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

Comparing fractions is one of the forms of fraction math that 4th graders and even older grades still learn and do this exercise. Therefore, to help children conquer the math of comparing fractions, Nguyễn Tất Thành will share detailed solution methods below.

The theory of comparing fractions needs to be mastered

Not as simple as comparing natural numbers, to compare fractions, you need to master the following theory:

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Compare fractions with the same denominator

When comparing fractions with the same denominator, then:

• Whichever fraction has the smaller numerator is the smaller fraction.

• Whichever fraction has the larger numerator is the larger fraction.

• If the numerators of two fractions are equal, then the two fractions are equal

For example: 1/2 > 1/4; 2/7

Compare fractions with the same numerator

When comparing fractions with the same numerator, then:

• The smaller the denominator of a fraction, the larger the fraction.

• The larger the denominator of a fraction, the smaller the fraction.

• If the denominators of two fractions are equal, compare the numerators.

For example: 1/2 > 1/4; 2/7

Compare fractions with different denominators

To compare fractions with different denominators, we will do the following:

Method 1: Similarize the denominators of two fractions and then compare the numerators.

See details on how to solve the same denominator exercise

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

Solution instructions:

We have a common denominator of 21

Reducing the denominators of two fractions 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 both have denominators 21 and 14.

So: 2/3

Method 2: Refer to pupil number

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

Solution instructions:

We have: common factor is 6.

When we reduce the number of pupils to two fractions, we have

2/123 = (2×3) / (123×3) = 6/369;

3/185 = (3×2) / (185×2) = 6/370

Now we see that the two fractions 6/369 and 6/370 both have a numerator of 6.

Simultaneous 369 6/370

So 2/123 > 3/185

To compare two fractions other than by referring to pupils or denominators. Depending on some specific cases and characteristics of fractions, everyone can apply their own method.

Methods for comparing fractions to remember

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

Method 1: Use number 1 as an intermediary

In this method, we will use the number 1 as an intermediary when we see that this fraction has a numerator greater than the denominator and another fraction has a numerator smaller than the denominator.

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

Solution instructions:

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Because 2017/2018 1, so 2017/2018

Method 2: Use a fraction as an intermediary

We will use the method of using a fraction as an intermediary to compare the other two fractions. There are two cases that will happen:

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

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

Solution instructions:

Method 1:

Consider the intermediate fraction 15/31 (We see that the numerator of this fraction is the numerator of the first fraction, and the denominator is the denominator of the second fraction).

Because 15/37

Method 2:

Consider the intermediate fraction 18/37 (We take the numerator as the numerator of the second fraction, with the denominator as the denominator of the first fraction).

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

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

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

Solution instructions:

We see that both fractions 3/8 and 4/13 are close to 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

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

Method 3: Compare the “excess” of two fractions

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

Case 1: If both fractions have a numerator greater than the denominator, and the difference between the numerator and denominator of the two fractions is equal, then we will compare the “excess” compared to 1 of those two fractions.

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 different “excess” compared to 1. Whichever fraction has the larger excess, it follows that that fraction will also be larger.

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

Solution instructions:

We proceed to divide the numerator by the denominator: 43: 14 = 3 (remainder 1), 10:3 = 3 (remainder 1).

We choose the integer part of the quotient result as the common number, 3

Proceed to subtract: 43/14 – 3 = 1/14; 10/3 – 3 = 1/3

Now we have: 43/14 = 3 + 1/14; 10/3 = 3 + 1/3. Because 1/3 > 1/14, so 43/14

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

Example: Compare two fractions 13/41 and 19/71

Solution instructions:

First, we will divide the denominator by the numerator: 41:13=3 (remainder 2); 71:19=3 (remainder 14).

Next, choose the denominator of the common fraction by taking the integer part of what the quotient will be

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

Do the 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

Method 4: Compare the “missing part” of two fractions

Accordingly, M and N are the “complement” or “missing part” compared to m of those two fractions.

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

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Case 1: If both fractions have a numerator smaller than the denominator and the denominator and numerator of both are equal, then we will compare the complement compared to 1 of both fractions.

Example: Compare two fractions 42/43 and 58/59

Solution instructions:

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

Because 3/14 > 1/59, so 42/43

Comment, if two fractions have a missing part to different units, whichever fraction has the larger missing part will be smaller.

Case 2: Both fractions have a numerator smaller than the denominator. If we divide the denominator by the numerator in both fractions, we will have equal quotients.

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

Solution instructions:

Divide the denominator by the numerator: 5:2 = 2 (remainder 1); 7:3 = 2 7 (remainder 1).

At this point, we choose the denominator of the common fraction by taking the integer part of the quotient. (yes 1/2)

We perform 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, so 2/5

Method 5: Multiply the same number into two fractions

Example: Compare two fractions 11/52 and 17/76

Solution instructions:

We see that if the 2 fractions above are divided by the numerator, the quotient is 4, with a remainder of 8, so we will multiply the 2 fractions by 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, so 44/52

Method 6: Perform “dividing two fractions”

In the division calculation, if the dividend is greater than the divisor, the quotient is greater than 1. If the dividend is smaller than the divisor, the quotient is less than 1. At this point, we apply the “dividing two fractions” method when Seeing that the numerator and denominator are not too large numbers, it doesn’t take much time to solve multiplication in both numerator and denominator.

Example: Compare two fractions 2/23 and 9/41

Solution instructions:

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

Method 7: Invert fractions to compare

In two division operations where the dividend is equal, the division with the larger number will have the smaller quotient. At this point, we will use the method of inverting fractions when we see that both fractions have a numerator smaller than the denominator. If we divide the denominator by the denominator, the quotient and remainder will be equal. At that time, we proceed to invert the fraction to return to complement comparison form.

Example: Compare two fractions 21/89 and 2003/8017

We see that if the two fractions above are divided by the denominator, the quotient will be 4 and the remainder will be 5.

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

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

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

Deduce 21/89

Exercises comparing two fractions

Based on the knowledge shared above, below are some exercises for you to practice:

The secret to learning and solving exercises comparing fractions effectively

To improve the effectiveness of learning math and solving exercises comparing two fractions, parents can refer to and apply the following shared tips:

• Master the theory: Comparing fractions is not too difficult if you understand the theory well. Therefore, parents need to explain in detail, as well as ways to solve exercises so that children can understand and practice more effectively.

• Grasp relevant knowledge: To solve exercises about comparing fractions, you will have a lot of related knowledge such as simplifying fractions, converting denominators, learning about common factors, specific factors, and common denominators. … Therefore, you should understand clearly to solve math problems more accurately.

• Practice regularly: After mastering the theory, parents should practice more with their children by solving exercises in textbooks, workbooks, searching for knowledge on the internet, and referring to many advanced exercises. ,… thereby helping to improve your child’s mathematical thinking and memory ability better.

• Build a foundation for early childhood math with Nguyễn Tất Thành Math: This is a bilingual math teaching application for preschool and elementary school children, with content closely following the latest GDPT program. Along with lessons taught in video form, funny animated images 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 completely help improve their child’s math learning ability.

Conclude

Above is the sharing of basic knowledge of fraction comparison math. Hopefully the above information will help your child improve learning efficiency and achieve high results while studying and taking exams.

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