Comparison of fractions. How do you compare fractions with different denominators? Comparing mixed fractions How to compare mixed fractions with different denominators
The purpose of the lesson: develop the skills of comparing mixed numbers.
Lesson Objectives:
- Learn to compare mixed numbers.
- Develop thinking, attention.
- Cultivate neatness when drawing rectangles.
Equipment: table "Ordinary fractions", a set of circles "Fractions and fractions"
During the classes
I. Organizational moment.
Writing the date in a notebook.
What is the date today? What month? what year? What's the month? What's the lesson?
II. Oral work
1. Work on the plate:
| 347 | 999 | 200 | 127 |
- Read the numbers.
- Name the largest, smallest number.
- Name the numbers in descending, ascending order.
- Name the neighbors of each number.
- Comparison of 1 and 2 numbers.
- Compare numbers 2 and 3.
- How much is 3 less than 4.
- Expand the last number into the sum of the digit terms, name: how many units are in this number, how many tens, how many hundreds.
2. What numbers are we studying now? (Fractional.)
- What are the fractional numbers (1 number each).
- What are the mixed numbers (1 number each)
3. Using the "Fractions and Fractions" set on magnets, show the numbers and.
Today we will learn how to compare such numbers. writing the topic of the lesson in the notebook.
III. Study of the topic of the lesson.
1. Compare numbers using circles:
| and |
2. Draw rectangles and mark the numbers and.
 |
 |
Conclusion: of two mixed numbers, the larger is the number that has more integers.
3. Work according to the textbook: p. 83, figure 12.
(Whole apples and lobes are shown.)
We read the rule in the textbook (teacher, then children 2-3 times)
IV. Physical education minute.
Conducted by the teacher and students for the back and trunk muscles.
This article will focus on mixed numbers comparison... First, we will figure out which mixed numbers are called equal and which are called unequal. Next, we will give a rule for comparing unequal mixed numbers, which allows you to find out which number is greater and which is less, and consider examples. Finally, we will focus on comparing mixed numbers with natural numbers and fractions.
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Equal and unequal mixed numbers
First you need to know which mixed numbers are called equal and which are unequal. Let us give the corresponding definitions.
Definition.
Equal mixed numbers- these are mixed numbers, in which both whole parts and fractional parts are equal.
In other words, two mixed numbers are said to be equal if their records completely coincide. If the records of mixed numbers are different, then such mixed numbers are called unequal.
Definition.
Unequal mixed numbers- these are mixed numbers, the records of which are different.
The voiced definitions allow you to determine at a glance whether the given mixed numbers are equal or not. For example, mixed numbers and equal, since their entries completely coincide. These numbers have equal whole parts and equal fractional parts. And the mixed numbers and are unequal, since they have unequal whole parts. Other examples of unequal mixed numbers are and as well as and.
Sometimes it becomes necessary to find out which of two unequal mixed numbers is greater than the other, and which is less. We will consider how this is done in the next paragraph.
Comparison of mixed numbers
Comparing mixed numbers can be reduced to comparing ordinary fractions. To do this, it is enough to convert the mixed numbers to improper fractions.
For example, let's compare a mixed number and a mixed number by representing them as improper fractions. We have and. So the comparison of the original mixed numbers is reduced to the comparison of fractions with different denominators and. Since, then.
Comparing mixed numbers by comparing equal fractions is not the best solution. It is much more convenient to use the following mixed number comparison rule: greater is the mixed number, the integer part of which is greater, if the whole parts are equal, then the greater is the mixed number, the fractional part of which is greater.
Let's consider how the mixed numbers are compared according to the sounded rule. To do this, we will analyze the solutions of examples.
Example.
Which of the mixed numbers or more?
Solution.
The integer parts of the compared mixed numbers are equal, so the comparison is reduced to comparing the fractional parts and. Since then 
... Thus, the mixed number is greater than the mixed number.
Answer:
Comparison of a mixed number and a natural number
Let's figure out how to compare a mixed number and a natural number.
It's fair a rule for comparing a mixed number with a natural number: if the integer part of the mixed number is less than this natural number, then the mixed number is less than this natural number, and if the whole part of the mixed number is greater than or equal to this mixed number, then the mixed number is greater than this natural number.
Let's look at examples of comparing a mixed number and a natural number.
Example.
Compare the numbers 6 and.
Solution.
The integer part of the mixed number is 9. Since it is greater than the natural number 6, then.
Answer:
Example.
Given a mixed number and a natural number 34, which of the numbers is less?
Solution.
The integer part of the mixed number is less than 34 (11<34 ), поэтому .
