Question

lesson 5 - 2 generate equivalent ratios
quick review
you can multiply or divide both terms of a ratio by the same nonzero number to find equivalent ratios.
example
find two ratios that are equivalent to $\frac{21}{126}$.
one way
multiply.
$\frac{21\times2}{126\times2}=\frac{42}{252}$
another way
divide.
$\frac{21div3}{126div3}=\frac{7}{42}$
practice
in 1 - 4, find two ratios equivalent to the given ratio.

1. $\frac{5}{12}$
2. $14:32$
3. 3 to 4
4. $\frac{7}{8}$
5. for every 4 bagels sold at a bakery, 7 muffins are sold. how many muffins are sold when the bakery sells 24 bagels? complete the table.

bagels	4	8	12	16	20	24
muffins	7

Explanation:

Step1: Recall the method for equivalent ratios

Multiply or divide both terms of a ratio by the same non - zero number.

Step2: Solve for problem 1 ($\frac{5}{12}$)

Multiply both terms by 2: $\frac{5\times2}{12\times2}=\frac{10}{24}$; multiply both terms by 3: $\frac{5\times3}{12\times3}=\frac{15}{36}$.

Step3: Solve for problem 2 ($14:32$)

Divide both terms by 2: $14\div2:32\div2 = 7:16$; multiply both terms by 2: $14\times2:32\times2=28:64$.

Step4: Solve for problem 3 ($3$ to $4$)

Multiply both terms by 2: $3\times2$ to $4\times2 = 6$ to $8$; multiply both terms by 3: $3\times3$ to $4\times3=9$ to $12$.

Step5: Solve for problem 4 ($\frac{7}{8}$)

Multiply both terms by 2: $\frac{7\times2}{8\times2}=\frac{14}{16}$; multiply both terms by 3: $\frac{7\times3}{8\times3}=\frac{21}{24}$.

Step6: Solve for problem 5

The ratio of bagels to muffins is $4:7$.
For 8 bagels: Since $8\div4 = 2$, then the number of muffins is $7\times2=14$.
For 12 bagels: Since $12\div4 = 3$, then the number of muffins is $7\times3 = 21$.
For 16 bagels: Since $16\div4=4$, then the number of muffins is $7\times4 = 28$.
For 20 bagels: Since $20\div4 = 5$, then the number of muffins is $7\times5=35$.
For 24 bagels: Since $24\div4 = 6$, then the number of muffins is $7\times6 = 42$.

Answer:

1. $\frac{10}{24},\frac{15}{36}$
2. $7:16,28:64$
3. $6$ to $8,9$ to $12$
4. $\frac{14}{16},\frac{21}{24}$

5.

Bagels	4	8	12	16	20	24