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How do you decide when to compare numbers using ratios rather by finding the difference of the two numbers?
Finding the difference between two numbers involves rationalising them
How do you compare two ratios in two ways?
Treat the ratios as fractions. One way you can compare them is to convert them to decimal (divide the numerator by the denominator, or the first number of the ratio by the second number), then compare. Another way is to find a common denominator, then compare the numerators.
What methods is used to determine if 2 ratios form a proportion?
To determine if two ratios form a proportion, you can use cross-multiplication. If the cross-products of the ratios are equal, the ratios are proportional. For example, for the ratios ( \frac{a}{b} ) and ( \frac{c}{d} ), if ( a \times d = b \times c ), then the two ratios form a proportion. Additionally, you can also compare the decimal values of the ratios; if they are equal, they are proportional.
What numbers represent irrational numbers?
These are the numbers which cannot be expressed as ratios of two integers.
Why are some numbers irrational?
There are numbers which cannot be expressed as ratios of two integers. These are called irrational numbers.
When do two ratios form a proportion?
When both can multiply its comparisons to when both ratios share the exact same numbers.
How are ratios and rates similar and different?
They are different because a ratiocompares two different numbers or measurements from different units but the rate does not. They are similar because they both compare numbers. EX) ratio: 4/3 rate: 1.333 etc.
Can you compare two complex numbers?
You can compare their magnitude (absolute values) but not the numbers themselves.
The product of numbers on the diagonal when comparing two ratios?
cross product.
When two numbers have the same value?
Equivalent ratios.
Is it true that the first numbers in the 2 equivalent ratios will always have a common factor?
Yes, it is true that the first numbers in two equivalent ratios will always have a common factor. This common factor is known as the scale factor, which is used to create equivalent ratios by multiplying or dividing both parts of the ratio by the same number. This ensures that the ratios maintain the same proportionality.
What is used to compare two numbers on a graph?
Their position relative to a reference point - often the origin.
