What is the relationship between ratios and fractions?

Ratios compare quantities; fractions represent parts.

• Ratios show relative sizes.

• Fractions indicate parts of a whole.

• Both are essential in mathematics.

Fill in the blank: Ratios can be treated as ___.

Fractions

True or False: Equivalent ratios can only be formed by adding the same number to both terms of the ratio.

False, equivalent ratios can be formed by multiplying or dividing both terms by the same non-zero number.

If a and b are in direct proportion and a = 4 when b = 8, what is the value of b when a = 10?

20, since the ratio a/b remains constant, thus 4/8 = 10/b leads to b = 20.

Fill in the blank: The ratio 45 : 25 in its lowest form can be written as ___.

9 : 5

True or False: Inverse proportion means that as one quantity increases, the other quantity also increases.

False, in inverse proportion, as one quantity increases, the other quantity decreases.

Using the unitary method, if 15 artists can complete a statue in 48 hours, how many artists are needed to finish it in 30 hours?

24 artists, calculated using the inverse proportion formula: 48 * 15 = 30 * y.

If two quantities a and b are in inverse proportion, what is the expression that relates them?

A * b = k, where k is a constant.

Fill in the blank: The symbol used to denote direct proportion is ___.

∝

What is the significance of the order of quantities when expressing a ratio?

The order affects the relationship; for example, 4 : 5 is not the same as 5 : 4.