Track quiz
Fourteen ideas, fourteen checks. The table goes first, so there is somewhere to look back at.
| Move | How it goes |
|---|---|
| Name an amount past one whole | Count every piece for the top-heavy name. Count filled wholes first for the mixed one. |
| Swap between the two names | Whole times the bottom, plus the top. Or share the top into bottoms. |
| Find a shared bottom number | Count up in steps of each bottom number until both lists meet. |
| Add unlike fractions | Rename both onto the shared bottom number. Add the tops. Keep the bottom. |
| Subtract unlike fractions | Rename the same way, then take the tops. Never subtract the bottoms. |
| Combine mixed numbers | Flatten both, or carry and borrow between wholes and parts. |
| Take a fraction of a whole number | Divide by the bottom, multiply by the top. |
| Multiply two fractions | Tops together, bottoms together. No shared bottom needed. |
| Say which way a product moves | Top under bottom shrinks. Top over bottom grows. Equal leaves it. |
| Divide by a fraction | Count how many copies fit, or multiply by the flip. |
| Cancel first | Before multiplying, divide a top and a bottom by the same number. The answer stays the same. |
| Share a fraction | Multiply the bottom number by the number of shares. The top stays. |
| Which way dividing moves | Dividing by a number between 0 and 1 makes the amount bigger. Dividing by a number above 1 makes it smaller. Dividing by 1 leaves it alone. That holds for any amount above zero. |
| What is left | Find what is left first. Then take the fraction of that, not of the whole. |
You have 7 third-pieces of a paper strip. What is that as a mixed number?
Which bottom number can both 1/2 and 1/5 be renamed onto?
What is 1/4 + 1/3?
What is 5/6 − 1/3?
What is 2 1/3 + 1 5/6?
Two fifths of 20 tiles is how many tiles?
What is 3/5 × 2/3?
30 is multiplied by each of 4/5, 5/5 and 6/5. Which one comes out bigger than 30?
What is the reciprocal of 7?
How many twelfths fit inside 5/6?
What is 8/15 × 9/10, if you cancel first?
What is 7/9 ÷ 3?
30 is divided by each of 3/5, 5/5 and 6/5. Which one comes out bigger than 30?
A rope loses 1/3 of its length. Then 1/4 of what is left is cut. What part of the rope remains?
Chapter 8 of Part I is Working with Fractions. You have placed pieces on strips and matched bottom numbers. You have shared a whole into groups. You have seen a multiplier below one shrink an amount.
Next: Geometric Twins. Two figures that match exactly. And the tests that tell you so without measuring everything.