Question

1 which is closer to 1? 0.9 0.99 explain your answer: 2 ◆ mental math ◆ try to solve these in your head then write the answer. 24÷3=______ 240÷3=____ 2,400÷3=____ 24,000÷3=____ 3 what is the area of this rectangle? ____ sq ft what is the perimeter of this rectangle? ______ ft 4 1 - \frac{1}{2}= 1 - \frac{2}{5}= 1 - \frac{1}{8}= 1 - \frac{3}{8}= 1 - \frac{1}{4}= 1 - \frac{3}{4}= 5 this planet is surrounded by rings. solve each. then write the letter that goes with each answer in the spaces above. \frac{240÷3}{u} \frac{360÷6}{s} \frac{400÷4}{r} \frac{720÷8}{t} \frac{450÷9}{a} \frac{120÷3}{n}

Explanation:

Step1: Calculate the distance from 0.9 to 1

The distance is \(1 - 0.9=0.1\).

Step2: Calculate the distance from 0.99 to 1

The distance is \(1 - 0.99 = 0.01\).

Step3: Compare the two distances

Since \(0.01<0.1\), 0.99 is closer to 1.

Step4: Solve \(24\div3\)

Using basic division, \(24\div3 = 8\).

Step5: Solve \(240\div3\)

\(240\div3=(24\times10)\div3 = 24\div3\times10=8\times10 = 80\).

Step6: Solve \(2400\div3\)

\(2400\div3=(24\times100)\div3=24\div3\times100 = 8\times100=800\).

Step7: Solve \(24000\div3\)

\(24000\div3=(24\times1000)\div3=24\div3\times1000=8\times1000 = 8000\).

Step8: Calculate the area of the rectangle

The area formula for a rectangle is \(A = l\times w\). Here \(l = 3\) ft and \(w=\frac{3}{4}\) ft. So \(A=3\times\frac{3}{4}=\frac{9}{4}=2.25\) sq ft.

Step9: Calculate the perimeter of the rectangle

The perimeter formula for a rectangle is \(P=2(l + w)\). \(l = 3\) ft and \(w=\frac{3}{4}\) ft. \(P=2(3+\frac{3}{4})=2\times\frac{12 + 3}{4}=2\times\frac{15}{4}=\frac{15}{2}=7.5\) ft.

Step10: Solve fraction - subtraction problems

• \(1-\frac{1}{2}=\frac{2 - 1}{2}=\frac{1}{2}\)
• \(1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\)
• \(1-\frac{1}{8}=\frac{8 - 1}{8}=\frac{7}{8}\)
• \(1-\frac{3}{8}=\frac{8-3}{8}=\frac{5}{8}\)
• \(1-\frac{1}{4}=\frac{4-1}{4}=\frac{3}{4}\)
• \(1-\frac{3}{4}=\frac{4 - 3}{4}=\frac{1}{4}\)

Step11: Solve division problems for the planet - related question

• \(240\div3 = 80\) (corresponds to \(U\))
• \(360\div6=60\) (corresponds to \(S\))
• \(400\div4 = 100\) (corresponds to \(R\))
• \(720\div8=90\) (corresponds to \(T\))
• \(450\div9 = 50\) (corresponds to \(A\))
• \(120\div3=40\) (corresponds to \(N\))

Answer:

1. \(0.99\) is closer to \(1\) because \(1 - 0.9=0.1\) and \(1 - 0.99=0.01\), and \(0.01<0.1\).
2. \(24\div3 = 8\), \(240\div3=80\), \(2400\div3 = 800\), \(24000\div3=8000\).
3. Area: \(2.25\) sq ft, Perimeter: \(7.5\) ft.
4. \(1-\frac{1}{2}=\frac{1}{2}\), \(1-\frac{2}{5}=\frac{3}{5}\), \(1-\frac{1}{8}=\frac{7}{8}\), \(1-\frac{3}{8}=\frac{5}{8}\), \(1-\frac{1}{4}=\frac{3}{4}\), \(1-\frac{3}{4}=\frac{1}{4}\).
5. \(U:80\), \(S:60\), \(R:100\), \(T:90\), \(A:50\), \(N:40\). The planet is \(S\)aturn.