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Comparing numbers
When shopping or counting, we often need to compare natural numbers. In mathematics, we use relation symbols to make comparisons.
Relation symbol | How to read out |
\latex{2} \latex{=} \latex{1}\latex{+} \latex{1} | \latex{2} is equal to \latex{1 + 1.} |
\latex{b} \latex{\geq} \latex{4} | \latex{b} is greater than or equal to \latex{4.} |
\latex{7} \latex{\lt} \latex{10} | \latex{7} is less than \latex{10}. |
\latex{c} \latex{\leq} \latex{5} | \latex{c} is less than or equal to \latex{5.} |
\latex{c} \latex{\gt} \latex{5} | \latex{c} is greater than \latex{5}. |
\latex{5} \latex{\neq } \latex{7} | \latex{5} is not equal to \latex{7.} |
Example 1
Place the following natural numbers on a number line.
a) greater than \latex{ 3 }
b) less than \latex{ 3 }
c) not greater than \latex{ 3 }
d) not less than \latex{ 3 }
e) greater than \latex{ 3 } but less than \latex{ 7 }
f) at least \latex{ 3 } but no more than \latex{ 7 }
Solution
Look for the natural numbers on the coloured part of the number line.
a) greater than \latex{ 3 } ( \latex{\color{88449a}\blacksquare} > \latex{ 3 } )
b) less than \latex{ 3 } ( \latex{\color{2dabe2}\large\bull} < \latex{ 3 } )
c) not greater than \latex{ 3 } ( at most; \latex{\color{ec2227}\blacktriangle} ≤ \latex{ 3 } )
\latex{\color{88449a}\blacksquare} = {\latex{ 4 }; \latex{ 5 }; \latex{ 6 }; ...}
\latex{\color{2dabe2}\large\bull} = {\latex{ 0 }; \latex{ 1 }; \latex{ 2 }}
\latex{\color{ec2227}\blacktriangle} = {\latex{ 0 }; \latex{ 1 }; \latex{ 2 }; \latex{ 3 }}
\latex{ 0 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ 9 }
\latex{ 10 }
\latex{ 0 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ 9 }
\latex{ 10 }
\latex{ 0 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ 9 }
\latex{ 10 }
d) not less than \latex{ 3 } ( at least \latex{ 3 }; \latex{\color{07a64f}\blacktriangledown} ≥ \latex{ 3 } )
e) greater than \latex{ 3 } but less than \latex{ 7 } ( \latex{ 3 } < \latex{\color{ec2227}\large\bull} < \latex{ 7 } )
f) at least \latex{ 3 } but no more than \latex{ 7 } ( \latex{ 3 } ≤ \latex{\color{2dabe2}\blacktriangle} ≤ \latex{ 7 } )
\latex{\color{07a64f}\blacktriangledown} = {\latex{ 3 }; \latex{ 4 }; \latex{ 5 }; ...}
\latex{\color{ec2227}\large\bull} = {\latex{ 4 }; \latex{ 5 }; \latex{ 6 }}
\latex{\color{2dabe2}\blacktriangle} = {\latex{ 3 }; \latex{ 4 }; \latex{ 5 }; \latex{ 6 }; \latex{ 7 }}
\latex{ 0 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ 9 }
\latex{ 10 }
\latex{ 0 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ 9 }
\latex{ 10 }
\latex{ 0 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ 9 }
\latex{ 10 }
How do you compare natural numbers with multiple digits?
Example 2
Arrange the following numbers in ascending order.
a) \latex{ 1,848 }; \latex{ 2,004 }; \latex{ 896 }
b) \latex{ 1,848 }; \latex{ 1,867 }; \latex{ 1,830 }
Solution
Show the numbers on a properly chosen number line, then arrange them in ascending order.
\latex{\textcolor{#ff0000}{0}896\lt \textcolor{#ff0000}{1},848\lt \textcolor{#ff0000}{2},004}
\latex{1,8\textcolor{#ff0000}{3}0\lt 1,8\textcolor{#ff0000}{4}8\lt 1,8\textcolor{#ff0000}{6}7}
\latex{ 500 }
\latex{ 1,000 }
\latex{ 1,500 }
\latex{ 2,000 }
\latex{ 1,820 }
\latex{ 1,840 }
\latex{ 1,860 }
\latex{ 1,880 }
\latex{ 896 }
\latex{ 1,848 }
\latex{ 2,004 }
\latex{ 1,830 }
\latex{ 1,848 }
\latex{ 1,867 }
Exercises
{{exercise_number}}. Five children collected walnuts into baskets and then counted them. Zoe collected \latex{ 342 }, Martha \latex{ 348 }, Greg \latex{ 402 }, Frank \latex{ 384 } and Helga \latex{ 420 }. Write the number of walnuts in each child's basket in descending order.
{{exercise_number}}. At the market, you notice that \latex{ 1 } \latex{ kg } of lemons costs no more than €\latex{ 2 } but at least €\latex{ 1 }. How much does \latex{ 1 } \latex{ kg } of the cheapest lemon cost, and how much does \latex{ 1 } \latex{ kg } of the most expensive lemon cost?
