Use structural patterns and factorization to simplify multiplication of large numbers.
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Introduce replacing multiplication by 5 or 25 with division and shifting zeroes.
Have you ever tried to multiply large numbers in your head? It can be slow and prone to errors. But numbers often hide patterns that make calculations much easier.
Process flowchart showing standard vs shortcut multiplication.
Breaking numbers into easier factors like 2 and 10 allows you to perform mental math rapidly.
Worked example showing 116 x 5.
Problem. Calculate the product of quickly using a multiplication shortcut.
Generalization of the shortcuts for 5, 25, and 125.
Faded practice for 824 x 25.
Let's evaluate 824 × 25 using Estu's shortcut method. Since multiplying by 25 is exactly the same as multiplying by 100 and dividing by 4, we write: 824 × 25 = 824 × (100 ÷ 4).
Multiplying by and dividing by gives the same result. We can compute this more easily by performing the division first: 824 ÷ 4 = .
Finally, we multiply this intermediate result by 100 to get the final answer of .
Solve 25 x 240 using the shortcut.
What is the quickest way to calculate using the shortcut method taught in the chapter?
Use grouping and shortcuts for a multi-term product.
Use the associative and commutative properties to rearrange the terms so you can utilize powers of 10.
State the expression you are asked to evaluate.
What property allows you to reorder these numbers?
Rearrange the numbers into pairs that multiply easily into powers of 10.
Show the intermediate product of each pair.
Provide the final multiplied value.
Does the magnitude of your answer make sense?