Solving Word Problems with Rational Numbers

Solving Word Problems with Rational Numbers

In our daily lives, we often encounter situations that involve rational numbers, such as fractions and decimals. These numbers can be found in various contexts, from cooking recipes to finance, and solving word problems with them is a crucial mathematical skill. As you dive into the world of rational number word problems, let's break them down into four main categories: addition, division, subtraction, and multiplication.

Addition Word Problems

These problems typically involve finding the sum of two or more quantities that are expressed as rational numbers or combinations of rational numbers. For example:

John has 1 ⅔ apples and his neighbor gives him 2 ⅛ more apples. How many apples does John have now?

To solve this problem, you'll need to find the sum of the fractions:

[ 1 \frac{3}{6} + 2 \frac{1}{8} = \frac{11}{6} + \frac{17}{8} = \frac{28 + 15 \cdot 3}{24} = \frac{103}{24} ]

So, John now has (\frac{103}{24}) apples.

Division Word Problems

In these problems, you'll often be given a quantity and asked to determine the number of equal groups that make up the quantity. For example:

Tina has 5 ⅞ pounds of sugar. She wants to divide the sugar equally among 12 friends. How much sugar will each friend receive?

First, convert the mixed number to an improper fraction:

[ 5 \frac{7}{8} = 5 + \frac{7}{8} = \frac{40 + 7}{8} = \frac{47}{8} ]

Next, divide by the number of friends:

[ \frac{47}{8} \div 12 = \frac{47 \cdot 1}{8 \cdot 12} = \frac{47}{96} ]

So, each friend will receive (\frac{47}{96}) pounds of sugar.

Subtraction Word Problems

These problems often involve finding the difference between two quantities that are expressed as rational numbers or combinations of rational numbers. For example:

Last year, the student council earned $1,032 from a bake sale. This year, they spent $867 on decorations and food. How much money do they have left?

First, find the difference between the amounts earned and spent:

[ 1,032 - 867 = 165 ]

So, the student council has $165 left.

Multiplication Word Problems

These problems involve finding the product of two quantities that are expressed as rational numbers or combinations of rational numbers. For example:

A recipe calls for 2 ⅛ cups of sugar and 1 ⅛ cups of flour. How many cups of flour are needed for 4 batches of the recipe?

First, find the product of the number of batches and the amount of flour per batch:

[ 4 \cdot 1 \frac{1}{12} = 4 + \frac{1}{12} = \frac{4 \cdot 12 + 1}{12} = \frac{49}{12} ]

So, 4 batches of the recipe will need (\frac{49}{12}) cups of flour.

Tips for Solving Rational Number Word Problems

1. Read the problem carefully and make sure you understand all the information given.
2. Identify the operation(s) involved in solving the problem (addition, division, subtraction, or multiplication).
3. Convert mixed numbers to improper fractions if necessary.
4. Perform the operations in the order of their precedence, using the order of operations (PEMDAS).
5. Check your answer to make sure it makes sense in the context of the problem.

With practice and patience, you'll develop the skills needed to solve word problems involving rational numbers confidently and accurately. Good luck on your mathematical journey!