Similar terms definition. Similar terms

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Lesson in 6th grade on the topic “Similar terms” 04/06/2018

Lesson objectives: Review the rules for calculating the sum of two numbers. Repeat the coefficients of the terms. Repeat the algorithm for reducing similar terms. Consolidate the acquired knowledge. Develop communication skills.

Oral counting “Adding rational numbers” -22 + 35 -3.7 + 2.8 1.5 + (-6.3) 8.2 + (-8.2) 22 – 27 -13 – 8 19– (- 2) -27 – (-3) -35 + (-9) 13 -0.9 -4.8 0 -5 -21 21 -24 -44

Distributive property of multiplication (a + b) c = ac + sun (a - b) c = ac - sun c (a + b) = ca + ca c (a - b) = ca – ca or OPENING BRACKETS

Open the brackets. 2(x+1); 3(a-2); -2(2x+1); (2a-4b+3)(-3); -(4x-2y+9); -5(-а+2в+3); 5(-2a+4); -(3v-5); -2(-5x-8).

Textbook p. 224 No. 1281 (c, e)

At 5 45. Name the coefficients in these expressions: expression coefficient 2 x - 15 y 18 z - 9 t a -b 2 - 15 18 -9 1 - 1 Name the coefficients of the terms and simplify the expression 3 x – 8 x. Coefficients of terms: 3 and -8. The expression can be simplified: 3 x – 8 x = (3 – 8) x = – 5 x 3 x – 8 x = – 5 x 3 x and – 8 x differ only in similar coefficients

Conclusion: terms with the same letter part are called similar. Similar terms differing only in coefficients

NAME THE COEFFICIENTS OF THE TERMS AND SIMPLIFY THE EXPRESSION: 6 x + 8 x = 6 and 8 14 x 6 x – 8 x = 6 and –8 – 2 x – 6 x – 8 x = – 6 and –8 – 14 x – 6 x + 8 x = – 6 and 8 2 x

NAME THE COEFFICIENTS OF THE TERMS AND SIMPLIFY THE EXPRESSION: x + 3 x = 1 and 3 4 x 5 x – x = 5 and – 1 4 x – x – 7 x = – 1 and – 7 – 8 x – 9 x + x = – 9 and 1 – 8 x

NAME THE COEFFICIENTS OF THE TERMS AND SIMPLIFY THE EXPRESSION: x + x = 1 and 1 2 x x – x = 1 and – 1 0 – x – x = – 1 and – 1 – 2 x – x + x = – 1 and 1 0

Commented completion of tasks. Simplify 1. 3x + 5x; 2. 2x – 4x; 3. – 5у – 3у; 4. – 12a + 2a; 5. V + 15 V; 6. – y – 13u; 7. 8k – k.

Mathematical dictation: “Opening brackets and bringing similar terms.” Simplify the expression: 4 x – 9 x = Check yourself: – 5 x; 1) – 14 y; 2) – 10 a; 3) 1 4 b ; 4) – 19 n; 5) 3 p; 6) – 6 y – 8 y = – 14 a + 4 a = 13 b + b = – n – 18 n = 4 p – p =

Task: give similar terms No. Expression 1) 3t + 4t – 10t = 2) 0.9v - 1.3v + 0.7v = 3) 5t – (3t – 5) + (2t – 5) = 4) 3(v – 5) – (in – 3) = 5) 0.2t – 2/9 – 4t + 2/9 = 6) 1/3(3in – 18) – 2/7(7in – 21) = 7) – 4t + 8t – t = Answer -3 m 0.3b 4m 2b-12 -3.8m -b 3m

Task: bring similar terms 1) 3a + 0.2a – 5.2a + 4a = 2) –4c + 6.7c – 2c +7.3 c = 3) x – 2.45x + 3x + 2.45x = 4 ) –2d + d – 0.2d + 9.2d = 5) 5.6t – 2t – 3.6t + t = 2a 8c 4x 8d m

Example 1. Let's open the brackets in the expression - 3*(a - 2b).

Solution. Let's multiply - 3 by each of the terms a and - 2b. We get - 3*(a - 2b)= - 3*a + (- 3)*(- 2b)= - 3a + 6b.

Example 2. Let's simplify the expression 2m - 7m + 3m.

Solution. In this expression, all terms have a common factor m. This means, according to the distribution property of multiplication, 2m - 7m + Зm = m (2 - 7 + 3). The amount is written in parentheses coefficients all terms. It is equal to -2. Therefore 2m - 7m + 3m = -2m.
In the expression 2 m - 7 m + 3m, all terms have a common letter part and differ from each other only by coefficients. Such terms are called similar.