Answer:
The mixed number is less than 34.
Example.
Compare the number 5 and the mixed number.
Solution.
The integer part of this mixed number is equal to the natural number 5, therefore, this mixed number is greater than 5.
Answer:
In conclusion of this paragraph, we note that any mixed number is greater than one. This statement follows from the rule for comparing a mixed number and a natural number, and also from the fact that the integer part of any mixed number is either greater than 1 or equal to 1.
Comparison of mixed numbers and fractions
First, let's say about comparison of a mixed number and a regular fraction... Any regular fraction is less than one (see right and wrong fractions), therefore, any regular fraction is less than any mixed number (since any mixed number is greater than 1).
The purpose of the lesson: develop the skills of comparing mixed numbers.
Lesson Objectives:
- Learn to compare mixed numbers.
- Develop thinking, attention.
- Cultivate neatness when drawing rectangles.
Equipment: table "Ordinary fractions", a set of circles "Fractions and fractions"
During the classes
I. Organizational moment.
Writing the date in a notebook.
What is the date today? What month? what year? What's the month? What's the lesson?
II. Oral work
1. Work on the plate:
| 347 | 999 | 200 | 127 |
- Read the numbers.
- Name the largest, smallest number.
- Name the numbers in descending, ascending order.
- Name the neighbors of each number.
- Comparison of 1 and 2 numbers.
- Compare numbers 2 and 3.
- How much is 3 less than 4.
- Expand the last number into the sum of the digit terms, name: how many units are in this number, how many tens, how many hundreds.
2. What numbers are we studying now? (Fractional.)
- What are the fractional numbers (1 number each).
- What are the mixed numbers (1 number each)
3. Using the "Fractions and Fractions" set on magnets, show the numbers and.
Today we will learn how to compare such numbers. writing the topic of the lesson in the notebook.
III. Study of the topic of the lesson.
1. Compare numbers using circles:
| and |
2. Draw rectangles and mark the numbers and.
 |
 |
Conclusion: of two mixed numbers, the larger is the number that has more integers.
3. Work according to the textbook: p. 83, figure 12.
(Whole apples and lobes are shown.)
We read the rule in the textbook (teacher, then children 2-3 times)
IV. Physical education minute.
Conducted by the teacher and students for the back and trunk muscles.
V. Securing the material.
1. Repetition according to the table "Ordinary fractions".
(Numbers where the whole parts are the same are covered in the next lesson.)
2. Compare.
Vi. Homework on individual cards, learn the rule on page 83 of the textbook.
Vii. Individual work on cards.
VIII. Lesson summary.
Grading.
The rules for comparing ordinary fractions depend on the type of fraction (correct, incorrect, mixed fraction) and on the denominational (the same or different) of the fractions being compared.
This section discusses options for comparing fractions that have the same numerators or denominators.
Rule. To compare two fractions with the same denominator, you need to compare their numerators. Greater (less) is the fraction with the greater (less) numerator.
For example, compare fractions:
Rule. To compare regular fractions with the same numerators, you need to compare their denominators. Greater (less) is the fraction with the lesser (greater) denominator.
For example, compare fractions: 
Comparison of correct, incorrect and mixed fractions among themselves
Rule. Irregular and mixed fractions are always larger than any regular fraction.
The correct fraction is, by definition, less than 1, therefore, the improper and mixed fractions (having a number equal to or greater than 1) are greater than the correct fraction.
Rule. Of the two mixed fractions, the larger (smaller) is the one with the larger (smaller) integral part of the fraction. If the whole parts of the mixed fractions are equal, the greater (less) is the fraction with the greater (less) fractional part.
Outline plan 6th grade math lesson
Lesson topic: "Comparison of mixed numbers"
The purpose of the lesson: learn the rules for comparing mixed numbers; to consolidate the skills and abilities of comparing ordinary fractions and mixed numbers when solving problems.
Tasks:
to generalize the knowledge of students about ordinary fractions and mixed numbers, to form the ability to compare ordinary fractions and mixed numbers;
continue work on the development of logical thinking, memory, imagination, the formation of mathematically literate speech;
instill in students a sense of responsibility, improve the skills of independent activity.
Lesson type: lesson in learning new knowledge.
Equipment: projector, interactive whiteboard, handouts.
Lesson structure:
1. Organizational moment (3 minutes).
2. Updating knowledge (10 min).
3. Studying new material (8min).
4. Physical education (1 min).
5. Reinforcement of the passed (15min).
6. Homework (1 min).
7. Lesson summary (2 min).
During the classes.
