Add and subtract rational numbers: word problems

Key notes:

Understanding Rational Numbers

  • Rational numbers include fractions, decimals, and integers.
  • They can be positive or negative.

Addition of Rational Numbers

  • When adding numbers with the same sign, add their absolute values and keep the sign.
  • When adding numbers with different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger number.

Subtraction of Rational Numbers

  • Change the subtraction into addition by using the rule: a – b = a + (-b).
  • Follow the rules for adding rational numbers after changing the sign.

Finding Common Denominators for Fractions

  • Convert fractions to have the same denominator before adding or subtracting.
  • Perform operations on numerators while keeping the denominator unchanged.

Working with Decimals

  • Align the decimal points before performing addition or subtraction.
  • Add zeros if necessary for proper alignment.

Word Problem Strategies

  • Identify key information: numbers, operation keywords (sum, difference, increase, decrease).
  • Write an equation based on the problem statement.
  • Solve using the correct addition or subtraction rules.
  • Check the answer by substituting it back into the problem context.

Common Keywords in Word Problems

  • Addition: sum, total, increase, gain, combined, together
  • Subtraction: difference, decrease, loss, less than, remaining

Learn with an example

🎯 Over the weekend, Darren drank 9/10 of a bottle of soda and Tori drank 2/5 of a bottle. How much more soda did Darren drink than Tori?

Simplify your answer and write it as a fraction or as a whole or mixed number.

_____ bottles

Find how much more soda Darren drank by subtracting 2/5 from 9/10.

You can use 10 as the common denominator.

Multiply the numerator and the denominator of 2/5  by 2 to find an equivalent fraction.

2 x 2 / 5 x 2 = 4/10

Now subtract the fractions. Subtract the numerators and keep the denominators the same.

9/10 – 4/10 = 5/10

Write the answer in simplest form. Divide both the numerator and the denominator by 5.

5 ÷ 5 / 10 ÷ 5 = 1/2

Now write the answer.

9/10 – 2/5 = 1/2

Darren drank 1/2 of a bottle more soda than Tori.

🎯 On a school trip, a class travels 4.7 kilometres by train and 9.9 kilometres by bus. How far did the class travel?

​______ kilometres

Add the numbers of kilometres. Remember to line up the decimal points.

1

4.7

+9.9

= 14.6

The class travelled 14.6 kilometres.

🎯 At a pizza party, Duncan and his friends drank 3 3/8 bottles of lemon-lime soda and 2 bottles of cola. How much soda did they drink in all?

Simplify your answer and write it as a fraction or as a whole or mixed number.

_______ bottles

Find how much soda they drank in all by adding 3 3/8 and 2.

Add. Remember to add whole numbers to whole numbers and fractions to fractions.

3 3/8 + 2 = 5 3/8

This answer is in simplest form.

Duncan and his friends drank 5 3/8 bottles in all.

Let’s practice!🖊️