Question

1. danu earns $560 in commissions one wee much did she earn in the second week?

$560\square 1\frac{2}{5} = 560 \times \frac{\square}{\square} = \\$\square

Explanation:

Step1: Determine the operation

Since we need to find the earnings in the second week which is a multiple of the first week's earnings (as indicated by the mixed number \(1\frac{2}{5}\)), the operation is multiplication. So the first box is filled with \(\times\).

Step2: Convert mixed number to improper fraction

To convert \(1\frac{2}{5}\) to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). Here, \(a = 1\), \(b = 2\), \(c = 5\), so \(1\frac{2}{5}=\frac{1\times5 + 2}{5}=\frac{7}{5}\). So the fraction boxes are filled with \(7\) (numerator) and \(5\) (denominator).

Step3: Calculate the product

Now we calculate \(560\times\frac{7}{5}\). We can simplify this as \(\frac{560\times7}{5}\). \(560\div5 = 112\), then \(112\times7=784\). So the last box is filled with \(784\).

Answer:

The first box (operation) is \(\times\), the fraction is \(\frac{7}{5}\), and the result is \(784\). So filling in the boxes: \(560\times1\frac{2}{5}=560\times\frac{7}{5}=\$784\)