Terms that have the same letter part are called similar terms.

Similar terms can differ only in coefficients.

To add (or say: bring) similar terms, you need to add their coefficients and multiply the result by the common letter part.

Example 3. Let us present similar terms in the expression 5a+a -2a.

Solution. In this sum, all terms are similar, since they have the same letter part a. Let's add the coefficients: 5 + 1 - 2 = 4. So, 5a + a - 2a = 4a.

Which terms are called similar? How can similar terms differ from each other? Based on what property of multiplication is the reduction (addition) of similar terms performed?
1265. Open the brackets:
a) (a-b+c)*8; e) (3m-2k + 1)*(-3);
b) -5*(m - n - k); e) - 2a*(b+2c-3m);
c) a*(b - m + n); g) (-2a + 3b+5c)*4m;
d) - a*(6b - Зс + 4); h) - a*(3m + k - n).

1266. Perform the steps by applying the distributive property multiplication:

1267. Add similar terms:

Expressions of the form 7x-3x+6x-4x read like this:
- the sum of seven x, minus three x, six x and minus four x
- seven x minus three x plus six x minus four x

1268. Reduce similar terms:

1269. Open the brackets and give similar terms:

1270. Find the meaning of the expression:

1271. Decide equation:

a) 3*(2x + 8)-(5x+2)=0; c) 8*(3-2x)+5*(3x + 5)=9.
b) - 3*(3y + 4)+4*(2y -1)=0;

1272. A kilogram of potatoes costs 20 kopecks, and a kilogram of cabbage costs 14 kopecks. They bought 3 kg more potatoes than cabbage. We paid 1 ruble for everything. 62 k. How many kilograms of potatoes and how much cabbage did you buy?
1273. The tourist walked for 3 hours and rode a bicycle for 4 hours. In total he traveled 62 km. At what speed did he walk if he walked 5 km/h slower than he rode a bicycle?

1274. Calculate orally:

1275. What is the sum of a thousand terms, each of which is equal to -1? What is the product of a thousand factors, each of which is equal to -1?

1276. Find the value of the expression

1-3 + 5-7 + 9-11+ ... + 97-99.

1277. Solve the equation orally:

a) x + 4=0; c) m + m + m = 3m;
b) a+3=a -1; d) (y-3)(y + 1)=0.

1278. Perform multiplication:

1279. What is the coefficient in each of the expressions:

1280. The distance from Moscow to Nizhny Novgorod is 440 km. What scale should the map be for this distance to be 8.8 cm long?

1285. Solve the problem:

1) The combine operator exceeded the plan by 15% and harvested grain on an area of ​​230 hectares. How many hectares is the combine harvester expected to harvest?

2) A team of carpenters used 4.2 m3 of boards to repair the building. At the same time, she saved 16% of the boards allocated for repair. How many cubic meters of planks were allocated for the renovation of the building?

1286. Find the meaning of the expression:

1) - 3,4 7,1 - 3,6 6,8 + 9,7 8,6; 2) -4,1 8,34+2,5 7,9-3,9 4,2.
1287. Using the graph, solve the problem: “Marina, Larisa, Zhanna and Katya can play on different instruments (piano, cello, guitar, violin), but each only on one. They know foreign languages ​​(English, French, German, Spanish), but each only one. Known:

1) the girl who plays the guitar speaks Spanish;

2) Larisa does not play the violin or cello and does not know English;

3) Marina does not play the violin or cello and does not know either German or English;

4) a girl who speaks German does not play the cello;

5) Zhanna knows French, but does not play the violin. Who plays what instrument and what foreign language does he know?”

1288. Open the brackets:
a) (x+y-z)*3; d) (2x-y+3)*(-2);
b) 4*(m-n-р); e) (8m-2n+p)*(-1);
c) - 8*(a - b-c); e) (a+5- b-c)*m.

1289. Find the value of the expression by applying the distributive property of multiplication:

1290. Give similar terms:

1291. Open the brackets and give similar terms:

1292. Solve the equation:

1293. Bought one table and 6 chairs for 67 rubles. A chair is 18 rubles cheaper than a table. How much does a chair cost and how much does a table cost?

1294. There are 119 students in three classes. There are 4 more students in the first grade than in the second grade, and 3 fewer students than in the third grade. How many students are in each class?

