5+ Phương pháp giải toán so sánh phân số cực đơn giản chính xác

Comparing fractions is one of the fractional mathematical forms that 4th grade students, even larger classes still study and do this exercise. So, to help students can conquer the comparison form of fractions, Mầm non Cát Linh will share the following detailed solutions.

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The theory compares fractions to be mastered

Not just as comparing the natural numbers, to compare fractions, they need to master the following theory:

Compare fractions and samples

When comparing fractions with the same form, then:

• Which fraction has a smaller number, the fraction is smaller.

• If the fraction has a larger number, the fraction is larger.

• The number of the two fractions is equal, the two fractions are equal

For example: 1/2> 1/4; 2/7 <2/5; 5/6 = 5/6

Compare fractions and numbers

When comparing fractions with the same number, then:

• The number of fractions is smaller, the fraction will be greater.

• The number of fractions is larger, the fraction will be smaller.

• If the number of 2 fractions is equal, then compare the numerator.

For example: 1/2> 1/4; 2/7 <2/5; 5/6 = 5/6

Compare other fractions

To compare other fractions, we will follow the following ways:

Method 1: Concentration of the two -fraction form and then compare the numerator.

See details of the solutions to solve the number of forms

Example: Compare two fertilizers 2/3 and 5/7

Solution instructions:

We have a common denominator 21

The two -fracted format we have

2/3 = (2 × 7)/(3 × 7) = 14/21;

5/7 = (5 × 3)/(7 × 3) = 15/21

We see that the two fractions 14/21 and 15/21 have the forms of 21 and 14 <15 so 14/21 <15/21

So: 2/3 <5/7

Method 2: Rules pupils

In the case of two fractions with different samples but very large numbers, and small numbers, we can apply the number of pupils to compare easier. Similar to Method 1, to compare two other fractions, we can attribute the number of pupils and compare the samples of the two new fractions.

Example: Compare two fractions: 21/23 and 31/85

Solution instructions:

We have: The common factor is 6.

When the number of pupils number two fractions we have

2/123 = (2 × 3)/(123 × 3) = 6/369;

3/185 = (3 × 2)/(185 × 2) = 6/370

At this time we see, two fractions 6/369 and 6/370 have numbers 6

At the same time 369 6/370

So 2/123> 3/185

To compare two fractions outside the pupil or denominator. Depending on some specific cases, the characteristics of fractions so that people can apply their own method.

Methods of comparing fractions to remember

To solve fraction comparison exercises, they can apply the following methods:

Method 1: Use 1 as an intermediary

If a/b> 1 and c/d c/d

In this method, we will use the number 1 as an intermediate when we see that this fraction is larger than the number and the other fraction has a small number than the number.

Example: Compare two fractions 2017/2018 and 2016/2015

Solution instructions:

Because 2017/2018 1, 2017/2018 <2016/2015

Method 2: Use a fraction as an intermediary

We will use the method to use a fraction as an intermediate to compare the other two fractions. There are two cases that will occur:

Case 1: If the numerator of this fraction is smaller than the number of the other fraction, the same denominator of this fraction is greater than the form of the other fraction.

Example: Compare two fractions 15/37 and 18/31

Solution instructions:

Method 1:

Considering the intermediate fraction of 15/31 (we see the number of this fraction is the number of the first fraction, the same denominator is the denominator of the second fraction).

Because 15/37 <15/31 and 15/31 <18/31, 15/37 <18/31

Method 2:

Consider the intermediate fraction 18/37 (we take the number as the number of the second fraction, with the denominator is the denominator of the first fraction).

Because 18/31> 18/37 and 18/37> 15/37, 18/31> 15/37

Case 2: If the death and the denominator of this fraction are smaller than the death of the other fraction, but both are almost equal with a certain fraction, we can choose that as an intermediate fraction.

Example: Compare two fractions 3/8 and 4/13

Solution instructions:

We see both 3/8 and 4/13 fertilizers are nearly 1/3. So we can choose 1/3 as an intermediate fraction. We have:

3/8> 3/9 = 1/3 so 3/8> 1/3 (1);

4/13 <4/12 == 1/3 so 4/13 <1/3 (2);

From (1) and (2) deduce: 3/8> 4/13

Method 3: Compare the “redundant” of two fractions

If 1/b = m + m; c/d = m + n but m> n then a/b> c/d

Accordingly, M and N in the order will be called “redundant” compared to M of two fractions. At this time we will use this “redundant” to compare the two fractions in the following cases:

Case 1: If both fractions have a larger death than the sample, the difference of the death and the sample of the two fractions are equal, we will compare the “redundant” compared to the one of those two fractions.

For example, compare two fractions 79/76 and 86/83

Solution instructions:

We have:

79/76 = 1 + 3/76;

86/83 = 1 + 3/83

Because 3/76> 3/83, 79/76> 86/83

Case 2: The fraction has a “redundant part” compared to 1 different, which fraction has a larger part, deducing that fraction will also be larger.

Example: Compare two fractions 43/14 and 10/3

Solution instructions:

We proceed to take the death by the form: 43: 14 = 3 (excess 1), 10: 3 = 3 (excess 1).

We choose the original part of the injury result as the common number 3

Perform subtraction: 43/14 – 3 = 1/14; 10/3 – 3 = 1/3

At this time we have: 43/14 = 3 + 1/14; 10/3 = 3 + 1/3. Because 1/3> 1/14, 43/14 <10/3

Case 3: If both fractions have a small number than the number, if the number is divided by the numerator in both fractions, we will have equal results.

