Question

wednesday review packet
this packet will be used on wednesdays during small group/review days remember to read through all of the directions before starting on a problem.
problem 1
in a classroom, there are 12 boys and 8 girls. write the ratio of boys to girls in three different ways.

problem 2
a recipe calls for 2 cups of flour for every 3 cups of sugar. if you want to triple the recipe, how much flour and sugar do you need?

problem 3
are 4:6 and 6:9 equivalent ratios? explain how you know.

problem 4
at a juice stand, the ratio of apple juice to orange juice is 3:2. if there are 15 cups of apple juice, how many cups of orange juice are there?

Explanation:

Problem 1

Step1: Identify the numbers for ratio

We have 12 boys and 8 girls. The ratio of boys to girls is boys : girls.

Step2: Write as a fraction

The ratio as a fraction is $\frac{12}{8}$, which simplifies to $\frac{3}{2}$.

Step3: Write with a colon

Using a colon, the ratio is $12:8$, which simplifies to $3:2$.

Step4: Write in words

In words, it is "12 to 8" or "3 to 2" (after simplifying).

Step1: Determine the original amounts

Original flour: 2 cups, original sugar: 3 cups.

Step2: Triple the flour amount

To triple the flour, multiply 2 by 3: $2\times3 = 6$ cups of flour.

Step3: Triple the sugar amount

To triple the sugar, multiply 3 by 3: $3\times3 = 9$ cups of sugar.

Step1: Simplify the first ratio

For $4:6$, divide both parts by 2: $\frac{4\div2}{6\div2}=\frac{2}{3}$, so $4:6 = 2:3$.

Step2: Simplify the second ratio

For $6:9$, divide both parts by 3: $\frac{6\div3}{9\div3}=\frac{2}{3}$, so $6:9 = 2:3$.

Step3: Compare the simplified ratios

Since both $4:6$ and $6:9$ simplify to $2:3$, they are equivalent.

Answer:

• As a fraction: $\frac{12}{8}$ (or $\frac{3}{2}$)
• With a colon: $12:8$ (or $3:2$)
• In words: 12 to 8 (or 3 to 2)

Problem 2