Question

for problems 7–10, circle true or false.

1. $\frac{8}{8} > \frac{12}{12}$

true false

1. $\frac{12}{50} = \frac{6}{25}$

true false

1. $2.2 > 2.0\dot{9}$

true false

1. $8.15 = 8 + \frac{1}{10} + \frac{5}{100}$

true false

Explanation:

Problem 7:

Step1: Simplify fractions

Simplify \(\frac{8}{8}\) and \(\frac{12}{12}\). Both equal \(1\) since a non - zero number divided by itself is \(1\), so \(\frac{8}{8}=1\) and \(\frac{12}{12}=1\).

Step2: Compare the values

Since \(1 = 1\), the statement \(\frac{8}{8}>\frac{12}{12}\) is false. But looking at the "TRUE" and "FALSE" options, if we made a mis - step? Wait, no, \(\frac{8}{8}=1\), \(\frac{12}{12}=1\), so \(1\) is not greater than \(1\). But maybe the original problem was a typo? Wait, the problem says "circle True or False". If we follow the calculation, the answer for problem 7 should be "FALSE". But let's check again. \(\frac{8}{8}=1\), \(\frac{12}{12}=1\), so \(1\) is not greater than \(1\), so the statement is false.

Problem 8:

Step1: Simplify \(\frac{12}{50}\)

We can simplify \(\frac{12}{50}\) by dividing both the numerator and the denominator by \(2\). \(\frac{12\div2}{50\div2}=\frac{6}{25}\).

Step2: Compare with \(\frac{6}{25}\)

Since \(\frac{12}{50}=\frac{6}{25}\) (after simplification), the statement \(\frac{12}{50}=\frac{6}{25}\) is true.

Problem 9:

Step1: Analyze the decimal numbers

The number \(2.2\) can be written as \(2.20\) (by adding a zero at the hundredths place, which does not change the value of the decimal).

Step2: Compare the decimals

Now we compare \(2.20\) and \(2.09\). Comparing the tenths place: \(2\) (in \(2.20\)) is greater than \(0\) (in \(2.09\)). So \(2.2>2.09\) is true.

Problem 10:

Answer:

Step1: Calculate the right - hand side

First, calculate \(8+\frac{1}{10}+\frac{5}{100}\). \(\frac{1}{10}=0.1\) and \(\frac{5}{100}=0.05\). Then \(8 + 0.1+0.05=8.15\).

Step2: Compare with the left - hand side

The left - hand side is \(8.15\), and the right - hand side is also \(8.15\). So the statement \(8.15 = 8+\frac{1}{10}+\frac{5}{100}\) is true.

Final Answers (for each problem):

• Problem 7: FALSE
• Problem 8: TRUE
• Problem 9: TRUE
• Problem 10: TRUE