Test
Multiplication and division by 0, 1, 10. Division of a number by itself.
This test explores multiplication and division rules involving 0, 1 and 10. Students also examine division of a number by itself, recognise that division by zero is undefined and justify the selected answer.
Time left: 00:00:00
Sample questions
- Calculate
- Calculate: ___ ___.
- Calculate: ___ ÷ ___.
- One box contains ___ pencils. How many pencils will 10 such boxes contain?
- A ___-centimetre ribbon is divided into 10 equal parts. How many centimetres are in one part?
Multiplication and division by 0, 1 and 10
The numbers 0, 1 and 10 follow clear rules in multiplication and division. Understanding these rules makes calculation faster and helps identify impossible answers, but the dividend and divisor must not be confused.
Multiplication rules
- a × 0 = 0 because there are no groups.
- a × 1 = a because there is one group of that size.
- When a whole number is multiplied by 10, its digits shift one place to the left and 0 occupies the ones place.
Division rules
- 0 ÷ a = 0 when a is not 0.
- a ÷ 1 = a.
- a ÷ a = 1 when a is not 0.
- a ÷ 0 is undefined.
The expressions 0 ÷ 5 and 5 ÷ 0 are not equivalent: the first equals 0, while the second cannot be calculated. A division result can be checked by multiplication only when the divisor is non-zero.
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