There are some three-digit numbers which can be divided by the product
of their digits without leaving a remainder.
175
Example (i) Take the number 175, 1 x 7 x 5 = 35,
= 5
35
816
(ii) Take the number 816, 8 X 1 X 6 = 48, =17
48
612
(iii) Take the number 612, 6 x 1 x 2 = 12, =51
12
The numbers 135, 312, 672 are some more numbers like these.
Can you find other such numbers?
please help me
Answers
Step-by-step explanation:
ASSUMED KNOWLEDGE
Much of the building of understanding of early mathematics occurs concurrently, so a child can be developing the basic ideas related to multiplication and division whilst also investigating the place-value system. However, there are some useful foundations necessary for multiplication and division of whole numbers:
Some experience with forwards and backwards skip-counting.
Some experience doubling and halving small numbers.
(see F-4 Module Counting and Place Value and F-4 Module Addition and Subtraction)
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MOTIVATION
One way of thinking of multiplication is as repeated addition. Multiplicative situations arise when finding a total of a number of collections or measurements of equal size. Arrays are a good way to illustrate this. Some division problems arise when we try to break up a quantity into groups of equal size and when we try to undo multiplications.
Multiplication answers questions such as:
1
Judy brought 3 boxes of chocolates. Each box contained 6 chocolates. How many chocolates did Judy have?
2
Henry has 3 rolls of wire. Each roll is 4m long. What is the total length of wire that Henry has?
Division answers questions such as:
1
How many apples will each friend get if four friends share 12 apples equally
between them?
2
If twenty pens are shared between seven children how many does each child receive, and how many are left over?
Addition is a useful strategy for calculating ‘how many’ when two or more collections of objects are combined. When there are many collections of the same size, addition is not the most efficient means of calculating the total number of objects. For example, it is much quicker to calculate 6 × 27 by multiplication than by repeated addition.
Fluency with multiplication reduces the cognitive load in learning later topics such as division. The natural geometric model of multiplication as rectangular area leads to applications in measurement. As such, multiplication provides an early link between arithmetic and geometry.
Fluency with division is essential in many later topics and division is central to the calculations of ratios, proportions, percentages and slopes. Division with remainder is a fundamental idea in electronic security and cryptography.
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CONTENT
Multiplication and division are related arithmetic operations and arise out of everyday experiences. For example, if every member of a family of 7 people eats 5 biscuits, we can calculate 7 × 5 to work out how many biscuits are eaten altogether or we can count by ‘fives’, counting one group of five for each person. In many situations children will use their hands for multiples of five.
For whole numbers, multiplication is equivalent to repeated addition and is often introduced using repeated addition activities. It is important, though that children see multiplication as much more than repeated addition.
If we had 35 biscuits and wanted to share them equally amongst the family of 7, we would use sharing to distribute the biscuits equally into 7 groups.
We can write down statements showing these situations:
7 × 5 = 35 and 5 × 7 = 35
Also,
35 ÷ 5 = 7 and 35 ÷ 7 = 5