Real-World Problems with Rational Numbers
Aligned to 7.NS.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
Real-world problems often mix the four operations with positive and negative rational numbers. Track each change with its correct sign, then combine the values in order.
Worked examples
Example 1
A diver starts at −8 m (below sea level), descends 5.5 m, then rises 3 m. Position = −8 − 5.5 + 3 = −10.5 m.
Example 2
A checking account holds $120. Three $45 withdrawals: 120 − 3(45) = 120 − 135 = −$15, an overdraft.
Example 3
The temperature drops 2.5 °C per hour from 6 °C. After 4 hours: 6 − 4(2.5) = −4 °C.
Practice questions
- An account has $120, then charges of $15.50 and $22.75 post. Find the balance.
- The temperature falls 2.5°C each hour for 4 hours, starting at 6°C. Find the final temperature.
- A $45 debt is split equally among 3 people. Write each person's share as a signed number.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Problemas del Mundo Real con Números Racionales
Los problemas reales suelen combinar las cuatro operaciones con números racionales positivos y negativos. Anota cada cambio con su signo correcto y luego combina los valores en orden.
Ejemplo 1: Un buzo empieza en −8 m (bajo el nivel del mar), desciende 5.5 m y después sube 3 m. Posición = −8 − 5.5 + 3 = −10.5 m.
Ejemplo 2: Una cuenta tiene $120. Tres retiros de $45: 120 − 3(45) = 120 − 135 = −$15, un sobregiro.
Ejemplo 3: La temperatura baja 2.5 °C por hora desde 6 °C. Después de 4 horas: 6 − 4(2.5) = −4 °C.
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