1295. Determine the map scale if the distance between two points on the ground is 750 m, and on the map it is 25 mm.

1296. How long is the distance 6.5 km depicted on the map if the map scale is 1: 25,000?

1297. On the map, the segment has a length of 12.6 cm. What is the length of this segment on the ground if the map scale is 1: 150,000?

N.Ya.Vilenkin, A.S. Chesnokov, S.I. Shvartsburd, V.I. Zhokhov, Mathematics for grade 6, Textbook for high school

Mathematics for 6th grade free download, lesson plans, preparing for school online

“Similar terms” - Mathematics textbook, grade 6 (Vilenkin)

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The presentation was prepared by mathematics teacher Irina Valentinovna Chernova, 2016. MCOU "Kuznetsovskaya OOSH" Similar terms.

Objectives: introduce the definition of similar terms, show with examples the addition (reduction) of similar terms; consolidate the use of the distributive property of multiplication when performing actions; develop students' logical thinking.

Mental calculation “Adding rational numbers” -3.7 + 2.8 -22 + 35 1.5 + (- 6.5) 8.2 + (-8.2) 22 – 27 -12 – 8 - 35 + ( -9)

Lesson topic: Similar terms. ?!

Today we will learn how to reduce similar terms. We will use the distributive property of multiplication. a (b + c) = a b + ac

Distributive property of multiplication (a + b)c = ac + bc c(a + b) = ca + bc

Example No. 1. Open the brackets 6(a - 4b) = 6a + 6(-4b) = = 6a + (-24b) = 6a - 24b

Let's train... Open the brackets: 2(a + c) = -4(t - 2) = 12(-5 - t) = 3(-a - 2) = -3(-a - 2) = 2a + 2 c - 4t + 8 -60 - 12t -3a - 6 3a + 6

Distribution property of multiplication ac + sun = (a + b)c sa + sv = c(a + b)

Example No. 2. Let's take the common factor out of brackets 1) 24a + 3a – 18a = = a(24 + 3 – 18) = a * 9 = 9a; 2) 27*19 -- 17*19 = = 19(27 – 17) = 19*10 = 190.

We are training. Take the common factor out of brackets. 4a + 4 b = 9a - 9 c = 2c+ 8c = 4n – 7 n = -9x + x = 4(a + b) 9(a - c) c(2 + 8) = 10 a n(4 - 7) = - 3 n x (-9 + 1) = -8x

Rule 1 Terms that have the same letter part are called similar terms. 5 n + 10 n - 8 n - 0.4y -- 8.9x + 3.9x – 1.03y

Rule 2 To add (or say: bring) similar terms, you need to add their coefficients and multiply the result by the common letter part. 12a – a + 4a = = (12 – 1 + 4)a = 15a

Work on the board No. 1281 (a, b, f, g), No. 1282 (a, f, g, h), No. 1283 (a, b, d, f, g). Additional task: No. 1284 (a, b, f, g) No. 1296.

Let's repeat the rules. Terms that have the same letter part are called similar terms. To add (or say: bring) similar terms, you need to add their coefficients and multiply the result by the common letter part.

Homework assignment No. 1304, No. 1305 (g, d, f), No. 1306 (a-e)

Thanks for the lesson

The work was carried out according to the textbook by N.Ya. Vilenkin "Mathematics 6" publishing house Mnemosyne

Preview:

Mathematics. 6th grade

Lesson topic: "Similar terms."

Goals: introduce the definition of similar terms, show with examples the addition (reduction) of similar terms; consolidate the use of the distributive property of multiplication when performing actions; develop students' logical thinking. (slide 2)

Progress of the lesson.

1.Organizational moment of the lesson.

2.Updating students' basic knowledge. (slide 2)

Solve orally “Addition of rational numbers”

1. -22 + 35
2. -3,7 + 2,8
3. 1,5 + (-6,5)
4. 8,2 + (-8,2)
5. 22 – 27
6. -12 – 8
7. -35 + (-9)

3. Studying new material. (slides 5-10)

Distributive property of multiplication (a+ c)c = ac + everything is true for any numbers a, b, c.

Replacing the expression (a + b) with the expression ab+ ac or expressions with (a + b) expression ca + св are also called opening brackets (slide 6)

Example No. 1. Open brackets 6(a - 4c) (slide 7)

6(a - 4b) = 6a + 6(-4b) = 6a + (-24b) = 6a - 24b

Let's train...

