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# Rational Number Word Problems

In the world of mathematics, the application of rational numbers goes far beyond numerical calculations.

From everyday scenarios to complex problem-solving, rational numbers play a vital role in solving real-world challenges.

• Rational Number Word Problems
• Formula
• Solved Examples
• FAQs

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### Solving Measurement Problems:

Rational numbers are often used in measurement contexts. Students will encounter word problems involving lengths, areas, volumes, and more.

For example, they might be asked to calculate the area of a rectangular garden, find the volume of a cylindrical container, or determine the length of a diagonal in a right-angled triangle. By applying their knowledge of rational numbers, students can solve these measurement problems with confidence and accuracy.

### Money and Currency Conversion:

Rational numbers are essential when dealing with money and currency. Grade 7 students will encounter word problems related to calculating prices, discounts, taxes, and currency conversions.

They might be asked to determine the total cost of multiple items, find the discounted price of a product, or convert currency from one unit to another. These problems provide practical applications for understanding rational numbers in the context of financial transactions.

### Ratio and Proportion Problems:

Ratio and proportion word problems provide an opportunity for students to apply their knowledge of rational numbers. They might encounter scenarios where they need to compare quantities, find missing values, or solve problems involving direct or inverse proportions.

For example, students might be asked to determine the ratio of boys to girls in a classroom, find the missing term in a proportion, or solve a problem involving the relationship between distance and time.

### Scaling and Enlargement Problems:

Rational numbers are also useful in solving problems involving scaling and enlargement. Students might be presented with scenarios where they need to resize or enlarge figures while maintaining the same proportion.

They might be asked to determine the new dimensions of a scaled-down model or find the original dimensions of an enlarged image. Rational numbers help students accurately calculate the changes in size and maintain the relative proportions of objects.

## Formulas

To add two rational numbers, a/b and c/d, with the same denominator, we add their numerators and keep the common denominator unchanged:

(a/b) + (c/b) = (a + c)/b

### Subtraction of Rational Numbers:

To subtract one rational number from another, a/b – c/b, with the same denominator, we subtract their numerators while keeping the common denominator unchanged:

(a/b) – (c/b) = (a – c)/b

### Multiplication of Rational Numbers:

To multiply two rational numbers, (a/b) * (c/d), we multiply their numerators to get the new numerator and multiply their denominators to get the new denominator:

(a/b) * (c/d) = (a * c)/(b * d)

### Division of Rational Numbers:

To divide one rational number by another, (a/b) ÷ (c/d), we multiply the first number by the reciprocal of the second number:

(a/b) ÷ (c/d) = (a/b) * (d/c) = (a * d)/(b * c)

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## Solved Examples

Measurement Problem: A rectangular garden has a length of 4.5 meters and a width of 3.25 meters. What is the total area of the garden?

Solution:

To find the total area, we multiply the length by the width:

Area = Length × Width

Area = 4.5 meters × 3.25 meters

Area = 14.625 square meters

Therefore, the total area of the garden is 14.625 square meters.

Money and Currency Conversion: Sarah has \$120, and she wants to buy a pair of shoes that costs \$48. How much money will she have left after purchasing the shoes?

Solution:

To find the money left after purchasing the shoes, we subtract the cost of the shoes from the initial amount:

Money Left = Initial Amount – Cost of Shoes

Money Left = \$120 – \$48

Money Left = \$72

Therefore, Sarah will have \$72 left after purchasing the shoes.

Ratio and Proportion Problem: In a school, the ratio of boys to girls is 2:3. If there are 180 girls, how many boys are there?

Solution:

To find the number of boys, we can set up a proportion based on the given ratio:

2 (boys) / 3 (girls) = x (boys) / 180 (girls)

Cross-multiplying, we get:

3x = 2 * 180

3x = 360

Dividing both sides by 3, we find:

x = 120

Therefore, there are 120 boys in the school.

Scaling and Enlargement Problem: A blueprint of a house has a scale of 1:50. If the actual length of a room is 10 meters, what is the length of the room on the blueprint?

Solution:

To find the length on the blueprint, we multiply the actual length by the scale factor:

Blueprint Length = Actual Length × Scale Factor

Blueprint Length = 10 meters × 50

Blueprint Length = 500 meters

## FAQs

##### What are rational numbers?

Rational numbers are numbers that can be expressed as fractions or ratios of two integers, where the denominator is not zero. They can be positive, negative, or zero. Examples of rational numbers include 1/2, -3/4, 5, -7, and 0. Rational numbers can be written in the form p/q, where p and q are integers and q is not equal to zero.

##### What is the difference between rational numbers and whole numbers?

Whole numbers include all the natural numbers (counting numbers) along with zero. Rational numbers, on the other hand, encompass not only whole numbers but also numbers that can be expressed as fractions or ratios of integers. Whole numbers are a subset of rational numbers.

##### Can rational numbers be negative?

Yes, rational numbers can be negative. Rational numbers can be positive, negative, or zero. For example, -3/4 and -7 are negative rational numbers.

##### Are all fractions rational numbers?

Yes, all fractions are rational numbers. Fractions represent the division of two integers, and rational numbers are defined as numbers that can be expressed as fractions or ratios of integers. Therefore, any fraction can be considered a rational number.

##### Can rational numbers be repeating decimals?

Yes, rational numbers can be repeating decimals. Repeating decimals are decimals that have a repeating pattern of digits. For example, 1/3 is a rational number that can be expressed as the repeating decimal 0.333…, where the digit 3 repeats indefinitely.

##### Can irrational numbers be rationalized?

Yes, irrational numbers can sometimes be rationalized. Rationalizing an irrational number involves manipulating the expression to eliminate the radical or irrational part. For example, the square root of 2 (√2) is an irrational number, but by multiplying it by itself (√2 * √2), we can rationalize it as 2. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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