Understanding inequalities and measurements involves correctly interpreting when one quantity is less than, greater than, or equal to another and sometimes converting units for comparison. Examples include determining if a picture has a width less than 8.5 inches, if someone is at least 48 inches tall, if a baby's age is not 24 months, or if the number of quarters in a jar is less than 75.
When dealing with inequalities and measurements, it's important to understand how to compare different numbers and expressions appropriately. Consider the situation where a student needs to determine whether one measurement is less than, greater than, or equal to another. This involves interpreting inequalities correctly and sometimes converting units to make a direct comparison.
Examples of Comparing Measurements and Expressions
If we are given that w < 8.5 inches, and we have a picture of width w = 6 inches, then indeed 6 inches is less than 8.5 inches, satisfying the inequality w < 8.5 inches.
When comparing heights, such as h ≥ 48 inches, and we know Steve's height h = 50 inches, it's clear that 50 inches is at least 48 inches, hence meeting the condition h ≥ 48 inches.
Concerning ages, if Vera's baby brother's age b ≠ 24 months, and we know b = 18 months, then 18 months is not equal to 24 months, thus b ≠ 24 is true.
Finally, if we have q < 75 quarters in a jar and count q = 50 quarters, we correctly assert that 50 quarters is less than 75 quarters, which again satisfies the inequality q < 75.
The probable question may be:
Considering numerical values for simplicity, let's explore these mathematical statements:
The width of a picture, w, is such that w<8.5 inches.
Steve's height, h, is h≥48 inches.
Vera's baby brother's age, b, is such that bb is not equal to 24 months.
The number of quarters, q, in a jar is q<75.
Additional Information:
To illustrate, let's consider specific values. For statement 1, if w=6 inches, it satisfies w<8.5. For statement 2, if h=50 inches, Steve's height is at least 48 inches. In statement 3, if b=18 months, Vera's baby brother is not 24 months old. Finally, for statement 4, if q=50, the number of quarters in the jar is less than 75.