mozaMedical by Mozaik Education

Adding natural numbers

Counting appeared as early as the dawn of humanity. Prehistoric humans counted their belongings, prey, animal skins and weapons. When counting, they drew lines or used stones and pebbles.

The properties of addition

Based on the drawings above, you can write:

\latex{3+4=4+3}

\latex{3+4=7}

sum

addends

Addition is commutative, meaning that the sum does not depend on the order the numbers are added in.

If you would like to add three numbers, add two numbers first, then add the third number to their sum. The brackets show which numbers to add first.

\latex{(3 + 2) + 4 = 5 + 4 = 9}

\latex{3 + (2 + 4) = 3 + 6 = 9}

Based on the drawings above, you can write:

\latex{(3 + 2) + 4 = 3 + (2 + 4) = 3 + 2 + 4}

When having several addends, the order in which you add them does not affect the sum; therefore, in the case of addition, brackets are not necessary.

Changes of the sum

Observe how the sum changes when the addends are changed.

\latex{3 + 4 = 7}

\latex{3+4=7}

increased by \latex{ 2 }

decreased by \latex{ 1 }

decreased by \latex{ 3 }

increased by \latex{ 3 }

unchanged

\latex{5+4=9}

\latex{3+3=6}

\latex{6+1=7}

When one of the addends is
increased by \latex{ 2 },
the sum also increases by \latex{ 2 }.

When one of the addends is
decreased by \latex{ 1 },
the sum also decreases by \latex{ 1 }.

When one of the addends is
increased by \latex{ 3 },
while the other is decreased by \latex{ 3 },
the sum remains unchanged.

The sum does not change when one of the addends decreases by the same amount as the other addend increases.

Exercises

{{exercise_number}}. Grandpa is telling his grandson: the sum of \latex{ 28 } plus \latex{ 36 } and \latex{ 49 } is equal to the sum of \latex{ 28 } and \latex{ 49 } plus... At this point, Grandpa falls asleep. How can you finish the sentence?

{{exercise_number}}. Compare the two sums without performing the addition. Write the correct relation symbols in the box.

a) \latex{518+683⬜683+518}

b) \latex{528+683⬜683+518}

c) \latex{796+1,423⬜1,423+796}

d) \latex{12,645+8,355⬜8,355+12,645}

e) \latex{796+1,423⬜1,723+796}

f) \latex{12,645+8,355⬜12,545+8,455}

{{exercise_number}}. Use the simplest method to perform the additions. What properties of addition did you use?

a) \latex{43+205+157}

b) \latex{17+25+35}

c) \latex{11,169+15,831+642}

d) \latex{54+0+246}

e) \latex{349+1,666+151}

f) \latex{863+1,346+137+5,654}

{{exercise_number}}. Choose a menu for \latex{ 4 } people (soup, main course, dessert). No one wants to spend more than €\latex{ 30 }, and no one wants to choose the same three dishes as someone else. (→)

Soups:

Chicken soup €\latex{ 6 }
Tomato soup €\latex{ 5 }
Fruit soup €\latex{ 8 }
Bean soup €\latex{ 7 }

Main courses:

Turkey breast with potatoes €\latex{ 12 }
Chicken breast with cheese €\latex{ 16 }
Green peas with ham €\latex{ 11 }
Macaroni and cheese €\latex{ 12 }

Desserts

Rice pudding €\latex{ 3 }
Vanilla pudding €\latex{ 4 }
Pancakes €\latex{ 5 }
Fruit salad €\latex{ 8 }

{{exercise_number}}. You have €\latex{ 15 } in your left and right pockets in total. How much money will you have if you put €\latex{ 2 } from your left pocket into your right pocket?

{{exercise_number}}. Write down four odd numbers, so that their sum is \latex{ 25 }.

{{exercise_number}}. Four classes in the \latex{ 5 }^th grade collected the following amount of paper for recycling purposes: \latex{ 5.1 }: \latex{ 2,586\,kg }; \latex{ 5.2 }: \latex{ 2,178\,kg }; \latex{ 5.3 }: \latex{ 2,522\,kg } and \latex{ 5.4 }: \latex{ 2,414\,kg }. Arrange the classes in ascending order based on the amount of paper they collected. Which class gathered the most paper? Can the entire amount be loaded on a lorry with a maximum capacity of \latex{ 10 } \latex{ tonnes }?

{{exercise_number}}. Andrew had \latex{ 351 } stamps. His mum gave him \latex{ 186 }, and his grandpa gave him his collection of \latex{ 769 } stamps. How many stamps does Andrew have now? How many did he get from his mum rounded to the nearest ten? And from his grandpa? How many did he get in total?

{{exercise_number}}. In a forest, rounded to the nearest hundred, there are \latex{ 1,600 } oak trees, \latex{ 2,100 } pine trees and \latex{ 3,700 } beech trees. (There are no other tree species in the forest.)

a) At least how many trees are there?

b) At most how many trees are there?

{{exercise_number}}. You have two wallets; one with €\latex{ 8 } in it, while the other has €\latex{ 12 } in it.

a) How much money do you have in your wallets in total?

b) You spend €\latex{ 1 } from one of them and put €\latex{ 1 } you received as a gift in the other. How much money do you have now?

{{exercise_number}}. What do the following sums equal if \latex{4,563 + 2,589 = 7,152}?

a) \latex{4,663+2,589}

b) \latex{4,663+2,989}

c) \latex{5,663+1,589}

d) \latex{4,863+2,889}

e) \latex{4,783+2,369}

f) \latex{5,674+1,478}

{{exercise_number}}. Look at the following addition: \latex{18 + 17 + 5 = 40}

a) Increase the sum, so that it stays an even number after changing

• one addends;

• two addends;

• three addends.

b) Keep the sum constant while changing

• one addends;

• two addends;

• three addends.

{{exercise_number}}. The sum of the ages of a family of four is \latex{ 105 } \latex{ years }. What will the sum of their ages be in \latex{ 5 } \latex{ years? } How old could the family members be now?

{{exercise_number}}. Replace \latex{ 4 } digits with \latex{ 0 } in the addition shown on the right so that the sum is \latex{ 1,111 }.
(The first digit can also be \latex{ 0 }.)

{{exercise_number}}. Perform the additions. Which method is easier?

a) \latex{(642+958)+1,040}

or

\latex{642+(958+1,040)}

b) \latex{(1,673+569)+431}

or

\latex{1,673+(569+431)}

c) \latex{(3,918+82)+968}

or

\latex{3,918+(82+968)}

Quiz

Can you divide \latex{ 100 } nuts between \latex{ 5 } children, so that each child gets an odd number of nuts?

Mathematics 5.

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