (>, < or =).[/size][/size]
What do you notice about the numerators of these fractions?
[size=200]When fractions have the same numerator, does a larger denominator make the fraction larger or smaller than the other one?[br][br][/size][size=200]Which fraction is larger, the one on the left or the one on the right?[/size]
Compare these two fractions
[size=200]Which fraction is larger? Compare the fractions using the correct symbol (>, < or =).[br][br]How would you know which is larger if you did not use the images? [/size]
Equivalent Fractions Number Line
Equivalent Fractions Number Line
Use the sliders to set the numerator and denominator for each fraction. When you find fractions that come at the same place on the number line they are EQUIVALENT. Write down pairs of equivalent fractions and see what you notice.
Fraction Addition/Subtraction - Common Denominators
Adding/Subtracting Fractions with Common Denominators
[br]Suppose Josh ordered a pizza and sat down to watch football. The pizza was cut into 6 equal slices. During the first half of the game, he ate one slice and during the second half, he ate another. How much of the pizza did Josh eat?
Josh ate 2 out of 6 slices. 2 out of 6 is written as the fraction [math]\frac{2}{6}[/math]. However, when solving problems, it's always good to look at how to solve them in multiple ways.[br][br]Each piece of the pizza can be thought of as a [i]unit fraction[/i] of [math]\frac{1}{6}[/math]. Since Josh ate two slices, we can think of these are two separate unit fractions of [math]\frac{1}{6}[/math]. When we add them together, we see [math]\frac{1}{6}+\frac{1}{6}=\frac{2}{6}[/math]. However, we always want to think of our answers in reduced fraction form, so we reduce and find [math]\frac{2}{6}=\frac{1}{3}[/math]. This is illustrated for you in your workbook.[br][br]When adding fractions with [i]common denominators[/i], we can add together the two [i]numerators[/i] while leaving the denominators the same. The same is true for subtraction - to find the difference between two fractions with common denominators, subtract the numerators and leave the denominator the same (ex. [math]\frac{2}{6}-\frac{1}{6}=\frac{1}{6}[/math]).[br][br]
[size=200][color=#0000ff]Exercises[/color][/size]
Answer the following questions:
[math]\frac{5}{12}+\frac{2}{12}=[/math]
[math]\frac{3}{8}+\frac{7}{8}=[/math]
[math]\frac{5}{8}-\frac{1}{8}=[/math]
[math]\frac{11}{2}-\frac{7}{2}=[/math]
Subtracting Proper Fractions
This app explores subtracting proper fractions that may or may not start with common denominators using fraction circles.[br][list=1][*]Create your fractions you want to subtract. You will get a message if your fractions are not proper, if your common denominator is greater than 32, or if your difference would be negative. [/*][*]If you [i]need [/i]common denominators, click "Equivalent Fractions." Drag the slider until you find a common denominator that will create equivalent fractions.[/*][*]Drag the blue point on the right circle to the center of the left circle to see what subtracting will visually remove from the subtrahend.[/*][*]Click "Subtract Fractions" to actually subtract the two fraction circles.[/*][*]Write in your solution to see if you found the correct difference! [/*][/list]
Multiplying Fractions: Array model activity
6.5 a multiplying fractions with arrays
Dividing Fractions
[url=https://danpearcy.com/2021/11/05/prompt-36-dividing-fractions/]Dan Pearcy Website[br][/url]Inspiration [url=https://danpearcy.com/2021/11/05/prompt-36-dividing-fractions/]https://danpearcy.com/2021/11/05/prompt-36-dividing-fractions/[/url]
Fraction Between Two Fractions
In this applet, we model fractions as slopes of line segments. [list=1][*]Form two fractions by dragging the blue points. One fraction is the ratio of the lengths of the red segments. The ratio of the lengths of the green segments is the second fraction.[/*][*]Drag the slider to construct segments with slopes equal to the given fractions. [/*][*]Try the construction with other fractions by dragging the blue points.[/*][/list]What is the relationship between the original fractions and the fraction formed by adding their numerators and the denominators? In other words, how the slope of the blue segment relates to the slopes of the red and the green one?