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Multiplying and Dividing Fractions

  • Grade 5
  • Mathematics
  • 5.NF.B.4
  • Number & Operations—Fractions
  • ★ Enrichment

Aligned to 5.NF.B.4 — Common Core State Standards for Mathematics.

What this lesson teaches

Multiplying a number by a fraction less than one makes it smaller, because you are taking only part of it. To multiply two fractions, multiply the tops together and the bottoms together. To divide a unit fraction by a whole number, you split it into that many equal pieces.

Worked examples

Example 1

Find 1/2 of 1/2: multiply 1/2 times 1/2 to get 1/4. Folding a half-sheet in half again shows you really do get one fourth.

Example 2

Find 3/4 × 2/5: multiply tops (3×2=6) and bottoms (4×5=20) to get 6/20, which simplifies to 3/10.

Example 3

Dividing by a fraction gives a bigger answer: 4 ÷ 1/2 = 8, because there are 8 halves in 4 wholes.

Practice questions

  1. Multiply 2/3 times 3/4.
  2. Why is 1/2 times 1/2 smaller than 1/2?
  3. Divide 1/4 by 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 lesson

En español

Multiplicación y división de fracciones

Multiplicar un número por una fracción menor que uno lo hace más pequeño, porque solo estás tomando una parte de él. Para multiplicar dos fracciones, multiplica los numeradores entre sí y los denominadores entre sí. Para dividir una fracción unitaria entre un número entero, la divides en ese número de partes iguales.

Ejemplo 1: Encuentra 1/2 de 1/2: multiplica 1/2 por 1/2 para obtener 1/4. Doblar una hoja a la mitad y luego doblarla a la mitad otra vez muestra que realmente obtienes un cuarto.

Ejemplo 2: Halla 3/4 × 2/5: multiplica los de arriba (3×2=6) y los de abajo (4×5=20) para obtener 6/20, que se simplifica a 3/10.

Ejemplo 3: Dividir entre una fracción da una respuesta mayor: 4 ÷ 1/2 = 8, porque hay 8 mitades en 4 enteros.

More Number & Operations—Fractions lessons

Adding Fractions with Unlike Denominators5.NF.A.1Fraction Word Problems5.NF.A.2Fractions as Division5.NF.B.3Multiplying as Scaling5.NF.B.5Multiplying Fractions in Real Life5.NF.B.6Dividing with Unit Fractions5.NF.B.7

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