math 7 A unit 2 add and subtract rational numbers lesson 4 application of adding rational numbers

Answer 1

Certainly! Adding and subtracting rational numbers is an important skill in math, particularly for seventh graders. Here’s a general outline of how to approach applications of adding rational numbers, including some examples and practice problems.

Understanding Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers (where the denominator is not zero). This includes positive and negative fractions, whole numbers, and terminating or repeating decimals.

Adding Rational Numbers

When adding rational numbers, follow these steps:

1. Identify the Numbers: Determine if the numbers are like fractions (same denominator) or unlike fractions (different denominators).
2. Find a Common Denominator: If the fractions have different denominators, find the least common denominator (LCD).
3. Convert to Like Fractions: Adjust the fractions so they have the same denominator.
4. Add the Numerators: Keep the common denominator and add the numerators.
5. Simplify: If possible, reduce the fraction to its simplest form.

Examples of Adding Rational Numbers

1. Like Fractions:
   \( \frac{2}{5} + \frac{3}{5} = \frac{2 + 3}{5} = \frac{5}{5} = 1 \)

2. Unlike Fractions:
   \( \frac{1}{4} + \frac{1}{6} \)

   • Find LCD (12).
   • Convert: \( \frac{1}{4} = \frac{3}{12} \) and \( \frac{1}{6} = \frac{2}{12} \)
   • Then add: \( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \)

Subtracting Rational Numbers

The steps for subtracting rational numbers are similar to adding:

1. Identify the Numbers.
2. Find a Common Denominator.
3. Convert to Like Fractions.
4. Subtract the Numerators: Keep the common denominator and subtract the numerators.
5. Simplify.

Examples of Subtracting Rational Numbers

1. Like Fractions:
   \( \frac{5}{8} - \frac{3}{8} = \frac{5 - 3}{8} = \frac{2}{8} = \frac{1}{4} \)

2. Unlike Fractions:
   \( \frac{3}{5} - \frac{2}{3} \)

   • Find LCD (15).
   • Convert: \( \frac{3}{5} = \frac{9}{15} \) and \( \frac{2}{3} = \frac{10}{15} \)
   • Then subtract: \( \frac{9}{15} - \frac{10}{15} = \frac{-1}{15} \)

Application Problems

Here are a few application problems you can try:

1. Problem 1: You have a ribbon that is \( \frac{5}{6} \) meter long. You cut off \( \frac{1}{3} \) meter. How much ribbon do you have left?

2. Problem 2: A bank account shows a withdrawal of \( -\frac{1}{4} \) of your balance, followed by a deposit of \( \frac{2}{5} \). What is your net change in the balance?

3. Problem 3: You scored \( \frac{2}{3} \) points in one game and \( \frac{3}{4} \) points in another. What is your total score?

Practice Problems

1. \( \frac{1}{2} + \frac{2}{3} \)
2. \( \frac{3}{4} - \frac{5}{8} \)
3. \( -\frac{2}{5} + \frac{3}{10} \)

Answers to Practice Problems

1. \( \frac{1}{2} + \frac{2}{3} = \frac{3}{6} + \frac{4}{6} = \frac{7}{6} \)
2. \( \frac{3}{4} - \frac{5}{8} = \frac{6}{8} - \frac{5}{8} = \frac{1}{8} \)
3. \( -\frac{2}{5} + \frac{3}{10} = -\frac{4}{10} + \frac{3}{10} = -\frac{1}{10} \)

Incorporating these steps and examples should be helpful for understanding the applications of adding and subtracting rational numbers. If you have any specific questions or need further explanations, feel free to ask!