Multiplying as Scaling
Aligned to 5.NF.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
Multiplying can stretch or shrink a number. If you multiply by a number greater than 1, the result gets bigger. If you multiply by a fraction less than 1, the result gets smaller. You can tell this without doing the multiplication.
Worked example
Compare 5 × 2/3 to 5, without multiplying. Since 2/3 is less than 1, taking 2/3 of 5 gives less than 5. So 5 × 2/3 < 5. If instead you had 5 × 4/3, the fraction 4/3 is greater than 1, so the answer would be more than 5.
Practice questions
- Is 8 × 3/4 greater than or less than 8? Explain without multiplying.
- Is 6 × 5/2 greater than or less than 6? Explain.
- Order these from smallest to largest without solving: 10 × 1/2, 10 × 1, 10 × 3/2.
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
Multiplicar como escalar
Multiplicar puede agrandar o achicar un número. Si multiplicas por un número mayor que 1, el resultado se hace más grande. Si multiplicas por una fracción menor que 1, el resultado se hace más pequeño. Puedes saberlo sin hacer la multiplicación.
Ejemplo: Compara 5 × 2/3 con 5, sin multiplicar. Como 2/3 es menor que 1, tomar 2/3 de 5 da menos que 5. Así, 5 × 2/3 < 5. Si en cambio tuvieras 5 × 4/3, la fracción 4/3 es mayor que 1, así que la respuesta sería más que 5.
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