Math / Numbers & Operations

QuestionRatios. Proportons, and Measweimetus Writing ratios for real-world situations
There are 6 red marbles and 9 blue marbles in a bag. (a) What is the ratio of red marbles to all marbles in the bag? $\square$ (b) What is the ratio of all marbles in the bag to blue marbles? $\square$

Studdy Solution

STEP 1

1. There are $6$ red marbles in the bag.
2. There are $9$ blue marbles in the bag.
3. The total number of marbles in the bag is the sum of red and blue marbles.

STEP 2

1. Calculate the total number of marbles.
2. Determine the ratio of red marbles to all marbles.
3. Determine the ratio of all marbles to blue marbles.

STEP 3

Calculate the total number of marbles in the bag.
The total number of marbles is the sum of red and blue marbles: $6 \text{ (red)} + 9 \text{ (blue)} = 15 \text{ (total marbles)}$

STEP 4

Determine the ratio of red marbles to all marbles.
The ratio of red marbles to all marbles is: $\frac{6 \text{ (red marbles)}}{15 \text{ (total marbles)}}$
Simplify the ratio: $\frac{6}{15} = \frac{2}{5}$
The ratio of red marbles to all marbles is $\frac{2}{5}$ .

STEP 5

Determine the ratio of all marbles to blue marbles.
The ratio of all marbles to blue marbles is: $\frac{15 \text{ (total marbles)}}{9 \text{ (blue marbles)}}$
Simplify the ratio: $\frac{15}{9} = \frac{5}{3}$
The ratio of all marbles to blue marbles is $\frac{5}{3}$ .
The solutions are: (a) The ratio of red marbles to all marbles is $\frac{2}{5}$ . (b) The ratio of all marbles to blue marbles is $\frac{5}{3}$ .

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