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Fraction Word Problems

  • Grade 5
  • Mathematics
  • 5.NF.A.2
  • Number & Operations—Fractions
  • Free lesson

Aligned to 5.NF.A.2 — Common Core State Standards for Mathematics.

What this lesson teaches

To add or subtract fractions in a story, first estimate with easy benchmark fractions like 0, 1/2, and 1 to know about what to expect. Then rewrite the fractions with a common denominator and add or subtract. Check that your answer is close to your estimate.

Worked examples

Example 1

Maria ran 3/4 mile in the morning and 2/3 mile at night. How far total? Estimate: 3/4 and 2/3 are both a little under 1, so expect close to 1 1/2 miles. Now use denominator 12: 3/4 = 9/12 and 2/3 = 8/12. Add: 9/12 + 8/12 = 17/12 = 1 5/12 miles. That matches the estimate.

Example 2

A board is 5/6 yard long and you cut off 1/3 yard. Using twelfths: 10/12 − 4/12 = 6/12 = 1/2 yard left.

Example 3

Estimation catches errors. 1/2 + 1/3 must be less than 1, so an answer of 2/5 is too small and 5/6 is believable.

Practice questions

  1. A jug had 3/4 liter and you pour out 1/3 liter. How much is left?
  2. You read 2/5 of a book, then 1/2 more. How much have you read?
  3. Estimate first, then solve: 5/6 + 3/4. Is your answer more or less than 1 1/2?

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.

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En español

Problemas con fracciones

Para sumar o restar fracciones en un problema, primero estima con fracciones de referencia fáciles como 0, 1/2 y 1 para saber más o menos qué esperar. Luego reescribe las fracciones con un denominador común y suma o resta. Verifica que tu respuesta esté cerca de tu estimación.

Ejemplo 1: María corrió 3/4 de milla en la mañana y 2/3 de milla en la noche. ¿Cuánto en total? Estima: 3/4 y 2/3 son ambos un poco menos de 1, así que espera cerca de 1 1/2 millas. Ahora usa el denominador 12: 3/4 = 9/12 y 2/3 = 8/12. Suma: 9/12 + 8/12 = 17/12 = 1 5/12 millas. Coincide con la estimación.

Ejemplo 2: Una tabla mide 5/6 de yarda y le cortas 1/3 de yarda. Usando doceavos: 10/12 − 4/12 = 6/12 = 1/2 yarda queda.

Ejemplo 3: Estimar atrapa errores. 1/2 + 1/3 tiene que ser menos que 1, así que 2/5 es muy poco y 5/6 es creíble.

More Number & Operations—Fractions lessons

Adding Fractions with Unlike Denominators5.NF.A.1Multiplying and Dividing Fractions5.NF.B.4Fractions 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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