Estimating products of fractions & whole numbers

A three-step routine runs the whole page, shown on 15 × 5/6: round 15 to 20, round 5/6 to the whole number 1, multiply. The long division that turns 5/6 into 0.8333 is printed right inside the example.

The routine is quick. It works well when the fraction sits near 1, like 21/25 or 11/12. It drifts when the fraction sits near 1/2: 70 × 3/5 becomes 70, though the true product is 42. A sharper benchmark, rounding to 0, 1/2 or 1, would give 35.

Comparing a product with its factors without computing it is 5.NF.B.5.a, and the bottom half of the page practices exactly that.

Look hard at 592 × 2/5 against 300 × 1/6. Rounded the page's way, both fractions become 0, so both sides become 0. Ask, "Is 2/5 of 592 really nothing?" It is more than 200.

Parent note: the answer page marks that comparison as equal, and 199 against 199 × 7/8 too. The exact values are 236 4/5 against 50, and 199 against 174 1/8, so greater than is the true sign in both. The other four signs on the key match the exact products.

Have your child say which side holds the bigger fraction before choosing any sign, then check one pair by multiplying.

Estimation earns its keep at the store. A $49 jacket sells at 3/4 of the price: round to $50, and 3/4 of $50 is $37.50, close to the $36.75 on the receipt.

Fuel is another. A 13-gallon tank showing 7/8 full holds about 11 gallons, the same 13 × 7/8 as problem 4, and your child can check it from the passenger seat.

How Much Is a Million? by David M. Schwartz makes huge numbers feel real; read a page and estimate along with it.

Credit the judgment call: "You noticed the rule went too far, and you checked." Multiplying two fractions with area models is next.