Reciprocals

Two numbers are reciprocals when their product is 1. Flipping a fraction is the quick way to find the partner, and it works because 3/4 × 4/3 = 12/12. Whole numbers hide their denominator, so 12 becomes 12/1 before it flips to 1/12.

The grid mixes both kinds on purpose. Next to 1, the answer is 1 again. No other positive number is its own partner.

Reciprocals are the engine of dividing fractions by flipping the divisor, which comes later in the series.

That skill is 6.NS.A.1, computing quotients of fractions. This sheet stops just short of it and builds the tool.

Watch the first box, 10/15. Some children copy 10/15 back, or flip only the top and write 1/15. Ask, "What times 10/15 makes exactly 1?" and let them test 15/10 by multiplying.

The answer page leaves 15/10, 30/51 and 10,000/1,002 as they are. They are correct reciprocals, only not in lowest terms: 15/10 is 3/2, 30/51 is 10/17 and 10,000/1,002 is 5,000/501. If the teacher wants simplest form, simplify after flipping.

For 200 and 31, a quiet "Write it over 1 first" prevents the usual slip.

Uno players know the Reverse card: play two in a row and the direction of play is right back where it started. Reciprocals behave the same way. Flip 3/5, flip again, and you are back at 3/5; multiply the pair and you land on 1.

In the kitchen, a 1/3-cup scoop needs 3 trips to fill 1 cup, and 3 is the reciprocal of 1/3. Which scoop takes 4 trips? Let your child find it in the drawer.

Hand back the credit: "You checked each pair by multiplying, not by guessing." Dividing fractions by whole numbers in recipes is next.