Find the value of 5600 ÷ 400 without using a calculator.
5600 ÷ 400 = 5600 ÷ 100 ÷ 4 = 56 ÷ 4 = 14
Ans: 14
How to solve it
Split the multiple into its factors: 20 is 2 times 10, so multiply by both.
Multiply by 2 first: 47 times 2 is 94. Then times 10 moves every digit one place to the left, so the answer is 940.
Dividing works the same way: 8000 is 1000 times 8, so divide by 1000 first, then by 8.
240 000 divided by 1000 moves every digit 3 places to the right, which gives 240.
The divide by 8 is still there. 240 is 24 tens, and 24 tens divided by 8 is 3 tens, which is 30.
For 5600 divided by 400, divide by 100 to get 56, then divide by 4. The answer is 14.
Splitting the multiple leaves two factors, and we use both.
For parents
How do you multiply and divide whole numbers by 10, 100 and 1000 in P5?
This page teaches multiplying and dividing whole numbers by 10, 100, 1000 and their multiples without a calculator.
What your child learns here
This page teaches multiplying and dividing whole numbers by 10, 100, 1000 and their multiples without a calculator. It is the first Four Operations outcome in the Primary 5 Whole Numbers sub-strand, and it leads on to the same work with decimals.
Multiplying by 10, 100 or 1000 moves every digit 1, 2 or 3 places to the left, and zeros hold the empty places.
Dividing by 10, 100 or 1000 moves every digit 1, 2 or 3 places to the right.
A multiple such as 20 is 2 × 10, so 47 × 20 = 47 × 2 × 10 = 94 × 10 = 940.
To divide by 8000, divide by 1000 first and then by 8; the 8 is still part of the divisor.
Reading a number in tens or hundreds helps: 240 is 24 tens, and 24 tens ÷ 8 = 3 tens.
Does the answer make sense?
Count the zeros. Multiplying by 6000 adds three zeros' worth of size and a factor of 6, so 78 × 6000 must be in the hundreds of thousands. Dividing 240 000 by 8000 should give a small number, so an answer such as 240 shows the 8 was left out.
How to practise these questions
Basic questions give one calculation each, multiplying a two- or three-digit number by a multiple of 100 or 1000, or dividing by a multiple of 10. Intermediate questions put the same step into words, such as counting the seats in a hall, or ask for the number that was multiplied by 300. Challenge questions combine a division and a multiplication in one line, change cents into dollars at the end, or undo one division before doing a second. A good habit for every question is to write the multiple as its two factors before calculating anything.
Questions parents ask
Is it enough to add or remove zeros? Only for 10, 100 and 1000 themselves. For a multiple such as 400, the 4 must be used as well: 5600 ÷ 400 is 56 ÷ 4, which is 14.
Which factor should my child use first? Either order gives the same answer. For division the lesson takes the power of ten first, because it makes the number smaller and easier to divide.
How does this help with decimals later? The same place-value moves are used in the Primary 5 Decimals chapter, where decimals are multiplied and divided by 10, 100, 1000 and their multiples.
