Question

daily math practice wednesday 15

1. $\frac{2}{3} \times \frac{1}{5}=$
2. $\

$$\begin{array}{r}1.26 \\\\ \\times 0.8 \\\\ \\hline\\end{array}$$

$

1. name a pair of supplementary angles.
2. write this number in standard form.

one hundred three and sixteen thousandths

1. sheila and her sister sarah are baby - sitting three kids for 5 hours. if the parents pay $2.50 per hour for each kid, how much will sheila and sarah each make?

Explanation:

Step1: Multiply the numerators and denominators

$$\frac{2}{3}\times\frac{1}{5}=\frac{2\times1}{3\times5}$$

Step2: Calculate the result

$$\frac{2\times1}{3\times5}=\frac{2}{15}$$

Step3: Multiply decimals

$$1.26\times0.8 = (1 + 0.2+0.06)\times0.8=1\times0.8+0.2\times0.8 + 0.06\times0.8$$
$$=0.8+0.16 + 0.048=1.008$$

Step4: Write the number in standard form

One hundred three is \(103\), sixteen thousandths is \(0.016\). So the number is \(103 + 0.016=103.016\)

Step5: Identify supplementary angles

Supplementary angles add up to \(180^{\circ}\). In the diagram, \(\angle a\) and \(\angle b\) form a linear - pair (they are adjacent and their non - common sides form a straight line). So \(\angle a\) and \(\angle b\) are supplementary (other pairs like \(\angle a\) and \(\angle d\) also work as \(a + d=180^{\circ}\) etc.)

Step6: Calculate the earnings

There are \(3\) kids, paid \(\$2.50\) per hour per kid for \(5\) hours. The total amount earned is \(3\times2.50\times5=\$37.5\). Since there are \(2\) people (Sheila and Sarah), each makes \(\frac{3\times2.50\times5}{2}=\frac{37.5}{2}=\$18.75\)

Answer:

1. \(\frac{2}{15}\)
2. \(1.008\)
3. \(\angle a\) and \(\angle b\) (or other valid pairs like \(\angle a\) and \(\angle d\), \(\angle b\) and \(\angle c\), \(\angle c\) and \(\angle d\))
4. \(103.016\)
5. \(\$18.75\)