Expand the brackets:

2(a + c) = 2a + 2c;

4(m – 2) = -4m + 8 ;

12(-5 – t) = -60 + 12t ;

3(-a -2) = -3a – 6 ;

3(-a -2) = 3a + 6 . (slide 8)

The distributive property can also be considered from the position of taking the common factor out of brackets. (slide 9)

Replacing the expression ac+ with all expression (a+ c)c or expressions sa+ sv expression c(a+ c) is also called taking the common factor out of brackets.

Example No. 2. Let's take the common factor out of brackets (slide 10)

1. 24a + 3a – 18a = a(24 + 3 – 18) = a * 9 = 9a;

2) 27*19 - 17*19 = 19(27 – 17) = 19*10 = 190.

We are training.

Take the common factor out of brackets.

4a +4b = 4(a + b);

9a – 9b = 9(a –b);

2c + 8c = c(2 +8) = 10c;

4n – 7n = n(4 – 7) = -3n;

9x + x = x(-9 + 1) = -8x . (slide 11)

Rule 1: (slide 12)

Similar terms can differ only in coefficients.

5n + 10n - 8n

0.4y - 8.9x + 3.9x – 1.03y

Rule: To add (or say: bring) similar terms, you need to add their coefficients and multiply the result by the common letter part. (slide 13)

12a – a + 4a = (12 – 1 + 4)a = 15a

4. Reinforcing the topic(slide 14)

No. 1281(a, b, f, g) on ​​the board.

a) (a – b + c)8; e) -2a(b + 2c – 3m):

b) -5(m – n – k); g) (-2a + 3b + 5c)4m.

No. 1282(a, f, g, h) on the board

a) 19*13 + 9*7;

e) 0.9*0.8 – 0.8*0.8;

g) 2/3*5/7 + 2/3*2/7;

h) 1(1/19)*3/4 – 1/19*3/4.

No. 1283(a, b, d, f, g) on ​​the board

a) -9x + 7x – 5x + 2x;

b) 5a - 6a + 2a - 10a;

e) a + 6.2a – 6.5a – a;

e) -18n – 12n + 7.3n + 6.5n;

g) 2/9m + 2/9m – 3/9m – 5/9m.

Additional tasks:

No. 1284(a, b, f, g)

a) 10a + b – 10b – a;

b) -8y + 7x +6y + 7x;

e) -6a + 5a – x ​​+ 4;

g) 23x - 23 + 40 + 4x.

№1296 repetition task.

Reflection. Repetition of rules(slide 15)

• Terms that have the same letter part are called similar terms.
• To add (or say: bring) similar terms, you need to add their coefficients and multiply the result by the common letter part.

5. Lesson summary.

6. Homework:study paragraph 41; solve No. 1304, No. 1305 (d, d, f),

No. 1306(a-d) (slide 16).

Simple mathematical operations - addition, subtraction, multiplication, and so on - do not cause much difficulty for students. There is simply nothing to be confused about here. However, it happens that the expression from the problem has a very long alphanumeric notation. This distracts attention, disrupts the train of thought, and most importantly, most often takes a person away from the simplest decision.

It was to simplify mathematical operations that special concepts were invented - for example, similar terms. What is meant by this term, and how can the principle of similarity be used?

Which terms and in what expressions are considered similar?

The expression as such must consist of letter designations or letters and numbers - and of course, it must contain addition, because we are talking about terms. Moreover, in order to talk about similarity, the individual terms must have the same letter in their composition.

For example, let's look at the small expression 2a + 3c + 4a. The first and third parts of the expression contain the same letter “a”. Accordingly, by this criterion they are similar terms.

What does this understanding give us in practice?

In order to solve the above expression, you can go in two ways:

• Find the product 2*a, add the product 3*c to it, add the product 4*a to the sum. It's not that difficult - but the longer the expression, the more tedious the calculations become.
• Take advantage of the properties of similar terms and first transform the expression into a simpler and more convenient form in order to find a solution faster.

For any task, it is preferable to choose the second method - it saves time and reduces the possibility of making mistakes.

What does the term “reduction” mean for such terms?

This is a rearrangement of terms so that similar ones are next to each other. From earlier rules we remember that it does not matter in what order the terms of the expression appear when adding - the sum still turns out to be the same.

Thus, our example can be transformed as follows - write it as 2a + 4a + 3c. But that's not all. For simplicity, the numerical coefficients can be put in brackets and added separately - and the letter “a” can be left out of brackets for now.

It will look like this (2 + 4)a + 3c = (6)a + 3c = 6a + 3c. We no longer need to separately calculate the product for each of these terms - we can first add them together, and only then multiply the resulting result.