For example: Compare two fractions 13/41 and 19/71

Solution instructions:

First, we will get the number divided by the number: 41: 13 = 3 (excess 2); 71: 19 = 3 (excess 14).

Next, select the form of the general fraction by taking the whole part of the Communist will be

1: 3 + 1 = 4 (with 1/4)

Perform subtraction: 13/41−1/4 = 11/164 and 19/71 – 1/4 = 5/284

So we have: 13/41 = 1/4 + 11/164 and 19/71 = 1/4 + 5/284

Because: 5/284 <11/284 <11/164, 19/71 <13/41

Method 4: Compare the “shortage” of two fractions

Case a/b = m – m; c/d = m – n but m> n then a/b <c/d

Accordingly, M and N are the “compensation” or “shortage” compared to M of the two fractions.

So, we will use this compensation to compare the two fractions in the following cases:

Case 1: If both fractions are smaller than the sample and the sample and the death of both are equal, we will compare the compensation compared to the 1 of both fractions.

For example, comparing two fractions 42/43 and 58/59

Solution instructions:

We have: 1 – 42/43 = 1/43; 1 – 58/59 = 1/59

Because March 14> 1/59, 42/43 <58/59

Comment, if the two fractions of the part are missing to different units, which fraction is somewhat larger, the fraction will be smaller.

Case 2: Both fractions are smaller than the sample, if the sample is divided by the death in both fractions, we will have equal injuries.

Example: Compare two fertilizers 2/5 and 3/7

Solution instructions:

Take the number divided by the number: 5: 2 = 2 (excess 1); 7: 3 = 2 7 (excess 1).

At this time, we select the form of the general fraction by taking the whole part of the trade. (1/2)

We make subtraction: 1/2 – 2/5 = 1/10; 1/2 – 3/7 = 1/14

So we have: 2/5 = 1/2 – 1/10; 3/7 = 1/2 – 1/14

Because 1/10> 1/14, 2/5 <3/7

Method 5: Multiply the same number to two fractions

We will use the method to add the same number to 2 fractions given. When the number of numbers of the two fractions is even smaller than the denominator and if the sample is divided by the number, the injury and the balance are equal. At that time, we multiply both fractions and a natural number to bring about comparison of the missing part of up to 1.

For example, comparing two fractions 11/52 and 17/76

Solution instructions:

We see the above 2 fractions if the sample is divided by the number, we are injured by 4, 8 so we will multiply 2 fractions with 4.

We have:

11/52 × 4 = 44/52; 17/76 × 4 = 68/76.1 – 44/52 = 8/52; 1 – 68/76 = 8/76

Because 8/52> 8/76, 44/52 <68/76 or 11/52 <17/76

Method 6: Perform “division of two fractions”

In the division calculation, if the division number is greater than the division, the injury is greater than 1, if the number of divisions is smaller than the division, it will be less than 1. At this time, we apply the method of “dividing two fractions” when seeing the death and the sample is not too large, does not take much time when solving multiplication in both death and sample.

For example: Compare two inches 2/23 and 9/41

Solution instructions:

We have: 2/23: 9/41 = 2/23 × 41/9 = 82/207. Because 82/207 <1, 2/23 <9/41

Method 7: Reverse fractions for comparison

Of the two division numbers with equal divisions, which division with larger numbers will be smaller. At this time, we will use the method of reversing fractions when we see 2 fractions with smaller deaths than the sample, if the sampling is divided by the death, there will be love and equal balance. At that time, we reverse the fraction to bring back the compensation comparison form.

For example: Compare two fractions 21/89 and 2003/8017

We see the above 2 fractions if sampling divided by death will be loved by 4 and 5.

We have: 1: 21/89 = 89/21; 1: 2003/8017 = 8017/2003

but 89/21 = 4 + 5/21; 8017/2003 = 4 + 5/2003

Because 5/21> 5/2003, 89/21> 8017/2003

Inferred 21/89 <2003/8017

Exercise comparing two fractions

Based on the above knowledge, below will be some exercises for children to practice:

The secret to learning and solving exercises to compare effective fractions

In order to improve the effectiveness of mathematics and solve two fractions comparison exercises, parents can refer and apply the following sharing tips:

• Mastering theory: For comparison of fractions is not too difficult if they are sure the theory. Therefore, parents need to explain in detail, as well as the solutions for them to be able to understand and practice more effectively.

• Make sure the relevant knowledge: To solve exercises on comparing fractions, there will be a lot of relevant knowledge such as shortening fractions, converging the form, learning about common factor, separate excess, common denominator … Therefore, they should learn to solve math more accurately.

• Regular practice: After mastering the theory, parents should work with them more through the solving exercises on textbooks, exercises, learn knowledge on the Internet, refer to many advanced exercises, … to help improve their ability to think mathematics and memorize better.

• Building a mathematical platform for children with Mầm non Cát Linh Math: This is a bilingual math teaching application for preschool and elementary children, with the content of construction closely closely followed by the latest GDPT program. Along with the lesson taught in the form of video, funny animations should help children easily understand and remember knowledge. Combined with more than 10,000 interactive activities for children to play, learn and support stimulating thinking when learning math better. With only 2,000 VND/day, parents can help improve their math skills better.

https://www.youtube.com/watch?v=7dsjpvhfros

Conclude

Above are the sharing about the basic knowledge of fraction comparison format. Hopefully, the above information will help your baby improve their academic efficiency and achieve high results during study and examination.

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