Two common types of ratios we'll see are part to part and part to whole. For example, when we make lemonade:
The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients.
The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum of all ingredients.
\text{part}:\text{whole}=\text{part}:\text{sum of all parts}part:whole=part:sum of all partsstart text, p, a, r, t, end text, colon, start text, w, h, o, l, e, end text, equals, start text, p, a, r, t, end text, colon, start text, s, u, m, space, o, f, space, a, l, l, space, p, a, r, t, s, end text
To write a ratio:
Determine whether the ratio is part to part or part to whole.
Calculate the parts and the whole if needed.
Plug values into the ratio.
Simplify the ratio if needed. Integer-to-integer ratios are preferred.
Example: Part to whole
Examples: Simplifying ratios
Equivalent ratios are ratios that have the same value. Given a ratio, we can generate equivalent ratios by multiplying both parts of the ratio by the same value.
Example
How do we use proportions?
If we know a ratio and want to apply it to a different quantity (for example, doubling a cookie recipe), we can use proportional relationships, or equations of equivalent ratios, to calculate any unknown quantities.
To use a proportional relationship to find an unknown quantity:
Write an equation using equivalent ratios.
Plug in known values and use a variable to represent the unknown quantity.
If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it
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Answer:
How do we write ratios?
Two common types of ratios we'll see are part to part and part to whole. For example, when we make lemonade:
The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients.
The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum of all ingredients.
\text{part}:\text{whole}=\text{part}:\text{sum of all parts}part:whole=part:sum of all partsstart text, p, a, r, t, end text, colon, start text, w, h, o, l, e, end text, equals, start text, p, a, r, t, end text, colon, start text, s, u, m, space, o, f, space, a, l, l, space, p, a, r, t, s, end text
To write a ratio:
Determine whether the ratio is part to part or part to whole.
Calculate the parts and the whole if needed.
Plug values into the ratio.
Simplify the ratio if needed. Integer-to-integer ratios are preferred.
Example: Part to whole
Examples: Simplifying ratios
Equivalent ratios are ratios that have the same value. Given a ratio, we can generate equivalent ratios by multiplying both parts of the ratio by the same value.
Example
How do we use proportions?
If we know a ratio and want to apply it to a different quantity (for example, doubling a cookie recipe), we can use proportional relationships, or equations of equivalent ratios, to calculate any unknown quantities.
\begin{aligned} a:b &= c:d \\\\ \dfrac{a}{b}&=\dfrac{c}{d} \end{aligned}
a:b
b
a
=c:d
=
d
c
To use a proportional relationship to find an unknown quantity:
Write an equation using equivalent ratios.
Plug in known values and use a variable to represent the unknown quantity.
If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it