{{exercise_number}}. A bag can hold at least \latex{ 3 } but no more than \latex{ 12 } books. How many books can be in the bag?
{{exercise_number}}. No less than \latex{ 930 } and no more than \latex{ 945 } pupils went on a school trip. How many pupils could have gone on the trip?
{{exercise_number}}. How many natural numbers are there, that are
a) less than \latex{ 17 };
b) no more than \latex{ 17 };
c) at most \latex{ 17 };
d) greater than \latex{ 17 } but less than \latex{ 25 };
e) at least \latex{ 17 } but at most \latex{ 25 };
f) greater than \latex{ 17 } but no less than \latex{ 25 }?
{{exercise_number}}. Describe the size of the numbers on the number line below.
\latex{ 18 }
\latex{ 19 }
\latex{ 20 }
\latex{ 21 }
\latex{ 22 }
\latex{ 23 }
\latex{ 10 }
\latex{ 19 }
\latex{ 14 }
\latex{ 16 }
\latex{ 18 }
\latex{ 20 }
{{exercise_number}}. Put the prices of the items in ascending order. (→)
Fabatka Store
Zsivány str. \latex{ 11 }., Szeged
Zsivány str. \latex{ 11 }., Szeged
Peach \latex{ 1 } \latex{ kg }
Plum \latex{ 1 } \latex{ kg }
Apple pie
Croissant
Milk \latex{ 1 } \latex{ litre }
Canned fish
Chocolate
Total:
Plum \latex{ 1 } \latex{ kg }
Apple pie
Croissant
Milk \latex{ 1 } \latex{ litre }
Canned fish
Chocolate
Total:
€\latex{ 2.5 }
€\latex{ 4.5 }
€2.57
€\latex{ 1.99 }
€\latex{ 1.89 }
€\latex{ 0.99 }
€\latex{ 1.96 }
€\latex{ 16.4 }
€\latex{ 4.5 }
€2.57
€\latex{ 1.99 }
€\latex{ 1.89 }
€\latex{ 0.99 }
€\latex{ 1.96 }
€\latex{ 16.4 }
\latex{ 03 }/\latex{ 02 }/\latex{ 24 } \latex{ 17:32 }
Thank you for your custom.
{{exercise_number}}. In a school, each class has a different number of pupils. Each class has at least \latex{ 20 } and at most \latex{ 35 } pupils. How many classes can this school have?
{{exercise_number}}. At least how many children are in a family where each child has at least one brother and at least one sister?
{{exercise_number}}. Put Europe's peaks in ascending order by their height. Where are these peaks located?
A: Carrauntoohil, \latex{ 1,041 } \latex{ metres }
B: Grossglockner, \latex{ 3,798 } \latex{ metres }
C: Mount Olympus, \latex{ 2,919 } \latex{ metres }
D: Ben Nevis, \latex{ 1,344 } \latex{ metres }
E: Mont Blanc, \latex{ 4,810 } \latex{ metres }
F: Mount Elbrus, \latex{ 5,642 } \latex{ metres }
G: Kékes, \latex{ 1,014 } \latex{ metres }
H: Monte Rosa, \latex{ 4,634 } \latex{ metres }
{{exercise_number}}. Which number is greater: one containing \latex{ 13 } thousands, \latex{ 8 } tens and \latex{ 9 } units, or one containing \latex{ 1 } ten thousand, \latex{ 7 } hundreds, \latex{ 3 } thousands and \latex{ 19 } units?
{{exercise_number}}. How many digits can go in the ⬜ to make the relations true?
a) \latex{21 ,342 \lt 21 ⬜ 42}
b) \latex{7 ⬜ 832 \gt 72,632}
c) \latex{95 ⬜ 48 \leq 9 ⬜ 148}
{{exercise_number}}. Draw appropriate number lines and write the following natural numbers on them.
a) \latex{n \lt 5}
b) \latex{n \geq 86} and \latex{n} has two digits
c) \latex{200 \leq n \lt 1,000} and \latex{n} is a round hundred
d) \latex{79 \lt n \leq 88} and \latex{ n} is odd
Read the relations out loud using the following expressions: less than, no less than, greater than, not greater than, at least, at most.
{{exercise_number}}. Write down all the possible three-digit numbers where the unit place is occupied by the digit \latex{ 2 }, and the hundreds place by its double. The tens place should be determined by a roll of the dice. Draw a number line and then try to find the place of each number.
Quiz
A baker came up with three new biscuits. He named them rull, kump and son.
\latex{ 7 } rulls weigh as much as \latex{ 4 } kumps. \latex{ 5 } sons weigh the same as \latex{ 6 } kumps.
Put the biscuits in ascending order by their weight.
\latex{ 7 } rulls weigh as much as \latex{ 4 } kumps. \latex{ 5 } sons weigh the same as \latex{ 6 } kumps.
Put the biscuits in ascending order by their weight.
