There are many different ways to compare amounts or quantities. A ratio is a comparison of two quantities by division. For example, the ratio of

a

to

b

can be written in two different ways.

\frac{a}{b} or a : b

We want to find the value of the ratio of baking soda to salt. We can write the fraction that represents this ratio ratio. We will write the number of teaspoons of baking soda in the numerator and the number of teaspoons of salt in the denominator.

baking soda \to salt \to \frac{\frac{2}{3}}{3}

Recall that fractions can be thought of as dividing the numerator by the denominator.

\frac{\frac{2}{3}}{3} = \frac{2}{3} \div 3

Before we evaluate this expression, let's first rewrite the expression so that all of the numbers are fractions.

\frac{2}{3} \div 3

NumToDivByOne

$a = \frac{a}{1}$

\frac{2}{3} \div \frac{3}{1}

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

\frac{2}{3} \div \frac{3}{1} = \frac{2}{3} \cdot \frac{1}{3}

When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

\frac{2}{3} \cdot \frac{1}{3}

MultFrac

Multiply fractions

\frac{1 \cdot 2}{3 \cdot 3}

Multiply

\frac{2}{9}

The greatest common factor of

2

and

9

is

1 .

This means that the fraction cannot be simplified. The ratio is

\frac{2}{9},

2

to

9,

or

2 : 9 .

This means that the number of teaspoons of baking soda is

\frac{2}{9}

the number of teaspoons of salt.

Exercise

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