# Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

## Nutrition Labels

If you ever went to a supermarket, all packaged foods have a nutrition label. All nutrition labels gives people 4 important facts:

1) Serving size / Portion Size

Serving size is a measurement that reflects how much people usually eat. For example, if it says 4 serving sizes, it means that it usually serves 4 people. Also, there is usually a measurement with the serving size, where each serving size is related to a measurement, in the nutrition label below, it is 1 cup or 227g.

2) Calories for each serving

Measures the amount of energy from a serving of this food.

3) Amount of Nutrients

The label contains all the nutrients that are present in the food like fats, sodium and vitamins and provides the amount that is contained for each serving.

Get Less Nutrients: Fats, Saturated Fats, Trans Fats, Cholesterol, Sodium

Get More Nutrients: Carbohydrates, Fiber, Vitamin A, Vitamin C, Calcium, Iron

4) Percentage of Daily Value

The daily percentage value tells how much for each nutrients the person should consume for each day. A person should aim to eat less than 100% of daily value each day. For example, lets look at sodium, this food is high in daily value of sodium at 37% for each serving. If we eat 2 servings we would then get 74% of daily value of sodium. It is recommended to eat less than 100% of daily value. Daily value helps determine how much should you eat certain foods to not consume more nutrients than needed per day.

## Problems

All Nutrition Label questions involve referring to the nutrition label to get information to solve proportional questions.

Example

This the is the nutrition label that will be used to calculate the next few problems. This nutrition label is for maple syrup.

1) Involves Finding Amount of Nutrients: Albert ate $$\cfrac{3}{4}$$ cups of maple syrup. How much mg of sodium did he consume?

i) Look at the nutrients label and find the amount for each serving and mg of sodium for each serving. For each serving, it is $$\cfrac{1}{4}$$ cups and each of serving contains 10 mg of sodium.

ii) Place into a ratio:

$$\cfrac{1}{4} \text{cups} : 10 \text{mg}$$

iii) Find what is given and what we need to find

Given:  $$\cfrac{3}{4}$$ cups

Find: x mg of sodium

iv) Fill into the proportion to solve:

$$\cfrac{1}{4} \text{cups} : 10 \text{mg} :: \cfrac{3}{4} \text{cups} : x \text{ mg}$$

Notice: It is important to match the units, if cups is first for the first ratio then cups is first for the second ratio.

v) Solve the proportion:

$$\cfrac{1}{4} \text{cups} : 10 \text{mg} :: \cfrac{3}{4} \text{cups} : x \text{ mg}$$

$$\cfrac{1}{4} x = 10 \times \cfrac{3}{4}$$

$$\cfrac{1}{4} x = \cfrac{10}{1} \times \cfrac{3}{4}$$

$$\cfrac{1}{4} x = \cfrac{10 \times 3}{1 \times 4}$$

$$\cfrac{1}{4} x = \cfrac{30}{4}$$

$$\cfrac{4}{1} \times \cfrac{1}{4} x = \cfrac{4}{1} \times \cfrac{30}{4}$$

$$x = \cfrac{120}{4}$$

$$x = 30\text{ mg}$$

Hence, $$\cfrac{3}{4}$$ cups of maple syrup contains 30mg of sodium.

2) Involves Finding Amount of Daily Value: Albert ate $$\cfrac{1}{8}$$ cups of maple syrup. How much $$\%$$ of daily value of potassium did he consume?

i) Look at the nutrients label and find the amount for each serving and $$\%$$ of daily value of potassium for each serving. For each serving, it is $$\cfrac{1}{4}$$ cups and each of serving contains 4% of sodium.

ii) Place into a ratio:

$$\cfrac{1}{4} \text{cups} : 4 \% \text{ of daily value}$$

iii) Find what is given and what we need to find

Given:  $$\cfrac{1}{8}$$ cups

Find: x % daily value

iv) Fill into the proportion to solve:

$$\cfrac{1}{4} \text{cups} : 4 \% \text{ of daily value} :: \cfrac{1}{8} \text{cups} : x \% \text{ of daily value}$$

Note: When calculating with percentage, don't convert the percentage to decimal. For example 4% = 0.04. You can convert it, it won't be wrong, but this will add extra steps.

v) Solve the proportion:

$$\cfrac{1}{4} \text{cups} : 4 \% \text{ of daily value} :: \cfrac{1}{8} \text{cups} : x \% \text{ of daily value}$$

$$\cfrac{1}{4} x = 4 \times \cfrac{1}{8}$$

$$\cfrac{1}{4} x = \cfrac{4}{1} \times \cfrac{1}{8}$$

$$\cfrac{1}{4} x = \cfrac{4 \times 1}{1 \times 8}$$

$$\cfrac{1}{4} x = \cfrac{4}{ 8}$$

$$\cfrac{4}{1} \times \cfrac{1}{4} x = \cfrac{4}{1} \times \cfrac{4}{ 8}$$

$$x = \cfrac{16}{ 8}$$

$$x = 2 \% \text{ of daily value}$$

Hence, $$\cfrac{1}{8}$$ cups of maple syrup contains 2% daily value of potassium.