I. Organizing time . (Slide number 2)
Guys, we open notebooks, write down the date and topic of the lesson "Comparison of mixed numbers."
Today we will study a new topic, learn how to compare mixed numbers. But before that, we must repeat one important topic. And which one, you will find out ifsolve the puzzle :
( fraction )
II. Knowledge update. Oral work .
1) - Look at the screen (slide number 3 ).
- Write which part of the shape is painted over? write down the fraction (3/8)
What is the name of the number written under the line? (denominator )
What does the denominator of a fraction show? (the denominator shows how many equal parts the whole was divided )
What is the name of the number written above the line? (numerator )
What does the numerator of a fraction show? (the numerator shows how many pieces were taken )
2) - The next task "Find unnecessary "(slide number 4) :
A) numerator; sum; denominator; fraction.
B);. ()
Why is it superfluous? (this is an incorrect fraction, the rest are correct )
What fractions are called correct? (regular fractions have the numerator less than the denominator)
- What fractions are called incorrect? (for improper fractions, the numerator is greater than or equal to the denominator)
V) ;. ()
Why is it superfluous? (it's a mixed number) Writing on the board
What are the parts of the mixed number? (whole number and fraction or whole part and fractional part )
3) Independent work on cards.
Now let's remember how ordinary fractions are compared. To do this, executeindependent work ... We write down the solutions on pieces of paper with tasks:
…. ; …. ;
…. ; …. ;
…. ; …. .
Let's check your solutions. For whom it is correct, without errors - put "5", for whom 1-2 errors - "4", for whom 3 or more - "3".
Self-test (on slide number 5 answers)
What rules for comparing ordinary fractions did you use?(with the rules for comparing ordinary fractions with the same denominators and with the same numerators)
Let's read the comparison rules aloud together:
Rule 1: (Slide number 6)
Of two fractions with the same denominators, the larger is the fraction for which the numerator is greater .
Rule 2: (Slide # 6)
Of two fractions with the same numerators, the larger is the fraction for which denominator less .
Learning a new topic " Comparison of mixed numbers »
When comparing mixed numbers, there can be two comparisons.
Let's consider the first case. Look at the screen (Slide number 7 ).
What are the mixed numbers shown on the screen? (and )
Write them down in a notebook:
What is the integer portion of each number? (3 and 2)
Are the whole parts the same or different? (different )
In what mixed number is the whole part greater? (In the first )
Which number is greater? ()
- What can we conclude? Continue …
Meansto compare mixed numbers, compare the whole parts first.
Conclusion : Of the two mixed numbers, the greater is the one in which whole part ... ..more .
Examples for consolidation (Slide number 8)
- Let's do the following task orally:
Read and compare the numbers: and; and; and. That more?
Continuation and learning a new topic
Let's consider the second case. What are the mixed numbers on the next slide?(Slide number 9)
Write down mixed numbers in a notebook.
What about whole pieces of mixed numbers data? (they are the same )
How do you think how to compare two mixed numbers with the same integer parts? (look at fractional parts or fractions )
Which is greater than ¾ or ¼? (¾)
Which number is greater? ()
- So, if the whole parts are the same, then we look at the fractional parts
V Conclusion: (Slide number 8) Continue …
Of two mixed numbers with the same integer parts, the greater is the number that has whom fractional part ... ... more .
Physical education (slide number 9).
Once - got up, stretched.
Two - bent down, straightened out.
Three - three claps in your hands,
Head three nods.
Four arms wider.
Five - wave your hands.
Six - sit quietly at the desk.
V. Consolidation of what has been learned .
1 ) Working with the tutorial .
We open textbooks onP. 84 we decide № 317 (2)
It goes to the blackboard ... .., and the rest decide in notebooks.
2) - Solve the problem orally (on Slide 10) .
Masha has an orange, Alyona has an orange, Olya has an orange. Who has the biggest orange? Who has the smaller orange?
3) Game "Mathematical beads".
Beads are drawn on the board. You need to take turns to go to the board, come up with and write down in circlesmixed numbers in ascending order .
Vi. Lesson summary .
What topic did you learn in class today?
How do you compare mixed numbers with different whole parts?
How do I compare mixed numbers with the same integer parts?
- Grades for the lesson : .
Thanks for your work!
VI I . Homework : No. 320 p. 85. (compare mixed)
Additional assignment for independent work (at the end of the lesson):
Option 1.
Compare numbers:
…. ; … ; 10 ….. 10
…. ; … ; ….. 3
Independent work (for 3 min)
Option 1
…. ; …. ;
…. ; …. ;
…. ; …. .
