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mathematics UK Year 7 Mathematics (KS3)
 
Solved problems for the chapter:
 

Addition and Subtraction of Numbers

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:addition_and_subtraction_of_numbers/3831/


Example 1.

Write the difference as a sum and calculate.


    
Example 2.

Write the difference as a sum and calculate:


    
3.

Calculate:


    
4.

Calculate:


    
5.

Evaluate:


    
6.

Write the additive inverse of each of the numbers: .

    
7.

Evaluate:


    
8.

Evaluate:


    

9.

Evaluate:


    
10.

Evaluate:


    
11.

We want to walk from home to school by the shortest route. How many ways can we walk?


Walk from home to school

    
12.

16 people joined a dance school. Of these, 9 were women and 7 were men. How many dance couples can they put together if we know that the couple is made up of one woman and one man?

    
13.

Jack and Lisa each roll their own dice. Jack usually has a dice with numbers from 1 to 6, and Lisa has a dice tetrahedron with numbers from 1 to 4. How many different combinations can they roll if Jack always rolls his die first?

    
14.

A self-service restaurant has three soups, four main courses, two salads (celery and tomato) and two desserts (fruit bowl and donut). How many menus can we put together if we choose a tomato salad and a donut?

    
15.

The store offers three dry salamis, six types of chicken sausage, and three types of cheese. How many different cold cuts can we make if there is one type of sausage and one type of cheese on the cold cuts?

    
16.

Three vacancies were advertised in the factory: accountant, production manager and production worker. 6 accountants applied for the advertised positions, 4 for the production manager and 18 workers for the production work. How many ways can they fill all three jobs?

    
17.

James throws dominos. He throws it four times in a row and wonders if the domo is falling with dots or blank side. How many different ways can he throw a domino? Draw a combination.

    
18.

A cashier has a lot of 1, 2 and 5 euro coins in the cash register, two 10 euro banknotes and one 20 euro banknote. How many different ways can he return the amount of 28 euros?

    

19.

Electronic circuit consists of 5 ON-OFF switches (on or off switch). How many possible combinations are there if:


  • switches are in any position,


  • we know that the third switch must always be on,


  • we know that three series switches are always on and the other two are in any position,


  • we know that two series switches are not in the same positions,


  • we know that at least three switches are off,


  • we know that the second and fourth switches are in the ON position.


    
20.

We pull numbers from three different containers. In the first container we have numbers from 1 to 8, in the second container the numbers from 1 to 4 and in the third container the numbers from 1 to 6.


  • How many three-digit numbers can we compose if a hundred is from the first vessel, a ten from the second, and one from the third vessel?

  • How many of these numbers are divisible by 5?

  • How many of these numbers are divisible by 4?

    
21.

Mark and Martha invited six friends to dinner. They set up an elongated table and marked their seats at the ends of the table. How many different ways can they sit around the table if we know that Mark and Martha are sitting at both ends of the table?

    
22.

We want to compile a Tuesday schedule for 9th grade. We have the following instructions:


  • sports should be 5, 6 or 7 p.m.


  • Mathematics should be 1st hour.


  • the remaining 5 hours we choose from 10 subjects.


How many ways can we compile a Tuesday schedule if we know they don’t have a block of hours in elementary school?

    
23.

We have the letters O, B, L, A, K. How many words can we form from these letters to end with the letter B?

    
24.

How many songs do they have to play at a party if there are 9 boys and 11 girls on the stage and each of the boys wants to dance with all the girls (each girl determines a song she will dance)?

    
25.

A slot machine has two reels, with 10 symbols on each reel. How many stopping positions can we get from this machine.

    
26.

Morse code uses dots (·) and dashes (−) to represent characters. If we limit the representation to a maximum of 4 symbols (dots and/or dashes), how many characters can we be transmitted from the Morse code?

    
27. Please restore this question

We make new words from the letters of the word TRIGLAV. We use all the letters each time and each one only once.


  • How many different words can we make?


  • How many such words are there in which all the consonants stand together?


  • What is the probability of the event A ​​that a randomly composed word starts with the letter T and ends with the letter V?

    
28.

In the following tasks, note the properties of binomial symbols.


  • For which natural numbers n are , , the first three terms of the geometric sequence?


  • We have a polynomial . For which natural number n (n> 1) are the coefficients and of this polynomial equal?


  • Three different parallel lines p, q and r and 12 different points are drawn in the plane:

    • 5 points lie on a line p

    • 4 points on the line q

    • 3 points on the line r.


    How many triangles with vertices at these points can we draw if one side of the triangle is to lie on the line p?


    How many trapeziums with vertices at these points can we draw if one base of the trapezium is to lie on the line p?

    

29.

Mack came to the restaurant for Sunday lunch. When making lunch, she chose between 2 soups, 3 main dishes and 2 desserts. Draw a combination tree and write down how many different ways she put together her Sunday lunch.