Select all three true statements
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1 point
-4.5 = |-4.5|
86 = |86|
|-10 2/3|= 10 2/3
-|1/3| = 1/3
|-57| = 57
-4.5 = |-4.5|
86 = |86|
|-57| = 57
The three true statements are:
1. -4.5 = |-4.5|
2. |-10 2/3| = 10 2/3
3. |-57| = 57
To determine which statements are true, we can evaluate each one individually.
Statement 1: -4.5 = |-4.5|
The expression |-4.5| means the absolute value of -4.5. The absolute value of any number is its distance from zero on the number line, disregarding its sign. In this case, the absolute value of -4.5 is 4.5. So, the statement -4.5 = 4.5 is false.
Statement 2: 86 = |86|
Similar to the previous statement, the expression |86| represents the absolute value of 86. Since 86 is a positive number, its absolute value is simply itself. Therefore, the statement 86 = |86| is true.
Statement 3: |-10 2/3| = 10 2/3
The expression |-10 2/3| represents the absolute value of -10 2/3. To find the absolute value of a mixed number, we can find the absolute value of its fractional part and keep the whole number part the same. Thus, |-10 2/3| = 10 2/3. Therefore, the statement |-10 2/3| = 10 2/3 is true.
Statement 4: -|1/3| = 1/3
The expression -|1/3| represents the negative of the absolute value of 1/3. The absolute value of 1/3 is 1/3 itself since it is already a positive number. Thus, the negative of 1/3 is -1/3. Therefore, the statement -|1/3| = 1/3 is false.
Statement 5: |-57| = 57
The expression |-57| represents the absolute value of -57. Similar to the first statement, the absolute value of -57 is 57. Thus, the statement |-57| = 57 is true.
Based on the evaluations, the three true statements are:
1. 86 = |86|
2. |-10 2/3| = 10 2/3
3. |-57| = 57