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Comparing a Number and a Product

Alignments to Content Standards: 5.NF.B.5


Decide which number is greater without multiplying.

  1. $817$ or $235\times 817$

  2. $\displaystyle 99$ or $\displaystyle \frac{1}{4} \times 99$

  3. $\displaystyle \frac{51}{100}$ or $\displaystyle \frac{51}{100} \times 301$

  4. $\displaystyle \frac{13}{90}$ or $\displaystyle \frac23\times \frac{13}{90}$

  5. $\displaystyle \frac{101}{102}$ or $\displaystyle \frac{101}{102} \times \frac{101}{102}$

  6. $\displaystyle \frac{99}{5}$ or $\displaystyle \frac{99}{5} \times \frac{1}{2}$

  7. $\displaystyle \frac{8}{21} \times 40$ or $\displaystyle \frac{28}{21} \times 40$

  8. $\displaystyle \frac{8}{3} \times \frac57$ or $\displaystyle \frac{8}{3} \times \frac{9}{4}$

IM Commentary

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.


  1. $235\times 817$

  2. $\displaystyle 99$

  3. $\displaystyle \frac{51}{100} \times 301$

  4. $\displaystyle \frac{13}{90}$

  5. $\displaystyle \frac{101}{102}$

  6. $\displaystyle \frac{99}{5}$

  7. $\displaystyle \frac{28}{21} \times 40$

  8. $\displaystyle \frac{8}{3} \times \frac{9}{4}$ says:

about 5 years

Have students write to explain their thinking, "Show or explain how you arrived at your answer."

Kristin says:

about 5 years

That's a good suggestion--I've added it to the commentary.