Question

unit 2: multiplying and dividing rational numbers
spiral review
whole numbers
23 · 17 = _______\t720
decimals
22.3 · 7.8 = _______\t4.8
fractions

Explanation:

Step1: Calculate \(23 \cdot 17\)

We can use the distributive property: \(23\times17=(20 + 3)\times17=20\times17+3\times17\).
\(20\times17 = 340\) and \(3\times17=51\). Then \(340 + 51=391\).

Step2: Calculate \(22.3 \cdot 7.8\)

First, multiply the numbers as if they were whole numbers: \(223\times78\).
\(223\times78 = 223\times(70 + 8)=223\times70+223\times8=15610+1784 = 17394\).
Since \(22.3\) has 1 decimal place and \(7.8\) has 1 decimal place, the product has \(1 + 1=2\) decimal places.
So, \(22.3\times7.8=\frac{17394}{100}=173.94\).

Answer:

For \(23 \cdot 17\), the answer is \(391\).
For \(22.3 \cdot 7.8\), the answer is \(173.94\).