Сагс хоосон байна
Dividing numbers by 10; 100 and 1,000
Dave and John want to buy a bicycle. How many banknotes do they need if they only have €\latex{ 100 } banknotes? And if they only had €\latex{ 10 } banknotes?
\latex{ }They rode \latex{ 25,000 } \latex{ metres } on the weekend. How many \latex{ km } is that?
You often divide numbers by \latex{ 10 }, \latex{ 100 } and \latex{ 1,000 } when changing to a larger unit or dealing with money. You can do this quickly and easily by changing the place values.
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 0 }
\latex{ 0 }
\latex{ 0 }
\latex{ 0 }
\latex{ 3 }
\latex{ 7 }
\latex{ 3 }
\latex{ 4 }
\latex{ 7 }
\latex{ 3 }
\latex{ 0 }
\latex{ 4 }
\latex{ 7 }
\latex{ 3 }
\latex{ 0 }
\latex{ 0 }
\latex{ 4 }
\latex{ 7 }
\latex{ 0 }
\latex{ 0 }
\latex{ 0 }
\latex{ 4 }
÷\latex{ 10 }
÷\latex{ 100 }
÷\latex{ 1,000 }
÷\latex{ 10,000 }
\latex{3,740,000 \div 10 = \textbf{\textcolor{#ff0000}{374,000}}}
\latex{3,740,000 \div 100 = \textbf{\textcolor{#ff0000}{37,400}}}
\latex{3,740,000 \div 1,000 = \textbf{\textcolor{#ff0000}{3,740}}}
\latex{3,740,000 \div 10,000 = \textbf{\textcolor{#ff0000}{374}}}
The table above shows how the place values change during division.
When dividing a natural number by \latex{ 10 }, each digit of the dividend moves back one place value.
\latex{\div10=}
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 0 }
\latex{ 0 }
\latex{ 7 }
\latex{ 4 }
\latex{ 3 }
\latex{ 0 }
\latex{3\textcolor{#ff0000}{7},400 \div 10 = 3,\textcolor{#ff0000}{7}40}
\latex{ 1,000 }s
\latex{ 100 }s
When dividing a natural number by \latex{ 100 }, each digit of the dividend moves back two place values.
\latex{\div100=}
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 0 }
\latex{ 0 }
\latex{ 7 }
\latex{ 4 }
\latex{ 3 }
\latex{3\textcolor{#ff0000}{7},400 \div 100 = 3\textcolor{#ff0000}{7}4}
\latex{ 1,000 }s
\latex{ 10 }s
When dividing a natural number by \latex{ 1,000 }, each digit of the dividend moves back three place values.
\latex{\div1,000=}
\latex{ 7 }
\latex{ 4 }
\latex{ 0 }
\latex{ 0 }
\latex{ 0 }
\latex{ 3 }
\latex{ 7 }
\latex{ 3 }
\latex{ 4 }
\latex{3\textcolor{#ff0000}{7}4,000 \div 1,000 = 3\textcolor{#ff0000}{7}4}
\latex{ 10,000 }s
\latex{ 10 }s
Example
Ida collects \latex{ euro } coins. She put her \latex{ 1 }, \latex{ 2 } and \latex{ 5 }-\latex{ cent } coins in stacks of \latex{ 10 }. There are \latex{ 80 } stacks of \latex{ 1 }, \latex{ 155 } stacks of \latex{ 2 } and \latex{ 42 } stacks of \latex{ 5 }-\latex{ cent } coins.
a) How many \latex{ euros } would she get if she exchanged all her coins?
b) Could she exchange her \latex{ cents } for \latex{ 10 } \latex{ euro } banknotes?
b) Could she exchange her \latex{ cents } for \latex{ 10 } \latex{ euro } banknotes?
Solutions
\latex{\begin{matrix}{1\, cents} \\ {2\, cents} \\ {5\, cents} \end{matrix} \quad \underbrace{\begin{matrix} 80 \times 10 = 800 \\ 155 \times 2 \times 10 = 3,100 \\ 42 \times 5 \times 10 = 2,100 \end{matrix}}_{{6,000\, cent}} }
a) Since \latex{ 1 } \latex{ euro } = \latex{ 100 } \latex{ euro } \latex{ cents }, thus \latex{ 6,000 } : \latex{ 100 } = \latex{ 60 } \latex{ euros. }
b) \latex{ 60 } : \latex{ 10 } = \latex{ 6 } → she can exchange her \latex{ cents } for six \latex{ 10 }-\latex{ euro } banknotes.
b) \latex{ 60 } : \latex{ 10 } = \latex{ 6 } → she can exchange her \latex{ cents } for six \latex{ 10 }-\latex{ euro } banknotes.
Exercises
{{exercise_number}}. What are the rules for dividing numbers by \latex{ 10,000 }?
{{exercise_number}}. What is the one-hundredth part of the following numbers?
a) \latex{ 7,400 }
b) \latex{ 4,700 }
c) \latex{ 74,000 }
d) \latex{ 40,700 }
e) \latex{ 47,000 }
f) \latex{ 70,400 }
g) \latex{ 36,000 }
h) \latex{ 130,600 }
{{exercise_number}}. Divide the following numbers by \latex{ 10 }, \latex{ 100 } and \latex{ 1,000 }.
a) \latex{ 6,000 }
b) \latex{ 71,000 }
c) \latex{ 120,000 }
d) \latex{ 374,000 }
{{exercise_number}}. Dividing a number by \latex{ 1,000 }, you get \latex{ 702 }. Which number was divided by \latex{ 1,000 }?
{{exercise_number}}. I thought of a number. I divided it by \latex{ 100 }, then divided the result by \latex{ 10 }, leaving \latex{ 52 }. What number did I think of?
{{exercise_number}}. The one-thousandth part of a number is \latex{ 48 }. What number do you get if
a) you multiply it by \latex{ 10 };
b) you divide it by \latex{ 10 };
c) you multiply it by \latex{ 10 }, then divide the result by \latex{ 10 }?
b) you divide it by \latex{ 10 };
c) you multiply it by \latex{ 10 }, then divide the result by \latex{ 10 }?
Quiz
You have \latex{ 25 } apples in your basket. You want to divide them among your friends, so you take out three, give Ida four, Kate five, Zoe two, Agnes four, George one and Louis two. How many apples are left?
